Datasets:

Mohamed-BC

/

papers-data

like 0

['Karthik Sridharan']

1204.4145v1

In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the general learning setting. The question of learnability is well studied and fully characterized for binary classification and for real valued supervised learning problems using the theory of uniform convergence. However we show that for the general learning setting uniform convergence theory fails to characterize learnability. To fill this void we use stability of learning algorithms to fully characterize statistical learnability in the general setting. Next we consider the problem of online learning. Unlike the statistical learning framework there is a dearth of generic tools that can be used to establish learnability and rates for online learning problems in general. We provide online analogs to classical tools from statistical learning theory like Rademacher complexity, covering numbers, etc. We further use these tools to fully characterize learnability for online supervised learning problems. II. In the second part, for general classes of convex learning problems, we provide appropriate mirror descent (MD) updates for online and statistical learning of these problems. Further, we show that the the MD is near optimal for online convex learning and for most cases, is also near optimal for statistical convex learning. We next consider the problem of convex optimization and show that oracle complexity can be lower bounded by the so called fat-shattering dimension of the associated linear class. Thus we establish a strong connection between offline convex optimization problems and statistical learning problems. We also show that for a large class of high dimensional optimization problems, MD is in fact near optimal even for convex optimization.

Learning From An Optimization Viewpoint

http://arxiv.org/pdf/1204.4145v1

Title Learning Optimization Viewpoint Summary dissertation study statistical online learning problem optimization viewpointThe dissertation divided two part first consider question learnability statistical learning problem general learning setting question learnability well studied fully characterized binary classification real valued supervised learning problem using theory uniform convergence However show general learning setting uniform convergence theory fails characterize learnability fill void use stability learning algorithm fully characterize statistical learnability general setting Next consider problem online learning Unlike statistical learning framework dearth generic tool used establish learnability rate online learning problem general provide online analog classical tool statistical learning theory like Rademacher complexity covering number etc use tool fully characterize learnability online supervised learning problem II second part general class convex learning problem provide appropriate mirror descent MD update online statistical learning problem show MD near optimal online convex learning case also near optimal statistical convex learning next consider problem convex optimization show oracle complexity lower bounded called fatshattering dimension associated linear class Thus establish strong connection offline convex optimization problem statistical learning problem also show large class high dimensional optimization problem MD fact near optimal even convex optimization Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.015704981982707977, -0.02029193937778473, -0.02126367576420307, -0.00420221034437418, -0.013314669951796532, 0.0021343121770769358, 0.05770261958241463, 0.011969279497861862, -0.01591114141047001, -0.02506544068455696, 0.02737111784517765, 0.048550795763731, -0.006957317236810923, 0.03511177375912666, -0.013752514496445656, -0.05991869047284126, -0.017252182587981224, -0.017639653757214546, 0.002591900061815977, -0.03369967266917229, 0.028745347633957863, -0.03328634053468704, -0.020230812951922417, -0.05019864812493324, -0.02855459414422512, -0.03370458632707596, 0.020758315920829773, -0.06684651225805283, 0.008531227707862854, -0.01891537755727768, 0.05486481264233589, -0.04566279798746109, -0.019350698217749596, 0.01055690087378025, 1.8844376654669759e-06, -0.05141327530145645, -0.036876849830150604, 0.02553483098745346, 0.01790233887732029, -0.04087048023939133, -0.003971907310187817, -0.013300136663019657, 0.007250300608575344, 0.03983406350016594, 0.0041360799223184586, -0.013547741807997227, 0.06030716747045517, 0.08476606756448746, 0.013856488279998302, 0.07408810406923294, 0.0021096225827932358, -0.07500395178794861, 0.035120926797389984, -0.011287961155176163, -0.03261234611272812, -0.0055525279603898525, 0.018967224285006523, 0.018665632233023643, -0.10192232578992844, -0.008836207911372185, -0.012513780035078526, 0.021029697731137276, 0.0018254806054756045, 0.012865457683801651, 0.0342063382267952, -0.02041042037308216, -0.00500891450792551, -0.006782968994230032, -0.005515154916793108, 0.018699847161769867, -0.04044271260499954, 0.007881729863584042, 0.017171349376440048, -0.011306771077215672, -0.014420079998672009, 0.0329052209854126, -0.016590891405940056, 0.03454602509737015, -0.038658514618873596, 0.04609021916985512, -0.052459605038166046, 0.0046179695054888725, -0.009636860340833664, -0.013576257042586803, -0.002627151319757104, 0.0867355465888977, -0.02777211181819439, -0.005494091659784317, 0.009110932238399982, -0.017886171117424965, -0.047372087836265564, 0.039125699549913406, -4.887289833277464e-05, 0.03507312014698982, -0.05680732801556587, 0.003772492054849863, 0.02153545804321766, -0.05345753952860832, 0.004690211266279221, -0.024238141253590584, 0.06301693618297577, -0.05390186607837677, 0.012442498467862606, 0.02204376645386219, -0.005332998000085354, 0.03260290250182152, 0.02576540969312191, -0.0016371732344850898, 0.013765071518719196, 0.05761019513010979, -0.050387438386678696, 0.0334940142929554, -0.006666874047368765, 0.09203894436359406, 0.041970960795879364, -0.0023586724419146776, -0.06266036629676819, 0.042662363499403, -0.0330708771944046, 0.032776277512311935, 0.00500032864511013, 0.00756840780377388, 0.003204676788300276, 0.02022431418299675, -0.04245400428771973, -0.04744500666856766, -0.014320682734251022, 0.030302323400974274, -0.05014174431562424, -0.008601345121860504, 0.06474223732948303, 0.020673371851444244, 0.006324263755232096, 0.05059346556663513, 0.010517796501517296, 0.08435705304145813, 0.011718107387423515, 0.026281602680683136, -0.042680151760578156, -0.044857773929834366, -0.012404528446495533, 0.002332439413294196, -0.0321875624358654, -0.055573735386133194, -0.02385827526450157, -0.04521246254444122, -0.02146236039698124, 0.049213044345378876, 0.004368474707007408, -0.03993804380297661, -0.024009335786104202, 0.027532316744327545, -0.015181458555161953, 0.011979646049439907, 0.07669426500797272, -0.035737719386816025, -0.017343686893582344, 0.05161337926983833, -0.02019166387617588, -0.005806751549243927, 0.051529258489608765, -0.027011750265955925, 0.02068817988038063, -0.008614862337708473, 0.04008740559220314, -0.02824571542441845, -0.008470844477415085, -0.0008246557554230094, 0.027083110064268112, 0.021615030243992805, -0.006442331243306398, 0.023930126801133156, -0.01499845739454031, -0.047292958945035934, 0.03779856115579605, 0.030498258769512177, 0.06633290648460388, 0.034765925258398056, -0.045952584594488144, 0.08849653601646423, -0.012172854505479336, 0.02625955641269684, 0.019634423777461052, 0.01913386769592762, -0.03897088021039963, -0.0028070835396647453, -0.013101438991725445, -0.02884402871131897, -0.046737074851989746, -0.05097895860671997, -0.009684018790721893, -0.032427605241537094, -0.09062907099723816, 0.041287124156951904, 0.039615992456674576, -0.004956797696650028, -0.03188531473278999, -0.029816336929798126, 0.02491925284266472, 0.03874008357524872, -0.0502517893910408, -0.06825341284275055, 0.0636514201760292, -0.05352179706096649, 0.0017160126008093357, -0.050329383462667465, 0.001376346917822957, -0.05814269557595253, 0.006754280999302864, -0.0568985641002655, -4.7607605665689334e-05, -0.00973682850599289, 0.014723551459610462, 0.003931313753128052, -0.0009091372485272586, 0.0289288479834795, -0.01628275401890278, -0.013834558427333832, -5.200457599130459e-05, -0.0034987693652510643, -0.014520242810249329, 0.039587799459695816, -0.04076840728521347, 0.0378819964826107, 0.007024590857326984, -0.004663445055484772, 0.04273315891623497, 0.052481215447187424, 0.05671994760632515, -0.04287152737379074, 0.013424878939986229, -0.04847974702715874, 0.017481770366430283, -0.0285625196993351, -0.05288892611861229, -0.010845979675650597, 0.021285774186253548, -0.036468081176280975, 0.02259949967265129, -0.054634228348731995, 0.037027306854724884, 0.027561787515878677, -0.026791099458932877, -0.05243638530373573, -0.03469466418027878, -0.0069438093341887, 0.00781110068783164, -0.04193297028541565, 0.03169991448521614, -0.01931426115334034, 0.09032256156206131, -0.03813730925321579, 0.023373626172542572, 0.0006306120194494724, 0.06448210775852203, -0.04908103123307228, -0.05310963839292526, 0.045035358518362045, -0.042725201696157455, -0.0017262648325413465, 0.00821992103010416, -0.06437592208385468, 0.01887132227420807, 0.021996207535266876, -0.0012591676786541939, 0.03491153568029404, -0.0057821194641292095, 0.020144900307059288, -0.01600373536348343, 0.002047767397016287, 0.01087138894945383, 0.01392212975770235, -0.026481986045837402, 0.02495112270116806, -0.03811381012201309, -0.019308600574731827, 0.07408283650875092, -0.028879227116703987, -0.007246461696922779, 0.049225643277168274, 0.008079860359430313, 0.022727372124791145, 0.02725847437977791, -0.043074216693639755, 0.018070632591843605, 0.002885285997763276, 0.03063645213842392, -0.008740091696381569, -0.056401778012514114, 0.05788099020719528, 0.004582350142300129, 0.011135516688227654, 0.006842781323939562, -0.00661670695990324, -0.032991956919431686, -0.025346484035253525, -0.05736551433801651, 0.07958894968032837, 0.05826248973608017, -0.004834842402487993, 0.04145527631044388, 0.09851696342229843, -0.029974717646837234, 0.013305103406310081, -0.03906721621751785, -0.019540222361683846, 0.054469138383865356, 0.040208715945482254, 0.057444728910923004, -0.0012665798421949148, 0.004872976336628199, -0.02189113013446331, 0.014899393543601036, -0.021448234096169472, 0.012476453557610512, -0.012258434668183327, -0.07661492377519608, 0.04207660257816315, -0.025142615661025047, -0.007681116461753845, 0.03928446024656296, -0.057738061994314194, 0.05191674828529358, 0.052648644894361496, -0.002318933140486479, -0.01680983044207096, -0.05716492608189583, -0.01391641516238451, -0.02599194087088108, 0.03145219758152962, 0.03996727615594864, -0.0572645328938961, -0.04479541257023811, -0.014385564252734184, -0.010802184231579304, 0.0969410166144371, -0.05437484756112099, -0.045121803879737854, 0.05681920424103737, -0.02896324172616005, -0.03590426594018936, 0.0006734550697728992, 0.02945869229733944, -0.01727641373872757, 0.019272882491350174, -0.04008614271879196, -0.03334449231624603, 0.0034518989268690348, 0.02437448501586914, 0.020854339003562927, -0.027131475508213043, 0.019540654495358467, -0.027601515874266624, -0.03422172740101814, 0.011643110774457455, -0.0010398613521829247, 0.05406361073255539, -0.027112767100334167, -0.028458209708333015, -0.00035608166945166886, 0.07348540425300598, -0.006567691918462515, -0.01563684269785881, 0.039665717631578445, -0.04126175865530968, 0.009465886279940605, 0.03291807323694229, -0.04073011502623558, -0.0456441305577755, 0.03113909624516964, -0.03478807955980301, -0.0032949906308203936, 0.036136116832494736, 0.047717273235321045, 0.0019125111866742373, -0.03838205337524414, -0.04010331258177757, -0.021525412797927856, -0.0220381710678339, 0.01739528775215149, 0.02399766817688942, -0.0085098622366786, 0.015348908491432667, -0.03786565363407135, 0.04469802603125572, -0.038975778967142105, -0.04592324420809746, -0.007569001521915197, -0.035929735749959946, 0.00017816273611970246, -0.04159640148282051, -0.05887749418616295, 0.0026414550375193357, -0.035291727632284164, -0.014855075627565384, -0.0632975697517395, 0.0074109905399382114, 0.0023295003920793533, 0.007995241321623325, 0.009245234541594982, 0.043859243392944336, -0.08487575501203537, 0.018277788534760475, -0.02090846560895443, -0.04218403995037079, -0.019963599741458893, 0.01868312805891037, 0.02010227181017399, -0.04232318326830864, -0.028195977210998535, 0.023004800081253052, 0.031796894967556, -0.018934078514575958, -0.019843878224492073, 0.07974740117788315, 0.026953980326652527, -0.026265088468790054, -0.03284648433327675, 0.05985826253890991, 0.03486509993672371, 0.08064460754394531, 0.048700157552957535, 0.07596681267023087, -0.0014945464208722115, -0.010797174647450447, -0.0017597055993974209, -0.004175055772066116, 0.006204976700246334, -0.01052240002900362, -0.05669226124882698, -0.035668108612298965, -0.03746093809604645, 0.013796760700643063, 0.046129196882247925, 0.03262387961149216, 0.05222253501415253, 0.018336506560444832, -0.007418116554617882, -0.04185068979859352, -0.0738622397184372, 0.04770524799823761, -0.04662729799747467, 0.09064164012670517, -0.010901507921516895, 0.026645855978131294, 0.01174059510231018, 0.0428210087120533, -0.03875621780753136, -0.03167812526226044, 0.053710177540779114, 0.02233714610338211, -0.03439059853553772, 0.048282742500305176, 0.06338924914598465, -0.024492371827363968, -0.013456055894494057, -0.08252125233411789, -0.0020732502453029156, -0.051950935274362564, -0.03546258434653282, 0.008465752005577087, 0.008512233383953571, -0.002502023009583354, -0.03725045174360275, -0.05642912909388542, 0.036569803953170776, 0.016061794012784958, -0.010021964088082314, -0.017247240990400314, 0.08514050394296646, 0.012470877729356289, -0.0022090885322541, 0.026254264637827873, 0.013790448196232319, -0.012634486891329288, -0.033351413905620575, -0.08384178578853607, -0.0333133265376091, 0.016426023095846176, -0.0215030275285244, 0.062686488032341, 0.05991175398230553, 0.04986384138464928, -0.08380090445280075, 0.008026659488677979, 0.047321025282144547, 0.08648957312107086, 0.01620550826191902, -0.01287264283746481, 0.04874725639820099, 0.045585088431835175, 0.02907329425215721, -0.006774609442800283, 0.02486393041908741, 0.0822698175907135, -0.08774109184741974, 0.024244189262390137, 0.005071317311376333, -0.02637682668864727, 0.022390376776456833, -0.006576318293809891, 0.020091688260436058, -0.02503195032477379, -0.01725166290998459, 0.04328792169690132, 0.0013932357542216778, 0.0047134412452578545, 0.031592365354299545, 0.0012146884109824896, 0.06746288388967514, -0.01783859357237816, -0.05083071067929268, 0.02471284195780754, -0.044818487018346786, -0.03595661744475365, 0.03879857808351517, 0.019948136061429977, 0.004248745273798704, -0.024361247196793556, -0.008302874863147736, -0.006811411585658789, -0.029229819774627686, 0.02219361811876297, -0.06814155727624893, -0.020120535045862198, 0.047902707010507584, -0.025424813851714134, -0.010598022490739822, 0.045338112860918045, 0.04645302891731262, 0.014446049928665161, -0.04059044271707535, -0.04776260256767273, -0.02695634216070175, -0.04018029943108559, 0.04033701866865158, 0.027109568938612938, 0.04440724477171898, 0.01728113554418087, -0.012878943234682083, 0.059084903448820114, -0.006571934092789888, 0.03327997401356697, -0.01556328684091568, 0.06683345139026642, -0.016812745481729507, 0.010644891299307346, 0.010591922327876091, 0.014912483282387257, 0.04963408038020134, -0.08393537998199463, 0.019009990617632866, 0.07823774218559265, 0.03187241777777672, -0.02641848661005497, -5.145914599820695e-33, 0.03346376493573189, -0.0426543690264225, -0.04627535492181778, 0.056570496410131454, -0.01236981712281704, -0.011457297019660473, -0.0018665671814233065, 0.041300829499959946, -0.013424345292150974, -0.030826397240161896, -0.0015137455193325877, 0.009282443672418594, 0.013749363832175732, 0.036979712545871735, 0.02380545809864998, -0.04811888560652733, -0.024896180257201195, -0.04057380557060242, 0.006485350430011749, -0.016310397535562515, 0.04525543004274368, 0.003635522909462452, -0.025876928120851517, -0.049552686512470245, -0.05361281335353851, 0.011146429926156998, 0.0001922674709931016, -0.00903935544192791, -0.003256283001974225, 0.01277066022157669, -0.013616624288260937, 0.03520560637116432, 0.00773829547688365, -0.031126104295253754, 0.023043697699904442, -0.014352632686495781, -0.0019018605817109346, -0.0277870986610651, -0.049127984791994095, 0.07336728274822235, -0.032502200454473495, 0.01287776418030262, 0.05346212536096573, -0.024864623323082924, -0.045372653752565384, -0.00785293523222208, 0.04752197116613388, -0.017760004848241806, -0.053104203194379807, -0.03460957482457161, -0.029659446328878403, 0.004615897312760353, 0.007645398378372192, 0.039062291383743286, 0.05003725737333298, 0.010587428696453571, 0.01068846508860588, -0.035278696566820145, 0.012285926379263401, 0.03930846229195595, -0.04446046054363251, 0.039894022047519684, -0.004233210813254118, 0.011630268767476082, 0.00466635636985302, 0.006216960493475199, 0.02163156494498253, -0.026114650070667267, 0.025234919041395187, -0.0012191088171675801, -0.002363435924053192, 0.02021271176636219, 0.019227540120482445, 0.024935798719525337, 0.048979032784700394, -0.08675922453403473, -0.03674563392996788, 0.013010376133024693, 0.042540885508060455, -0.043553732335567474, 0.009385641664266586, -0.0030801177490502596, 0.002696328330785036, -0.008898567408323288, -0.00606178306043148, -0.028242887929081917, -0.0029088687151670456, 0.014971630647778511, -0.006740874145179987, 0.013735150918364525, 0.009894989430904388, -0.005883860867470503, -0.032593294978141785, -0.047101277858018875, -0.0144928228110075, -0.025470076128840446, 0.026789015159010887, 0.03231688216328621, 0.012355895712971687, -0.024732932448387146, -0.02886473946273327, -0.046917304396629333, -0.05844160541892052, -0.0232092272490263, 0.020259911194443703, 0.0011594948591664433, 0.06191235035657883, -0.01804310828447342, -0.029973763972520828, -0.009327558800578117, 0.015842117369174957, -0.04912325739860535, 0.04083939269185066, 0.052198365330696106, 0.02604163996875286, -0.07070071250200272, 0.0029162829741835594, 0.10216841846704483, 0.010678297840058804, 0.010321094654500484, -0.04607674106955528, -0.036374159157276154, -0.00808543898165226, -0.025608627125620842, -0.029967548325657845, 0.01892871782183647, -0.002411461668089032, -0.02714339829981327, -0.02665881998836994, -0.036581750959157944, 0.002585864160209894, -0.010449905879795551, 2.3855679387452255e-07, -0.024177249521017075, 0.018779881298542023, -0.04030156508088112, -0.04957452043890953, 0.028221728280186653, -0.004585938528180122, 0.004336460959166288, 7.602927507832646e-05, -0.04634133726358414, 0.003311862936243415, 0.026346499100327492, -0.0827670693397522, 0.0718420073390007, -0.020619818940758705, -0.05031333118677139, -0.06862366944551468, -0.007634111680090427, 0.06628434360027313, -0.02616691030561924, 0.029840519651770592, 0.02036949433386326, 0.04639194905757904, 0.032304972410202026, -0.02599409595131874, 0.044647227972745895, 0.0023877571802586317, -0.004255903884768486, -0.010591810569167137, 0.06229040026664734, -0.0034560547210276127, 0.06352579593658447, 0.027709536254405975, 0.009617388248443604, -0.027296314015984535, -0.025687191635370255, 0.048744235187768936, -0.009647472761571407, 0.04233047366142273, 0.028714429587125778, 0.021763144060969353, 0.022901516407728195, -0.007787697017192841, 0.03979598358273506, -0.008689474314451218, 0.06644757837057114, 0.00020726742513943464, -0.03728271275758743, -0.04296233505010605, 0.0013820804888382554, -0.022339245304465294, 0.04890095070004463, -0.028072845190763474, 0.017679497599601746, -0.00788436084985733, -0.015507051721215248, -0.03529490903019905, 0.0011134238447993994, -0.004885442089289427, 0.019603263586759567, 0.05802851915359497, -0.0031589341815561056, -0.0097433440387249, 0.004004557151347399, 0.06881912052631378, 0.09409387409687042, -0.012085200287401676, 0.014984020963311195, 2.2806174568261103e-34, 0.013384055346250534, -0.02346864715218544, 0.04335422068834305, 0.0007638680399395525, -0.05548424646258354, -0.0335557796061039, 0.00471914280205965, -0.02708667889237404, 0.024644862860441208, -0.011026985011994839, -0.002688323613256216]

['Patrick Taillandier', 'Julien Gaffuri']

1204.4332v1

Automated generalisation has known important improvements these last few years. However, an issue that still deserves more study concerns the automatic evaluation of generalised data. Indeed, many automated generalisation systems require the utilisation of an evaluation function to automatically assess generalisation outcomes. In this paper, we propose a new approach dedicated to the design of such a function. This approach allows an imperfectly defined evaluation function to be revised through a man-machine dialogue. The user gives its preferences to the system by comparing generalisation outcomes. Machine Learning techniques are then used to improve the evaluation function. An experiment carried out on buildings shows that our approach significantly improves generalisation evaluation functions defined by users.

Designing generalisation evaluation function through human-machine dialogue

http://arxiv.org/pdf/1204.4332v1

Title Designing generalisation evaluation function humanmachine dialogue Summary Automated generalisation known important improvement last year However issue still deserves study concern automatic evaluation generalised data Indeed many automated generalisation system require utilisation evaluation function automatically ass generalisation outcome paper propose new approach dedicated design function approach allows imperfectly defined evaluation function revised manmachine dialogue user give preference system comparing generalisation outcome Machine Learning technique used improve evaluation function experiment carried building show approach significantly improves generalisation evaluation function defined user Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.06278237700462341, 0.0364791601896286, -0.033244308084249496, 0.004184253979474306, 0.0018737890059128404, 0.006356874015182257, 0.02155269682407379, 0.002999905264005065, -0.02301516756415367, -0.032038524746894836, 0.00280910637229681, -0.051932256668806076, 0.027451615780591965, 0.04261413589119911, -0.00803934596478939, -0.11245379596948624, 0.036849699914455414, 0.0071839941665530205, 0.010100956074893475, 0.010436677373945713, 0.018563997000455856, -0.028475213795900345, -0.00025914126308634877, 0.047446273267269135, -0.010349401272833347, -0.009315317496657372, -0.02044019103050232, -0.03454459086060524, 0.05649489536881447, -0.01552361436188221, -0.003627924947068095, 0.04832325130701065, -0.022227244451642036, 0.00903929490596056, 2.5021436158567667e-06, -0.0718439519405365, -0.015139758586883545, -0.005991381127387285, -0.003315598936751485, -0.010141951963305473, 0.07156544923782349, 0.023853302001953125, 0.018747784197330475, 0.017128482460975647, -0.029238348826766014, -0.019388623535633087, 0.03331439197063446, 0.03649325296282768, 0.05539502575993538, 0.04458591714501381, -0.014485521242022514, -0.04975004866719246, -0.03847057744860649, 0.007613185793161392, 0.011676794849336147, -0.07173451781272888, 0.00195233931299299, 0.031374718993902206, 0.05508849024772644, -0.024814991280436516, 0.007848742417991161, -0.01834002137184143, -0.015153015032410622, -0.015822404995560646, 0.04229757934808731, -0.0034464101772755384, -0.0372132807970047, -0.03943876549601555, -0.018868351355195045, 0.0739266648888588, 0.036398354917764664, 0.03660433366894722, 0.02157723717391491, -0.02191118337213993, 0.022121388465166092, -0.02210993319749832, -0.026267442852258682, -0.016568077728152275, -0.046638693660497665, -0.03377082198858261, -0.0337931327521801, 0.04299834370613098, -0.03399394452571869, -0.000695911527145654, -0.0199582539498806, 0.07729848474264145, -0.03146308287978172, -0.02177218161523342, 0.05582704767584801, -0.027457647025585175, -0.02867238037288189, -0.03395414352416992, 0.033070825040340424, 0.058421339839696884, -0.10826116055250168, -0.02754485048353672, 0.00236819707788527, -0.032620079815387726, 0.05907367542386055, -0.08365989476442337, 0.08085867017507553, 0.03815534710884094, 0.0004547106509562582, -0.014135832898318768, 0.015723951160907745, 0.07938667386770248, -0.014905611984431744, -0.011256412602961063, -0.05435327813029289, 0.027774183079600334, -0.05720466375350952, -0.015536952763795853, -0.03835582733154297, 0.0670773908495903, 0.0021535896230489016, -0.01228941511362791, -0.0909428596496582, 0.046571969985961914, -0.03125010058283806, -0.002084510400891304, 0.036858849227428436, 0.05223875865340233, -0.0026289934758096933, 0.0007481065695174038, -0.04903801530599594, -0.03423304855823517, -0.11376124620437622, 0.02418656088411808, -0.026562349870800972, -0.0178089402616024, 0.05421208217740059, 0.02470615692436695, -0.006754418835043907, 0.04068613797426224, 0.004079054109752178, 0.11566851288080215, -0.013955972157418728, 0.0359804704785347, -0.015720991417765617, -0.020723829045891762, -0.02320674993097782, -0.05410768836736679, -0.060910508036613464, -0.056459568440914154, -0.005336015019565821, -0.0008431704482063651, -0.021301962435245514, 0.04730232432484627, -0.014837738126516342, 0.011793202720582485, -0.006874246057122946, 0.042400021106004715, -0.029846899211406708, 0.03081265278160572, 0.09387294203042984, -0.006682584993541241, 0.0014442424289882183, 0.03151707723736763, -0.004984651226550341, 0.033304546028375626, 0.025087524205446243, -0.033408842980861664, 0.05900050327181816, 0.02912287227809429, -0.05950256437063217, -0.05517721548676491, 0.012914172373712063, 0.020700747147202492, -0.048310473561286926, 0.004012492019683123, -0.020145807415246964, 0.06141738221049309, -0.00854477845132351, 0.025038855150341988, -0.005102063994854689, 0.04478348419070244, 0.029951924458146095, 0.036293260753154755, 0.03532325476408005, 0.0351937897503376, 0.011513348668813705, 0.024832366034388542, 0.03245804086327553, 0.021296607330441475, -0.039528220891952515, -0.003566121682524681, 0.005394222680479288, -0.007676326669752598, -0.011040820740163326, -0.07432311028242111, 0.0031287597957998514, 0.00400435458868742, 0.03115093521773815, -0.009121616370975971, 0.020719410851597786, -0.012483428232371807, 0.006358236074447632, -0.033835917711257935, 0.02049245871603489, -0.014411045238375664, -0.06131334975361824, -0.06794004142284393, 0.034758925437927246, 0.027970533818006516, -0.00048074236838147044, -0.03313540667295456, -0.0003175356250721961, -0.008909504860639572, -0.022641437128186226, -0.017484096810221672, 0.06462660431861877, -0.03520285710692406, -0.006324481219053268, -0.05291653051972389, -0.01038112211972475, 0.05132174864411354, -0.00973557960242033, 0.03723190352320671, -0.01112499088048935, -0.016124270856380463, 0.020986057817935944, 0.002224719151854515, -0.01704559288918972, 0.0023302771151065826, 0.0802571102976799, -0.028223950415849686, 0.028395818546414375, 0.008549289777874947, 0.026194626465439796, 0.016905970871448517, 0.01833466812968254, 0.012706354260444641, 0.014807995408773422, 0.01126896496862173, -0.0528104342520237, 0.0020767045207321644, -0.04034718498587608, 0.021204113960266113, -0.0017339560436084867, -0.029362551867961884, -0.009183578193187714, -0.003289378946647048, -0.019598789513111115, -0.06073910742998123, -0.025189239531755447, -0.047447457909584045, 0.032416705042123795, -0.02195340394973755, 0.04429071769118309, -0.018751129508018494, -0.023889580741524696, -0.04434550926089287, 0.08922547101974487, 0.010253382846713066, -0.0030248695984482765, 0.016413584351539612, -0.029402483254671097, 0.04629341512918472, -0.0865083634853363, -0.041239116340875626, 0.031106803566217422, -0.03347570449113846, 0.020512981340289116, 0.010694116353988647, 0.037167202681303024, -0.04454689100384712, 0.04216017201542854, -0.15002194046974182, -0.037525247782468796, 0.01128454227000475, -0.0064504616893827915, 0.018136145547032356, 0.001749563030898571, 0.006196984555572271, -0.039864640682935715, -0.027354443445801735, -0.009604149498045444, 0.016189394518733025, -0.010341758839786053, 0.03916766867041588, 0.03292457014322281, 0.0054230885580182076, -0.029066484421491623, 0.004447838291525841, -0.013657137751579285, 0.03340061753988266, 0.043416887521743774, -0.011818028055131435, -0.033839788287878036, 0.0011306025553494692, -0.02951016277074814, -0.0005397385102696717, 0.014845994301140308, -0.026065338402986526, 0.010472524911165237, 0.011753367260098457, 0.012014907784759998, 0.0319979228079319, 0.02590567246079445, 0.013111157342791557, -0.007953508757054806, 0.02767390012741089, -0.03625049069523811, 0.009578889235854149, 0.003702856134623289, 0.011937256902456284, 0.05559862405061722, 0.0015578966122120619, -0.00314229354262352, 0.03217136114835739, 0.029974350705742836, 0.03608463704586029, -0.004074321128427982, 0.021667512133717537, -0.0032861134968698025, -0.01696208119392395, -0.08120963722467422, -0.043949149549007416, -0.05514512211084366, 0.06424897164106369, 0.0042951651848852634, -0.05581127852201462, 0.057418882846832275, 0.02290320210158825, -0.0020762314088642597, -0.026232942938804626, -0.03874550387263298, -0.005310801323503256, 0.0656437873840332, -0.03381333500146866, 0.023614194244146347, 0.012520342133939266, -0.04466797411441803, -0.033769577741622925, -0.02022346667945385, 0.026075445115566254, -0.030317271128296852, 0.04466643184423447, -0.04060159996151924, -0.002580831991508603, 0.008473437279462814, -0.037857361137866974, -0.05703970417380333, 0.020796777680516243, -0.014484715647995472, -0.008435922674834728, 0.030341558158397675, -0.005348816514015198, 0.009671922773122787, 0.02941286936402321, 0.0070602730847895145, 0.019682414829730988, -0.028302239254117012, -0.006560188718140125, 0.019481118768453598, 0.0030820672400295734, 0.009597956202924252, -0.0010904158698394895, -0.08094796538352966, 0.01811615750193596, 0.04295318201184273, 0.020458480343222618, -0.04454413801431656, 0.02703109197318554, -0.054304011166095734, 0.01610259711742401, -0.00803142786026001, -0.029628854244947433, -0.011686556972563267, 0.028599802404642105, 0.030728498473763466, -0.019834745675325394, 0.034740447998046875, 0.06806458532810211, 0.00843946635723114, -0.053359247744083405, 0.005052188411355019, -0.0405752956867218, -0.029767533764243126, -0.005293211434036493, 0.055403538048267365, -0.04653524234890938, 0.019322505220770836, -0.019861983135342598, 0.04226673021912575, -0.045981813222169876, -0.032062701880931854, 0.03719817474484444, -0.062429703772068024, 0.004691441077739, 0.008969766087830067, -0.08981424570083618, -0.03256525471806526, 0.011473460122942924, 0.003255176357924938, -0.018621761351823807, -0.0405435748398304, 0.05511459708213806, 0.026818282902240753, 0.0025122901424765587, 0.025360750034451485, -0.0837475061416626, -0.02162298373878002, 0.043845757842063904, -0.0020350459963083267, -0.008854351937770844, 0.07869982719421387, 0.041716136038303375, 0.005985913798213005, -0.043569210916757584, 0.03148147463798523, 0.05116543918848038, 0.040122680366039276, -0.05084523931145668, 0.06396517157554626, 0.01915173977613449, 0.003087311517447233, -0.05129842460155487, 0.028449827805161476, 0.039000146090984344, 0.03736628219485283, 0.03870079293847084, 0.05117927864193916, -0.04090491682291031, 0.0008853633189573884, -0.04642002657055855, 0.01984761282801628, 0.015610193833708763, -0.0063639478757977486, 0.006882224697619677, -0.04163261875510216, -0.030290409922599792, -0.040093716233968735, -0.005193336866796017, -0.04854552820324898, -0.03922513127326965, -0.006671745330095291, 0.0005123239243403077, -0.05320056155323982, -0.08448369801044464, -0.04515179619193077, 0.024228563532233238, 0.07822053134441376, 0.010918030515313148, -0.036499105393886566, -0.02025013603270054, 0.058310434222221375, -0.03191488981246948, -0.05134640634059906, 0.05596071109175682, 0.013271411880850792, -0.0436568409204483, -0.020152343437075615, 0.010900188237428665, -0.0063701653853058815, -0.02698160707950592, -0.01257284078747034, 0.002644537715241313, -0.04548826068639755, 0.014575863257050514, 0.04055602103471756, 0.03925275430083275, -0.012330504134297371, -0.026364296674728394, -0.03276801481842995, 0.0411282442510128, -0.0033143407199531794, 0.004748980980366468, -0.01459809485822916, 0.013759787194430828, 0.0749850645661354, -0.017190678045153618, -0.0018356378423050046, -0.008870050311088562, 0.05398372560739517, -0.006821086630225182, 0.0011861189268529415, -0.06970591843128204, -0.02081402763724327, 0.014033401384949684, 0.02227364107966423, 0.015111771412193775, 0.0017212918028235435, -0.025036826729774475, -0.013577938079833984, 0.014170417562127113, -0.012248986400663853, -0.042391471564769745, -0.038305703550577164, 0.03299175575375557, 0.024492355063557625, -0.006057987920939922, 0.012704838067293167, -0.07384422421455383, -0.042815931141376495, 0.008857907727360725, -0.011391041800379753, 0.039270032197237015, 0.023136071860790253, 0.08029620349407196, -0.008321672677993774, 0.001353556988760829, -0.0015297959325835109, 0.01273930910974741, 0.0259189922362566, 0.04403416067361832, 0.023221585899591446, 0.06916344910860062, -0.03060830570757389, -0.00063361506909132, 0.01427618507295847, 0.020814571529626846, -0.00761238019913435, -0.07638967782258987, -0.07185312360525131, 0.039580803364515305, -0.00042841071262955666, 0.022071976214647293, -0.03341418877243996, 0.04044428467750549, 0.008628265000879765, -2.9945869755465537e-05, 0.05481919273734093, -0.023896975442767143, 0.01938510313630104, -0.010664734058082104, 0.032765790820121765, -0.023283911868929863, -0.05104878172278404, 0.023051530122756958, -0.04027533158659935, -0.06054076924920082, -0.04869478568434715, -0.041935887187719345, -0.0722459927201271, 0.019488925114274025, 0.013626634143292904, -0.002650559414178133, -0.02075742557644844, -0.007630059029906988, -0.06772787868976593, -0.04096069931983948, -0.013173935003578663, 0.016343774273991585, 0.0956062376499176, 0.007670494262129068, 0.0632438212633133, 0.04172959923744202, -0.01358715258538723, -0.013692614622414112, -0.041318628937006, -0.012330837547779083, -0.016777144744992256, 0.029251188039779663, -0.087882399559021, -6.427813229911478e-33, -0.03450683876872063, -0.041777949780225754, -0.02946479804813862, -0.030048254877328873, -0.029190754517912865, -0.045904532074928284, 0.009486332535743713, 0.05916232243180275, 0.007991231977939606, -0.005874042399227619, 0.0034341374412178993, -0.023561447858810425, 0.02298477478325367, -0.019742105156183243, 0.05272627994418144, 0.01058481726795435, -0.0013523396337404847, 0.006209562532603741, -0.03148472309112549, -0.00652605015784502, 0.017711250111460686, 0.03758658841252327, 0.052622437477111816, -0.06761042028665543, 0.04161190614104271, 0.027267903089523315, -0.021553510800004005, -0.005865513347089291, -0.004192722029983997, 0.014153647236526012, 0.017996709793806076, 0.004241359420120716, 0.0334276519715786, -0.012803833931684494, -0.03186585381627083, 0.06143467128276825, -0.024465762078762054, -0.060178812593221664, -0.0020790055859833956, 0.004097330383956432, -0.008711506612598896, 0.007063772063702345, 0.028550995513796806, -0.012790818698704243, -0.029965979978442192, 0.02106107398867607, 0.060344938188791275, -0.016403265297412872, 0.0023352832067757845, -0.007522659841924906, -0.045746345072984695, 0.030576951801776886, 0.00087560317479074, 0.020614802837371826, -0.03377895429730415, 0.05677042528986931, -0.037071067839860916, -0.0303434319794178, -0.021218156442046165, 0.028993822634220123, 0.06896570324897766, -0.01902329921722412, 0.022529752925038338, 0.03641476854681969, -0.0012799594551324844, 0.002383402083069086, -0.00037249395973049104, -0.000527604075614363, -0.044329188764095306, -0.0168098583817482, -0.01209928561002016, 0.05621879920363426, 0.02135792002081871, 0.01865415647625923, 0.05738784745335579, -0.05722144991159439, -0.0023149624466896057, 0.055105093866586685, -0.011253676377236843, 0.07246987521648407, -0.016504205763339996, 0.023172780871391296, -0.05713564157485962, -0.012698743492364883, 0.017264004796743393, -0.03062174841761589, -0.042030636221170425, -0.07026180624961853, 0.027277754619717598, -0.03214172646403313, -0.007168384734541178, 0.012227670289576054, -0.008244713768362999, -0.022387610748410225, 0.05604182183742523, -0.05505749583244324, 0.004906035494059324, 0.02608056552708149, 0.0041970075108110905, -0.07246195524930954, -0.01061763521283865, -0.019283482804894447, 0.008905205875635147, 0.06953302770853043, 0.05863793566823006, 0.002661452628672123, -0.042286667972803116, -0.008759002201259136, -0.04462406411767006, 0.018145199865102768, 0.012234394438564777, -0.047971658408641815, -0.0006011408404447138, 0.041257016360759735, -0.017226804047822952, -0.022035758942365646, -0.04928315058350563, 0.08464961498975754, -0.05964897200465202, -0.032813508063554764, -0.11136491596698761, -0.04362158849835396, 0.034822262823581696, 0.02630750834941864, -0.05476837232708931, -0.016071373596787453, 0.011932275258004665, -0.035536423325538635, 0.04131210222840309, 0.009425749070942402, -0.006200308445841074, -0.024315519258379936, 3.009929798736266e-07, 0.003786229994148016, 0.03446894511580467, 0.0020024063996970654, 0.015100951306521893, -0.021180694922804832, 0.003256040858104825, 0.0354478694498539, 0.023029841482639313, 0.031296249479055405, -0.0050069596618413925, 0.08004018664360046, -0.03100896254181862, 0.015923472121357918, 0.04034707322716713, -0.055046021938323975, -0.05153542384505272, -0.06941485404968262, -0.008247299119830132, -0.021901655942201614, 0.03675834834575653, 0.08627858757972717, 0.046708691865205765, 0.024344827979803085, -0.0002756858302745968, 0.01307503879070282, 0.004174480214715004, -0.004912879783660173, -0.0026357739698141813, 0.031552139669656754, 0.027998797595500946, 0.03580505773425102, 0.02841511368751526, 0.0013690110063180327, 0.0609624981880188, 0.013583428226411343, 0.01596285216510296, 0.030446050688624382, 0.054802294820547104, -0.02503170445561409, -0.004151372238993645, 0.006561965681612492, -0.026262488216161728, 0.040113665163517, -0.0507982037961483, 0.01753830350935459, -0.01839437708258629, 0.007155814208090305, -0.004051538184285164, 0.006295937579125166, 0.0004939291393384337, 0.04899003356695175, -0.004641173407435417, 0.014440074563026428, 0.020186342298984528, -0.004843112546950579, 0.0076796612702310085, 0.009001275524497032, -0.0442749448120594, -0.0033083970192819834, 0.057853493839502335, -0.03601239249110222, -0.03754992410540581, 0.026313267648220062, -0.04593115299940109, 0.012008663266897202, -0.023306693881750107, 0.00719438586384058, 2.751652736879986e-34, 0.018238777294754982, 0.026037165895104408, 0.002270167227834463, 0.02512175776064396, 0.02540968358516693, 0.02868996001780033, 0.00019455881556496024, 0.012499077245593071, 0.05514291673898697, -0.020041313022375107, -0.03154044970870018]

['Dusko Pavlovic']

1204.5802v1

Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.

Quantitative Concept Analysis

http://arxiv.org/pdf/1204.5802v1

Title Quantitative Concept Analysis Summary Formal Concept Analysis FCA begin context given binary relation object attribute derives lattice concept concept given set object set attribute first set consists object satisfy attribute second vice versa Many application though provide context quantitative information telling whether object satisfies attribute also quantifying satisfaction Contexts form arise rating matrix recommender system occurrence matrix text analysis pixel intensity matrix digital image processing etc application attracted lot attention several numeric extension FCA proposed propose framework proximity set proxets subsume partially ordered set posets well metric space One feature approach extract quantified context quantified concept thus allows full use available information Another feature categorical approach allows analyzing universal property classical FCA new version may thus provides structural guidance aligning combining approach Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.013032167218625546, 0.05818217620253563, -0.04255775734782219, 0.029005248099565506, -0.024885203689336777, -0.015375061891973019, -0.008419855497777462, 0.044555436819791794, -0.07594721764326096, -0.03821533918380737, 0.029926009476184845, -0.030976226553320885, 0.026314927265048027, 0.06313207745552063, -0.022739969193935394, -0.06120847910642624, 0.03458326682448387, 0.046875592321157455, -0.03136738762259483, 0.022503433749079704, 0.003095533000305295, -0.02926611341536045, 0.0003616884059738368, 0.00587801868095994, -0.015968242660164833, -0.020391356199979782, -0.010084039531648159, -0.06002892553806305, 0.024798832833766937, -0.04594848304986954, 0.022570474073290825, 0.0483124703168869, -0.03575484827160835, -0.02821877971291542, 2.4691655653441558e-06, -0.05075481906533241, -0.059558019042015076, 0.02269173227250576, 0.032096825540065765, -0.038220036774873734, 0.0016260013217106462, -0.012361784465610981, 0.02787833847105503, -0.033663731068372726, -0.023188849911093712, 0.000450737657956779, 0.046703070402145386, 0.02702977880835533, -0.0346253402531147, -0.04108826443552971, -0.011443116702139378, -0.059734638780355453, 0.0232571791857481, 0.03430715203285217, 0.03720252215862274, 0.032784152776002884, -0.009028486907482147, 0.05234676972031593, 0.061688873916864395, 0.02352532558143139, 0.0015571544645354152, -0.015364859253168106, 0.011610330082476139, -0.001035910565406084, 0.06318268924951553, -0.002358054742217064, 0.0024535253178328276, -0.006136350333690643, 0.034047432243824005, 0.03997686877846718, 0.0766577199101448, 0.01486901193857193, -0.009989815764129162, 0.0026056875940412283, -0.03521117568016052, 0.016207018867135048, -0.020581137388944626, 0.008485592901706696, -0.04183211550116539, -0.017925485968589783, -0.03953276947140694, 0.08396501839160919, -0.01749456487596035, -0.001328077050857246, -0.01943025551736355, 0.05802968889474869, 0.0009085445781238377, 0.0028097645845264196, -0.03809799998998642, -0.04077141731977463, -0.012759087607264519, -0.022657940164208412, -0.0053888848051428795, 0.017715321853756905, 0.0001234235242009163, -0.02002725750207901, 0.07291558384895325, 0.03254061937332153, 0.08819740265607834, -0.04205211624503136, 0.019948335364460945, 0.002790416358038783, 0.0003283864352852106, 0.019435303285717964, 0.06321750581264496, 0.035624150186777115, 0.010540330782532692, -0.009227168746292591, -0.040219761431217194, 0.05394028127193451, -0.0931241512298584, -0.018707744777202606, 0.018008988350629807, 0.06239951029419899, 0.034807439893484116, 0.012860288843512535, -0.022276991978287697, -0.005573168862611055, -0.0436810739338398, 0.030267855152487755, -0.026823092252016068, -0.003205674234777689, 0.020936831831932068, 0.01495237648487091, -0.0392765998840332, -0.028699256479740143, -0.056817639619112015, 0.004840681329369545, -0.0423794724047184, -0.016608431935310364, 0.07587160915136337, -0.02117694355547428, 0.009106455370783806, -0.009554780088365078, -0.0005843545659445226, 0.019684217870235443, 0.04327404126524925, -0.01884438842535019, -0.003868130501359701, -0.058702949434518814, 0.008536135777831078, -0.040220893919467926, -0.053469397127628326, -0.07602419704198837, -0.011580483987927437, -0.02537832409143448, 0.015011287294328213, 0.020937960594892502, -0.015270356088876724, -0.014549537561833858, 0.013666912913322449, 0.05004895478487015, -0.025995880365371704, 0.033481746912002563, -0.014773302711546421, 0.03759897127747536, 0.11756281554698944, 0.03117418847978115, -0.02604914829134941, -0.011918858624994755, 0.04019660875201225, -0.031110242009162903, -0.048571981489658356, -0.05696577951312065, -0.015692535787820816, -0.036858368664979935, -0.02989397943019867, 0.03639513999223709, 0.0024950604420155287, -0.05326453223824501, -0.07756399363279343, -0.000659934536088258, -0.021116435527801514, 0.035101212561130524, 0.03226245939731598, -0.005923086777329445, 0.06113763898611069, 0.05988483503460884, -0.07956624776124954, 0.005992550868541002, 0.04511167109012604, -0.01225839089602232, 0.012128764763474464, 0.07912667840719223, -0.0011127968318760395, -0.006804467178881168, -0.06521832197904587, 0.008879154920578003, -0.006942109204828739, -0.08535545319318771, -0.0032268462236970663, -0.01223073061555624, -0.012116983532905579, -0.03666370362043381, 0.035111647099256516, 0.003299844218418002, 0.07569871842861176, -0.04184627905488014, 0.009824962355196476, -0.0008648585062474012, -0.05830977484583855, -0.018603995442390442, 0.05125020444393158, 0.031949739903211594, -0.010820935480296612, -0.09939393401145935, -0.016122575849294662, 0.03349468484520912, -0.025274183601140976, -0.041769761592149734, -0.004829422105103731, -0.02108624577522278, -0.021526357159018517, 0.013990846462547779, -0.014502034522593021, -0.0012192303547635674, 0.0029354223515838385, 0.0011968630133196712, -0.041407130658626556, 0.039896074682474136, -0.029535047709941864, 0.007507873233407736, 0.05777684226632118, -0.016065355390310287, 0.08265642076730728, 0.023515809327363968, 0.02766251564025879, 0.044212356209754944, 0.005781348794698715, 0.05959666147828102, 0.03106452152132988, 0.01427371334284544, 0.027762411162257195, -0.024102624505758286, -0.029628541320562363, 0.003000320866703987, 0.04217524826526642, 0.08916313201189041, 0.020971879363059998, -0.004758831113576889, 0.035214755684137344, -0.025231000036001205, -0.0001873755973065272, 0.009316793642938137, -0.013444041833281517, -0.005598013289272785, 0.031786028295755386, -0.01435496099293232, 0.044796258211135864, -0.03571666032075882, 0.01017296127974987, -0.012404792942106724, 0.04550632834434509, -0.01731167919933796, 0.03667273744940758, -0.0554170235991478, -0.05117476359009743, 0.0725305825471878, 0.012033860199153423, -0.020697008818387985, 0.028160415589809418, -0.03704015538096428, 0.03093678504228592, 0.043844472616910934, 0.034263744950294495, -0.041844990104436874, 0.04464811459183693, 0.01204410195350647, -0.023628178983926773, 0.035929977893829346, 0.019147617742419243, 0.039835840463638306, 0.018434181809425354, 0.011659400537610054, 0.007571551017463207, 0.00248076394200325, -0.01742834970355034, -0.04106343537569046, 0.011250598356127739, 0.04661032184958458, 0.01648596301674843, -0.06019967421889305, 0.008968598209321499, -0.016460923478007317, -0.03799111396074295, 0.014616565778851509, 0.03565517067909241, 0.005465805996209383, 0.023812877014279366, 0.036618564277887344, -0.0379672646522522, -0.034977566450834274, 0.004916393663734198, -0.022046450525522232, 0.013450168073177338, -0.014024106785655022, -0.05610007792711258, 0.008282729424536228, -0.0019488532561808825, 0.018240539357066154, 0.05410979315638542, -0.02977815642952919, -0.0006688134162686765, -0.014316076412796974, -0.02814457006752491, 0.028063759207725525, 0.09516573697328568, -0.014630154706537724, -0.001821302343159914, -0.023756522685289383, -0.001736871199682355, -0.030438562855124474, -0.032697465270757675, 0.05899588763713837, -0.02420920692384243, 0.03133286535739899, -0.10193625092506409, 0.00785969477146864, 0.03328610211610794, 0.1205756887793541, -0.018023349344730377, 0.010568366385996342, 0.00946534238755703, 0.009160550311207771, 0.06024310365319252, 0.02552718110382557, -0.031197363510727882, -0.03134353831410408, 0.05105794966220856, 0.024938851594924927, 0.032622646540403366, 0.008319124579429626, -0.006782264448702335, -0.02707858942449093, -0.008433465845882893, 0.03354203328490257, -0.042520251125097275, -0.000917882367502898, -0.013606314547359943, -0.009335646405816078, -0.0180995911359787, -0.044009365141391754, -0.016205666586756706, 0.10241734981536865, 0.07848452776670456, 0.02189745381474495, -0.0014096882659941912, -0.009888549335300922, 0.0411297082901001, 0.041441094130277634, -0.026020532473921776, -0.02803214266896248, 0.026058053597807884, -0.02435368485748768, 0.005733804777264595, 0.03629152104258537, 0.008099026046693325, -0.037939392030239105, -0.013879463076591492, 0.045924410223960876, 0.0037010193336755037, 0.04987136274576187, -0.05729157477617264, -0.017773380503058434, -0.055365175008773804, 0.02764960192143917, -0.0027640352491289377, -0.001698624691925943, -0.04900626838207245, -0.01644996926188469, -0.020723380148410797, -0.04115236923098564, 0.007755260448902845, 0.02522178366780281, 0.03746994957327843, -0.011277592740952969, 0.00633677514269948, -0.030181553214788437, -0.06359374523162842, 0.03438954055309296, 0.0052551510743796825, -0.0826602354645729, 0.07424969971179962, -0.03541477769613266, -0.03400615602731705, -0.056342121213674545, -0.04450811445713043, 0.017466098070144653, -0.045182667672634125, -0.006004045717418194, 0.00020255232811905444, -0.08512423932552338, -0.08855602145195007, -0.010261215269565582, 0.02872251346707344, -0.013289792463183403, -0.06612573564052582, 0.013568815775215626, 0.007425373885780573, 0.0063093784265220165, 0.0034956412855535746, -0.018841100856661797, -0.00011861797247547656, 0.03991139307618141, -0.017668012529611588, -0.01916707493364811, -0.0011156372493132949, 0.07648739963769913, -0.047096412628889084, -0.03195563703775406, -0.043881021440029144, -0.0378078818321228, -0.01381673477590084, -0.018427886068820953, 0.02650260739028454, 0.021486638113856316, -0.0005191080854274333, -0.03364535793662071, 0.01881631650030613, 0.012211861088871956, -0.02284224145114422, 0.01463631633669138, 0.04996514320373535, -0.002850152086466551, 0.02950177900493145, -0.07057783752679825, -0.05353350192308426, 0.015476612374186516, -0.040933188050985336, -0.0003847349726129323, 0.007258002180606127, -0.020139997825026512, -0.0003401875728741288, -0.008402311243116856, 0.010755489580333233, -0.03796006366610527, 0.010537683963775635, -0.03983344882726669, -0.06662742048501968, -0.06061752885580063, -0.010252279229462147, -0.028731029480695724, 0.02014635130763054, 0.014189711771905422, -0.021408604457974434, -0.023583343252539635, -0.024859799072146416, -0.08189354836940765, -0.05779802426695824, 0.07542849332094193, 0.04709542915225029, -0.0026227724738419056, 0.01037373673170805, 0.018905209377408028, 0.004674979951232672, -0.04136912524700165, -0.08828733116388321, 0.028550008311867714, -0.003285155864432454, 0.0033109576907008886, 0.04948241263628006, 0.03026452846825123, -0.036369383335113525, -0.019771946594119072, -0.010789993219077587, 0.03276565298438072, 0.06567981839179993, -0.04603783041238785, -0.02515508607029915, 0.01610436849296093, -0.0021150473039597273, -0.009741700254380703, 0.002166571794077754, 0.014039687812328339, 0.056420546025037766, -0.039022818207740784, -0.0012879854766651988, -0.06265388429164886, -0.02139000967144966, 0.014540850184857845, 0.03886546939611435, 0.010057482868432999, 0.05287673696875572, 0.014928944408893585, 0.01619815267622471, 0.01152545865625143, -0.017568359151482582, -0.03993920981884003, -0.01572526805102825, -0.023701436817646027, -0.013066324405372143, 0.0012567307567223907, -0.03279764950275421, -0.04371393844485283, 0.02073296159505844, -0.006570189725607634, 0.05398371070623398, 0.03573263809084892, -0.010897427797317505, 0.07091423124074936, 0.0009495767881162465, 0.008802257478237152, 0.013309908099472523, -0.03574764356017113, 0.009586833417415619, 0.06637829542160034, -0.00307449814863503, 0.014126704074442387, 0.023576976731419563, 0.0225695688277483, -0.046452488750219345, 0.05704810097813606, 0.06802000850439072, 0.009871033020317554, -0.023982657119631767, -0.012831827625632286, -0.05246635898947716, -0.00055994390277192, -0.03282683342695236, -0.021057505160570145, -0.005001175217330456, 0.01879553683102131, 0.0374043770134449, -0.0294148288667202, 0.0020039307419210672, 0.008914206176996231, 0.0347803570330143, 0.02813585102558136, -0.015155855566263199, 0.05384598672389984, -0.044202178716659546, -0.042632054537534714, -0.06650479137897491, -0.03681929036974907, -0.03153824061155319, 0.032723743468523026, -0.010227840393781662, 0.006724036764353514, -0.003054482862353325, -0.005078471731394529, -0.08414445072412491, -0.04425055906176567, -0.0023426443804055452, 0.023460235446691513, 0.06384602934122086, 0.029017632827162743, 0.015865622088313103, 0.020533572882413864, 0.035308703780174255, -0.031418994069099426, -0.008021887391805649, -0.07790746539831161, -0.06597349792718887, 0.028500789776444435, 0.02192295715212822, -6.0715484428260896e-33, -0.04144610837101936, -0.05827457085251808, -0.014885731972754002, 0.0719587579369545, -0.011907043866813183, -0.0164849404245615, 0.026267919689416885, 0.008442293852567673, -0.013563702814280987, -0.010096742771565914, 0.014983490109443665, -0.0033276895992457867, -0.0018269839929416776, -0.03878909721970558, 0.06692928820848465, 0.020152229815721512, -0.009381039999425411, 0.00038489175494760275, -0.010075666010379791, -0.007382552605122328, 0.030190816149115562, -0.030180832371115685, 0.0008170015644282103, -0.050190627574920654, 0.028337888419628143, 0.03248661383986473, -0.011772404424846172, 0.016833992674946785, -0.026154927909374237, 0.026216130703687668, -0.009849988855421543, 0.00530305365100503, 0.03370896726846695, -0.0023912384640425444, -0.0017236154526472092, 0.01099903043359518, -0.07709410041570663, -0.06396666169166565, -0.0006242460804060102, 0.034095946699380875, 0.04028400033712387, -0.004297368694096804, -0.013112705200910568, 0.0027672797441482544, 0.0379897765815258, -0.04041779041290283, 0.05980146303772926, -0.06172206252813339, -0.012518690899014473, -0.05317433550953865, -0.0017589983763173223, 0.02040783502161503, -0.03627615422010422, 0.0708937719464302, 0.058512382209300995, -0.008337287232279778, -0.040244463831186295, 0.010712574236094952, -0.0310357678681612, 0.05555808171629906, 0.036783382296562195, 0.025770196691155434, -0.005680580623447895, 0.0010589984012767673, 0.061133645474910736, -0.0037776604294776917, 0.021956192329525948, -0.04737565666437149, -0.00796661525964737, 0.03592650964856148, 0.002828180557116866, 0.10245873779058456, -0.010186955332756042, 0.05590283125638962, 0.06890852004289627, -0.004454593174159527, -0.06494975835084915, 0.04093240574002266, -0.05045905336737633, 0.06848879903554916, -0.034533627331256866, 0.02036084607243538, -0.01153210736811161, -0.01713205873966217, 0.025127148255705833, -0.016875775530934334, -0.0497162789106369, -0.045792218297719955, 0.003860216587781906, -0.05342491716146469, -0.04420190677046776, 0.023108014836907387, -0.03863021358847618, -0.047788430005311966, -0.036106303334236145, -0.03907029703259468, 0.008423429913818836, 0.05280027538537979, -0.003490596078336239, -0.011293962597846985, -0.030878311023116112, -0.040876466780900955, -0.043916698545217514, 0.04918627813458443, 0.047097086906433105, 0.014476720243692398, 0.026216499507427216, 0.015455278567969799, -0.034552112221717834, 0.0010805176571011543, 0.028991034254431725, -0.08599109947681427, 0.009625243954360485, -0.010488979518413544, -0.024483611807227135, -0.008059664629399776, 0.01915420964360237, 0.06628090143203735, 0.041739530861377716, 0.013196910731494427, -0.06190022826194763, 0.020588530227541924, -0.0200735442340374, -0.0033380677923560143, 0.011475416831672192, -0.043454017490148544, -0.04931149631738663, -0.057085853070020676, 0.09286963939666748, -0.0006263661198318005, -0.02927105873823166, -0.025556655600667, 3.161033816923009e-07, 0.014255644753575325, -0.012234796769917011, -0.0057207802310585976, 0.03995465114712715, -0.004846415016800165, 0.00812411867082119, -0.007147143594920635, 0.016296954825520515, -0.011223005130887032, -0.02207745797932148, 0.0879490002989769, -0.030721889808773994, -0.015635797753930092, 0.05123152211308479, 0.0066830795258283615, 0.04723016545176506, 0.014558566734194756, -0.05270663648843765, -0.03796185553073883, 0.022840576246380806, 0.006774548441171646, -0.014219257049262524, 0.03880532458424568, 0.009891422465443611, -0.0054989526979625225, -0.015262017026543617, -0.009129204787313938, -0.02358342707157135, 0.037304818630218506, 0.044018521904945374, 0.014461271464824677, -0.02982134371995926, -0.0001822730846470222, 0.0506661981344223, 0.03845716640353203, 0.005244194995611906, 0.02945449762046337, 0.00027848276658914983, -0.008265890181064606, 0.04543843865394592, -0.003968534059822559, -0.07013752311468124, 0.014276864007115364, -0.038900621235370636, 0.06976526230573654, -0.0009340298711322248, -0.042718641459941864, 0.0384645015001297, -0.03610442206263542, -0.014737604185938835, 0.025684602558612823, 0.015891971066594124, -0.013603022322058678, 0.0034196453634649515, -0.028753988444805145, -0.010340578854084015, 0.015065539628267288, -0.016826966777443886, 0.025752509012818336, 0.04520341008901596, 0.016219276934862137, -0.047631990164518356, 0.044166453182697296, -0.0071172043681144714, -0.002562343142926693, -0.02122693695127964, -0.023114070296287537, 3.340253752816659e-34, 0.023309336975216866, 0.022050658240914345, 0.018257761374115944, -0.008046401664614677, -0.014965402893722057, -0.027732614427804947, -0.0389307402074337, 0.011439037509262562, 0.019644076004624367, -0.00791856087744236, 0.0007639026152901351]

['Marco Molinaro', 'R. Ravi']

1204.5810v1

We consider packing LP's with $m$ rows where all constraint coefficients are normalized to be in the unit interval. The n columns arrive in random order and the goal is to set the corresponding decision variables irrevocably when they arrive so as to obtain a feasible solution maximizing the expected reward. Previous (1 - \epsilon)-competitive algorithms require the right-hand side of the LP to be Omega((m/\epsilon^2) log (n/\epsilon)), a bound that worsens with the number of columns and rows. However, the dependence on the number of columns is not required in the single-row case and known lower bounds for the general case are also independent of n. Our goal is to understand whether the dependence on n is required in the multi-row case, making it fundamentally harder than the single-row version. We refute this by exhibiting an algorithm which is (1 - \epsilon)-competitive as long as the right-hand sides are Omega((m^2/\epsilon^2) log (m/\epsilon)). Our techniques refine previous PAC-learning based approaches which interpret the online decisions as linear classifications of the columns based on sampled dual prices. The key ingredient of our improvement comes from a non-standard covering argument together with the realization that only when the columns of the LP belong to few 1-d subspaces we can obtain small such covers; bounding the size of the cover constructed also relies on the geometry of linear classifiers. General packing LP's are handled by perturbing the input columns, which can be seen as making the learning problem more robust.

Geometry of Online Packing Linear Programs

http://arxiv.org/pdf/1204.5810v1

Title Geometry Online Packing Linear Programs Summary consider packing LPs row constraint coefficient normalized unit interval n column arrive random order goal set corresponding decision variable irrevocably arrive obtain feasible solution maximizing expected reward Previous 1 epsiloncompetitive algorithm require righthand side LP Omegamepsilon2 log nepsilon bound worsens number column row However dependence number column required singlerow case known lower bound general case also independent n goal understand whether dependence n required multirow case making fundamentally harder singlerow version refute exhibiting algorithm 1 epsiloncompetitive long righthand side Omegam2epsilon2 log mepsilon technique refine previous PAClearning based approach interpret online decision linear classification column based sampled dual price key ingredient improvement come nonstandard covering argument together realization column LP belong 1d subspace obtain small cover bounding size cover constructed also relies geometry linear classifier General packing LPs handled perturbing input column seen making learning problem robust Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.036017876118421555, 0.024584461003541946, -0.0266119297593832, -0.0009014165843836963, -0.00993004534393549, -0.03561973571777344, 0.04846342280507088, 0.05225775018334389, -0.011772188358008862, -0.01244701910763979, 0.058236412703990936, 0.037774644792079926, -0.008634802885353565, 0.12393206357955933, -0.0002989988133776933, -0.001202676328830421, -0.03503473848104477, -0.022180987522006035, -0.02548002079129219, 0.011766614392399788, 0.01154264621436596, -0.0246728528290987, -0.02631520852446556, -0.05019596591591835, -0.015622376464307308, -0.024960601702332497, -0.07971076667308807, 0.001850332715548575, -0.05182969197630882, -0.03834828361868858, 0.02676296792924404, 0.014488990418612957, -0.0014303693315014243, -0.020361991599202156, 2.292058297825861e-06, -0.04014633595943451, -0.07572385668754578, -0.028381096199154854, -0.0017797219334170222, 0.009516172111034393, -0.001474514021538198, -0.060863301157951355, 0.0035298357252031565, -0.03234148025512695, -0.020603537559509277, 0.0067256721667945385, 0.01865416020154953, 0.07368475198745728, -0.005221513099968433, -0.025479217991232872, -0.0006950926617719233, -0.021435905247926712, 0.032577209174633026, -0.009525982663035393, 0.008302378468215466, -0.021848702803254128, -0.020259687677025795, -0.017540622502565384, -0.009335464797914028, -0.02350555546581745, -0.04377663508057594, 0.0235338993370533, 0.022804170846939087, -0.021916555240750313, 0.0631357878446579, -0.0021032842341810465, -0.04209405183792114, -0.006082396022975445, -0.03779103234410286, 0.019628899171948433, -0.0204565841704607, 0.014403938315808773, 0.008096745237708092, -0.03335897997021675, -0.023984426632523537, -0.024223629385232925, -0.00031050146208144724, 0.05047394707798958, -0.0493864044547081, -0.039586931467056274, -0.07497848570346832, 0.06164128705859184, -0.06297416985034943, 0.009304707869887352, -0.009350976906716824, 0.07268251478672028, -0.04532364383339882, -0.020813001319766045, 0.01735927350819111, -0.023884285241365433, -0.0403151772916317, -0.016326142475008965, 0.029714513570070267, -0.020895568653941154, -0.05019417405128479, -0.023073500022292137, 0.049602244049310684, -0.020521607249975204, 0.03604023531079292, -0.044465381652116776, 0.06269799917936325, -0.041375573724508286, 0.07864128053188324, 0.006827603559941053, -0.013864104636013508, 0.06625891476869583, -0.0384339764714241, 0.006324255373328924, -0.06946443021297455, 0.08852002024650574, 0.011296897195279598, -0.011322958394885063, -0.04833696037530899, 0.06628155708312988, -0.026941778138279915, -0.023904722183942795, -0.04172562435269356, 0.006270065903663635, -0.04631906375288963, 0.023070206865668297, 0.026188896968960762, 0.035092566162347794, -0.00027983394102193415, -0.030858218669891357, 0.02038273587822914, -0.025321219116449356, -0.03238648921251297, 0.011492829769849777, -0.01511357445269823, 0.027535462751984596, 0.03886624798178673, 0.04995754733681679, 0.0043536894954741, 0.021290631964802742, 0.016947142779827118, 0.06932318955659866, -0.007720688823610544, 0.010165676474571228, -0.01990143582224846, -0.05914491415023804, -0.03187122941017151, 0.029042400419712067, -0.06064470112323761, -0.03776443749666214, 0.009946536272764206, -0.0846574530005455, -0.008524426259100437, 0.05778587982058525, -0.002414729679003358, -0.025581656023859978, -0.023202216252684593, 0.06805608421564102, 0.0868978276848793, 0.03065919131040573, 0.07349153608083725, 0.02289704605937004, 0.001205539796501398, -0.011303972452878952, 0.03071964718401432, 0.09259699285030365, 0.034019552171230316, -0.01484692096710205, 0.01937965676188469, -0.017001327127218246, -0.004415574949234724, -0.03207188844680786, -0.03937238082289696, -0.0006368334288708866, -0.013669324107468128, 0.03107404336333275, -0.017740624025464058, -0.03338603302836418, -0.015725241973996162, 0.0061940038576722145, 0.04594471678137779, -0.0020550680346786976, 0.07690119743347168, 0.01043244544416666, -0.07752739638090134, 0.059292253106832504, -0.049731019884347916, -0.05789793282747269, 0.016333024948835373, 0.02604582905769348, -0.03199376165866852, 0.0004801252798642963, 0.009694940410554409, -0.02269783243536949, -0.01909446343779564, -0.043661389499902725, -0.0027054317761212587, -0.060158729553222656, -0.006733832415193319, -0.021098682656884193, 0.019254429265856743, -0.04698588326573372, -0.042725760489702225, -0.042206596583127975, -0.005820667836815119, 0.011958247981965542, -0.06477365642786026, -0.02008274383842945, 0.032063234597444534, -0.021037330850958824, -0.0013914721785113215, -0.02228321135044098, -0.03188217431306839, -0.004093195777386427, -0.029961885884404182, -0.032813072204589844, 0.04467075690627098, -0.027424583211541176, 0.017609095200896263, -0.0028562091756612062, 0.0076505704782903194, 0.024401089176535606, 0.00629415875300765, -0.016135724261403084, 0.01221398264169693, -0.010639505460858345, -0.020897328853607178, 0.0318668894469738, 0.03588496521115303, 0.028035715222358704, 0.00704966438934207, -0.036150380969047546, 0.04898301884531975, 0.04007255285978317, 0.03668082877993584, 0.021992720663547516, 0.05199417844414711, -0.04840051382780075, 0.0843488872051239, -0.05086476355791092, -0.04972415789961815, -0.02475503273308277, 0.027385786175727844, 0.006412782706320286, -0.018031045794487, 0.016985850408673286, -7.632715278305113e-05, -0.017359215766191483, -0.021804332733154297, 0.02371417172253132, -0.00992138683795929, 0.018402403220534325, -0.030699532479047775, -0.008941547945141792, -0.006111517548561096, 0.0024109736550599337, 0.0019807983189821243, -0.058033380657434464, 0.07630252838134766, -0.009114859625697136, 0.05709448084235191, -0.05068375542759895, -0.05282128229737282, 0.06314495950937271, -0.015201379545032978, 0.06587208807468414, 0.011375179514288902, -0.03381538763642311, -0.006909464951604605, 0.007155322469770908, 0.08318176120519638, 0.010934780351817608, -0.0017719785682857037, 0.01925070397555828, 0.031585756689310074, 0.02697909064590931, -0.027621986344456673, 0.0157505813986063, -0.04532197117805481, -0.00012057126878062263, -0.03058590553700924, -0.0527251660823822, -0.024262351915240288, -0.052006714046001434, -0.034012820571660995, 0.02402639575302601, 0.014294235035777092, 0.019497927278280258, 0.01866058260202408, -0.022555198520421982, 0.008839502930641174, -0.025684019550681114, 0.03582565858960152, -0.049546778202056885, -0.062078580260276794, 0.031018156558275223, -0.041011035442352295, -0.004623419139534235, 0.03642343357205391, -0.006108083296567202, -0.04889743775129318, -0.0510079599916935, -0.052399903535842896, 0.07534927874803543, 0.035920556634664536, 0.019165948033332825, 0.0476011224091053, 0.03303699940443039, -0.04290430620312691, 0.033677369356155396, -0.012578158639371395, 0.026919199153780937, 0.10604367405176163, -0.016405653208494186, -0.0057069892063736916, 0.019657788798213005, 0.02669595368206501, -0.002150247571989894, -0.010292107239365578, -0.024427887052297592, 0.013630577363073826, -0.04968727007508278, -0.06797457486391068, -0.001450198469683528, -0.013445090502500534, 0.09189790487289429, -0.010061085224151611, -0.04233555495738983, 0.034312691539525986, 0.01895790360867977, -0.025439836084842682, -0.026070641353726387, -0.04127581790089607, -0.02460329420864582, 0.0037449460942298174, 0.04856504127383232, 0.03427232429385185, -0.085816390812397, 0.019663484767079353, 0.010986708104610443, 0.03486902639269829, 0.010818948969244957, -0.039322517812252045, -0.024060523137450218, 0.012221322394907475, -0.016756420955061913, 0.002447431208565831, -0.07514141499996185, -0.015465585514903069, 0.011514914222061634, 0.06361181288957596, -0.07445795834064484, 0.006752236280590296, -0.0019113757880404592, 0.002809885423630476, 0.026351727545261383, 0.000823860231321305, 0.08027121424674988, -0.0181580800563097, -0.005618907045572996, -0.0015280322404578328, 0.0453915074467659, -0.0015718480572104454, 0.0001073472376447171, -0.013431482017040253, -0.014221057295799255, 0.03148544207215309, 0.015075759962201118, -9.355791553389281e-05, 0.037062786519527435, -0.00909271091222763, 0.06159863993525505, 0.07543887943029404, 0.024704502895474434, -0.04107547923922539, 0.02311454340815544, 0.011478278785943985, 0.008448628708720207, 0.020329710096120834, 0.0254836343228817, 0.048214346170425415, -0.04695361852645874, -0.02561035566031933, -0.019612325355410576, 0.049692653119564056, -0.003798452438786626, 0.07956450432538986, -0.028861481696367264, 0.045906782150268555, -0.0214875265955925, 0.03405310586094856, -0.013593030162155628, -0.06252345442771912, -0.08177394419908524, -0.10735532641410828, 0.04487141966819763, -0.014711158350110054, -0.008732476271688938, -0.03128396347165108, -0.028712986037135124, -0.022707322612404823, -0.06022430583834648, -0.0308492723852396, 0.011745339259505272, -0.008659101091325283, -0.024958545342087746, 0.028670940548181534, -0.023715337738394737, 0.0773814395070076, -0.03104582615196705, -0.006652110256254673, -0.006806572899222374, -0.04640316218137741, 0.02121805027127266, -0.043534040451049805, -0.07121305167675018, 0.05355395749211311, 0.04876874387264252, -0.02483292669057846, -0.007225603796541691, 0.02890613302588463, 0.0693209245800972, 0.05230972543358803, -0.014289448037743568, -0.0006234584143385291, -0.0024651905987411737, -0.03922273591160774, 0.05835490673780441, 0.04583391174674034, 0.048060979694128036, 0.01884833164513111, 0.0045111351646482944, 0.019601410254836082, 0.017060615122318268, -0.028068650513887405, -0.050080183893442154, -0.0304816123098135, -0.03947265073657036, -0.04220616817474365, 0.033690858632326126, -0.020798902958631516, 0.05777408555150032, 0.03768894821405411, -0.03396027162671089, -0.011803044937551022, -0.07022876292467117, 0.09030355513095856, -0.017248738557100296, 0.08060713857412338, -0.020498232915997505, -0.02724301628768444, -0.04999832063913345, 0.013395417481660843, -0.03292428329586983, -0.08358863741159439, 0.0642509013414383, 0.020112566649913788, -0.001554660382680595, 0.058518558740615845, 0.014287947677075863, -0.04567663371562958, 0.0025815374683588743, 0.0035624841693788767, -0.004050893243402243, -0.05533674359321594, 0.009565958753228188, 0.05523958057165146, 0.038387399166822433, -0.009978698566555977, -0.017502840608358383, 0.021562805399298668, 0.00490580452606082, 0.024076517671346664, 0.007564714178442955, 0.008818116039037704, 0.0068757189437747, 0.02189682610332966, 0.0074522122740745544, 0.0006238712230697274, 0.02605811133980751, 0.04479655623435974, -0.047833096235990524, -0.038439687341451645, -0.034879643470048904, -0.015739062801003456, 0.006969699170440435, 0.018508009612560272, 0.0010688344482332468, 0.041671063750982285, -0.028948292136192322, -0.0217379592359066, 0.0732368752360344, 0.001013532979413867, -0.023732738569378853, 0.014301502145826817, 0.0039445022121071815, 0.0020667188800871372, 0.0006884439499117434, 0.03110549971461296, 0.017849421128630638, 0.09065135568380356, 0.048699378967285156, 0.04371897131204605, -0.0194239504635334, -0.008852969855070114, 0.0023080487735569477, 0.0070131393149495125, 0.04225785285234451, 0.012779287062585354, 0.016044817864894867, 0.00664540845900774, 0.05910388007760048, 0.027031639590859413, -0.004588100593537092, 0.005775573197752237, 0.021307840943336487, -0.058726102113723755, -0.0019998224452137947, 0.032833702862262726, -0.0566709078848362, -0.023237381130456924, 0.013915451243519783, -0.06394752860069275, -0.02985474094748497, -0.0285871010273695, 0.008118956349790096, -0.03512975201010704, 0.021179500967264175, 0.04109927639365196, -0.009598850272595882, 0.029718339443206787, -0.01381268072873354, 0.03938578441739082, -0.021884609013795853, -0.0008186870836652815, 0.038263991475105286, 0.03645288571715355, -0.042614202946424484, -0.05563906207680702, -0.031479883939027786, -0.057879045605659485, 0.08486532419919968, -0.01460341177880764, 0.06422309577465057, -0.010807487182319164, -0.008550301194190979, -0.02621505782008171, 0.012136071920394897, 0.019919009879231453, 0.02526656910777092, 0.08416609466075897, 0.04359583184123039, -0.01673557050526142, -0.0006228843121789396, 0.03620446100831032, 0.042512938380241394, -0.027799488976597786, -0.013199551962316036, -0.0020010038278996944, 0.006932066287845373, 0.01232056599110365, -5.9675847837034895e-33, -0.006725409533828497, -0.060605186969041824, -0.06300719827413559, 0.02582126297056675, -0.02596764825284481, -0.006372067146003246, 0.047875676304101944, 0.005529074929654598, 0.06415840983390808, -0.030767178162932396, -0.010536286048591137, -0.026951521635055542, 0.009900001809000969, -0.02050722949206829, 0.05740814283490181, -0.007922816090285778, -0.0530502088367939, 0.005543672014027834, -0.05039895698428154, -0.043425463140010834, -0.029922280460596085, 0.028911013156175613, -0.0657397136092186, 0.01314946822822094, 0.002853057812899351, -0.012379340827465057, -0.020663369446992874, 0.033728986978530884, -0.05599319189786911, 0.0282389298081398, 0.02188398502767086, -0.0024149061646312475, 0.018817434087395668, -0.009812847711145878, 0.007604952901601791, 0.05064557492733002, -0.019816676154732704, -0.04591195657849312, -0.03884325549006462, 0.005179957952350378, -0.05058012902736664, 0.008834835141897202, 0.054629821330308914, 0.0002628200454637408, -0.02754472941160202, 0.019514355808496475, 0.027827223762869835, -0.02889462374150753, -0.024464087560772896, 0.00892952922731638, 0.04441952705383301, -0.025442034006118774, 0.02026595175266266, 0.033362697809934616, 0.051714710891246796, 0.0383836068212986, -0.012862399220466614, 0.019200997427105904, 0.01767301745712757, 0.0628041997551918, -0.008660009130835533, 0.0326988622546196, 0.01839122548699379, -0.028228823095560074, -0.01535767037421465, 0.022342439740896225, -0.03665214404463768, -0.008418862707912922, -0.01487415749579668, -0.06114310026168823, -0.034672774374485016, -0.0020509662572294474, 0.010542328469455242, -0.023475516587495804, 0.06669003516435623, -0.0033653476275503635, -0.01775861531496048, 0.01622837409377098, 0.0003576393355615437, -0.020844826474785805, -0.01320465188473463, 0.020030615851283073, -0.006597237195819616, -0.031123042106628418, 0.01220287661999464, -0.017280301079154015, -0.04643586277961731, -0.006109411828219891, -0.006827689241617918, 0.03433086350560188, -0.009822414256632328, -0.0069962493143975735, -0.048293258994817734, 0.0165493655949831, 0.012699970044195652, -0.020801179111003876, 0.03143388777971268, 0.017074190080165863, -0.01918966695666313, -0.0005164881586097181, -0.025392699986696243, -0.03322216495871544, -0.06970199942588806, -0.02957797236740589, 0.002630638424307108, 0.026174284517765045, 0.06637801229953766, -0.002418037736788392, -0.01352727971971035, 0.0402742400765419, 0.007932369597256184, -0.016567274928092957, 0.03898758813738823, 0.019130712375044823, 0.004263514187186956, -0.055194590240716934, -0.015168830752372742, 0.054580576717853546, 0.03837152197957039, -0.028060931712388992, -0.009324588812887669, -0.01888326182961464, -0.024805571883916855, -0.03943975269794464, -0.02067338488996029, -0.004127455409616232, -0.015132113359868526, 0.02667762152850628, 0.008106001652777195, -0.03788324445486069, -0.02787664718925953, -0.03125937283039093, 2.81191631756883e-07, 0.046715594828128815, 0.0669049620628357, 0.01134778093546629, -0.017654936760663986, 0.024961372837424278, -0.016897890716791153, -0.024980489164590836, 0.009175729937851429, -0.09630836546421051, -0.0009061060263775289, 0.03611248359084129, -0.02828037180006504, 0.029530415311455727, 0.009796126745641232, -0.029381539672613144, 0.012403391301631927, 0.008542986586689949, 0.022269470617175102, -0.051343586295843124, 0.02466549724340439, 0.07181544601917267, 0.031138073652982712, 0.07168620824813843, -0.02363116294145584, -0.018685877323150635, 0.009146610274910927, -0.035748280584812164, -0.034751854836940765, 0.047920431941747665, -0.04298422113060951, -0.005740331020206213, -0.051363520324230194, -0.05103623867034912, 0.02542879618704319, -0.02501065284013748, -0.021188298240303993, 0.017352985218167305, 0.07617724686861038, 0.0494505912065506, 0.019568121060729027, 0.05770207941532135, -0.0002829227887559682, 0.005226656794548035, -0.03153814747929573, 0.005695669911801815, -0.01023357268422842, -0.0022602726239711046, 0.03535178676247597, 0.016004495322704315, -0.02723619155585766, 0.02768191695213318, 0.017561370506882668, 0.03628861904144287, 0.033051930367946625, -0.059599246829748154, -0.008962216787040234, 0.06893443316221237, 0.042041242122650146, -0.020131081342697144, 0.046725187450647354, -0.010577608831226826, 0.021797705441713333, 0.03252110630273819, 0.0633883997797966, 0.056150369346141815, -0.053615983575582504, -0.025164948776364326, 3.199318638226538e-34, -0.006714250892400742, 0.030363647267222404, -0.006415973417460918, 0.005509067326784134, -0.044480759650468826, 0.011274582706391811, 0.034677423536777496, -0.004473128821700811, 0.031833697110414505, -0.011403219774365425, -0.014351403340697289]

['Yucheng Low', 'Joseph Gonzalez', 'Aapo Kyrola', 'Danny Bickson', 'Carlos Guestrin', 'Joseph M. Hellerstein']

1204.6078v1

While high-level data parallel frameworks, like MapReduce, simplify the design and implementation of large-scale data processing systems, they do not naturally or efficiently support many important data mining and machine learning algorithms and can lead to inefficient learning systems. To help fill this critical void, we introduced the GraphLab abstraction which naturally expresses asynchronous, dynamic, graph-parallel computation while ensuring data consistency and achieving a high degree of parallel performance in the shared-memory setting. In this paper, we extend the GraphLab framework to the substantially more challenging distributed setting while preserving strong data consistency guarantees. We develop graph based extensions to pipelined locking and data versioning to reduce network congestion and mitigate the effect of network latency. We also introduce fault tolerance to the GraphLab abstraction using the classic Chandy-Lamport snapshot algorithm and demonstrate how it can be easily implemented by exploiting the GraphLab abstraction itself. Finally, we evaluate our distributed implementation of the GraphLab abstraction on a large Amazon EC2 deployment and show 1-2 orders of magnitude performance gains over Hadoop-based implementations.

Distributed GraphLab: A Framework for Machine Learning in the Cloud

http://arxiv.org/pdf/1204.6078v1

Title Distributed GraphLab Framework Machine Learning Cloud Summary highlevel data parallel framework like MapReduce simplify design implementation largescale data processing system naturally efficiently support many important data mining machine learning algorithm lead inefficient learning system help fill critical void introduced GraphLab abstraction naturally express asynchronous dynamic graphparallel computation ensuring data consistency achieving high degree parallel performance sharedmemory setting paper extend GraphLab framework substantially challenging distributed setting preserving strong data consistency guarantee develop graph based extension pipelined locking data versioning reduce network congestion mitigate effect network latency also introduce fault tolerance GraphLab abstraction using classic ChandyLamport snapshot algorithm demonstrate easily implemented exploiting GraphLab abstraction Finally evaluate distributed implementation GraphLab abstraction large Amazon EC2 deployment show 12 order magnitude performance gain Hadoopbased implementation Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.002320626750588417, 0.004208630416542292, -0.01423365343362093, -0.020802568644285202, -0.015649810433387756, 0.016135765239596367, 0.03333500027656555, -0.0171915702521801, 0.09079177677631378, 0.020714541897177696, 0.03173218294978142, 0.0704285204410553, -0.024279169738292694, 0.08498358726501465, -0.022906197234988213, -0.03185581415891647, 0.010888798162341118, 0.0558682456612587, 0.016951046884059906, -0.040909282863140106, 0.036941513419151306, 0.03792634606361389, 0.03425191342830658, -0.03104354254901409, -0.06461350619792938, -0.05263116583228111, -0.007271728944033384, -0.004847140517085791, 0.011598736979067326, -0.00816420465707779, 0.030030326917767525, -0.009028137661516666, -0.01138604711741209, 0.04334433004260063, 2.2240678845264483e-06, -0.024518651887774467, -0.02073989436030388, 0.007047755178064108, 0.00875814352184534, -0.014108576811850071, 0.03733474761247635, 0.014799753203988075, 0.01657945290207863, 0.015427728183567524, -0.040964651852846146, -0.006232914049178362, 0.0442340187728405, -0.01073109544813633, 0.0621882826089859, 0.010751551948487759, -0.017114965245127678, -0.049344152212142944, -0.0017743159551173449, -0.0012458718847483397, -0.032475102692842484, -0.03136735036969185, 0.007595336530357599, 0.05810023099184036, 0.04242552071809769, -0.014942005276679993, -0.029075216501951218, 0.00866595096886158, 0.00692727928981185, -0.0034654007758945227, 0.05515157803893089, 0.03262374922633171, -0.0014005674747750163, -0.006409432739019394, -0.028544409200549126, 0.026952393352985382, 0.015002232976257801, -0.010364162735641003, 0.029757751151919365, 0.014965413138270378, -0.06515221297740936, -0.002476918278262019, 0.0016501130303367972, 0.007726034615188837, -0.01387746911495924, 0.007176659069955349, -0.019685998558998108, -0.039757125079631805, 0.02957204356789589, -0.009603261947631836, 0.010046731680631638, 0.11454174667596817, -0.010784747079014778, 0.02741922438144684, -0.03858834505081177, -0.014143585227429867, -0.016697660088539124, -0.011609078384935856, 0.07133658975362778, 0.0107406135648489, -0.055966973304748535, -0.03849469870328903, -0.013679609633982182, -0.04915226995944977, 0.015200551599264145, -0.055901188403367996, 0.036475904285907745, -0.04387141764163971, 0.05474582687020302, 0.048108428716659546, 0.05775165930390358, 0.010474931448698044, -0.038294266909360886, 0.05091839283704758, -0.0014652484096586704, -0.016926433891057968, -0.049988217651844025, 0.012154189869761467, 0.018797151744365692, 0.058037564158439636, 0.02271765097975731, -0.012868701480329037, -0.07357817888259888, 0.07487373799085617, -0.036618128418922424, -0.015436185523867607, -0.00736013101413846, 0.012598359026014805, 0.05896797776222229, 0.041007403284311295, -0.00969567708671093, 0.006563134957104921, -0.009812885895371437, 0.020905135199427605, -0.0003078236768487841, -0.017470987513661385, 0.031343474984169006, -0.02597101405262947, 0.011506585404276848, 0.017893098294734955, 0.04327267408370972, 0.02108166366815567, 0.03862921893596649, 0.045665569603443146, 0.0021999040618538857, -0.028064517304301262, 0.05363821983337402, -0.03208141028881073, -0.061740729957818985, -0.07049313187599182, 0.01308515015989542, 0.019854573532938957, 0.007763889618217945, -0.006648120004683733, -0.035264112055301666, -0.01268263440579176, -0.0508238784968853, 0.04175979644060135, -0.046638742089271545, 0.0087007787078619, 0.04257960990071297, -0.0006266986019909382, -0.04360600933432579, 0.002615842269733548, -0.036293089389801025, -0.0036821954417973757, 0.029639113694429398, -0.021007640287280083, -0.026661979034543037, -0.009316179901361465, 0.021201277151703835, -0.04962558671832085, -0.019217221066355705, 0.012152031995356083, 0.0041452934965491295, 0.012448652647435665, -0.014988282695412636, 0.050992075353860855, -0.01849502883851528, -0.05190622806549072, 0.03367193043231964, 0.055554408580064774, -0.009267567656934261, -0.014012126252055168, -0.021156592294573784, 0.04716313257813454, -0.02383364923298359, -0.03867604210972786, -0.04971142113208771, -0.0023782190401107073, 0.014950050041079521, -0.05826183408498764, -0.02640310674905777, 0.019896702840924263, -0.006714701186865568, 0.016422688961029053, 0.0019273884827271104, 0.01830415241420269, -0.0038630447816103697, -0.02932247333228588, 0.04115965589880943, 0.014044061303138733, 0.0008993578958325088, -0.002011929638683796, 0.02204502560198307, 0.0033355855848640203, -0.06506925821304321, 0.02055513486266136, -0.02240973338484764, 0.00953755248337984, 0.030657069757580757, 0.016084248200058937, -0.016174502670764923, -0.009238258004188538, 0.016963820904493332, -0.05562988296151161, 0.009570029564201832, -0.027630995959043503, -0.01642925851047039, -0.019135281443595886, -0.002907261485233903, 0.03513989970088005, -0.03183864802122116, -0.045668311417102814, -0.0026881126686930656, 0.028033366426825523, -0.026503868401050568, -0.01406667660921812, -0.06262250989675522, -0.005608130246400833, 0.04229994863271713, 0.037446554750204086, 0.02642022632062435, -0.011386698111891747, 0.0910341814160347, -0.015173527412116528, -0.0017951991176232696, -0.029693378135561943, 0.025982268154621124, 0.05137357860803604, -0.03650812804698944, 0.014980587176978588, 0.0027748653665184975, -0.003995840437710285, 0.06258033215999603, 0.006731157191097736, 0.002211185870692134, 0.027752690017223358, -0.07588126510381699, -0.01269677933305502, 0.02041938714683056, -0.04253793880343437, -0.030114810913801193, 0.007742703426629305, -0.0007735737599432468, -0.03512553125619888, 0.0757562592625618, -0.023087697103619576, -0.0055169700644910336, 0.026943886652588844, -0.013132939115166664, -0.08861686289310455, 0.009011352434754372, -0.004377634264528751, -0.010980852879583836, 0.030765585601329803, 0.039488524198532104, -0.022343957796692848, 0.04971281811594963, -0.016327356919646263, -0.012376192025840282, -0.03968871384859085, 0.09655583649873734, -0.008794143795967102, 0.04221149906516075, 0.021254541352391243, 0.008380983956158161, 0.025341980159282684, 0.01612994074821472, 0.03098813258111477, -0.048780642449855804, 0.02520533837378025, 0.09605692327022552, -0.0036713071167469025, 0.004915665835142136, -0.0053882780484855175, 0.013758615590631962, -0.011777290143072605, 0.06816645711660385, -0.0716361254453659, -0.023204907774925232, 0.03128116950392723, 0.07035765796899796, -0.011240525171160698, 0.03245117515325546, 0.03659217059612274, -0.06701619178056717, -0.0033370780292898417, 0.01228347048163414, 0.028589192777872086, -0.036280278116464615, -0.012626866810023785, 0.005232839845120907, -0.006842967122793198, -0.022881653159856796, -0.0016601711977273226, -0.008782793767750263, 0.002578637795522809, -0.006677009165287018, -0.0030782208777964115, -0.05275450646877289, 0.01092047430574894, -0.0014524306170642376, 0.005031369626522064, -0.025782881304621696, -0.024173101410269737, -0.0004068093257956207, -0.016779262572526932, 0.018256114795804024, 0.004403320606797934, 0.015595454722642899, 0.0014805351383984089, -0.08488573133945465, 0.025826364755630493, 0.01115003228187561, -0.046560198068618774, -0.01625494286417961, -0.08479292690753937, 0.057437460869550705, 0.04028668999671936, -0.009906195104122162, -0.028295230120420456, -0.10485059022903442, -0.016910724341869354, 0.007633522618561983, 0.03982770815491676, 0.029838912189006805, -0.09446360915899277, -0.020650289952754974, 0.014276767149567604, 0.025680527091026306, 0.017190782353281975, -0.06205330789089203, -0.07242436707019806, 0.08593501150608063, -0.025863507762551308, 0.0012078082654625177, -0.005523862317204475, -0.018642278388142586, 0.023623406887054443, -0.03643102943897247, -0.0007667191093787551, -0.009636208415031433, -0.03631097078323364, 0.0076896315440535545, 0.013159475289285183, -0.017520004883408546, 0.026607617735862732, -0.02597632445394993, -0.0004182329575996846, 0.02625100687146187, 0.00660330057144165, -0.0034229259472340345, -0.07357297092676163, -0.019853277131915092, 0.020664896816015244, 0.032150998711586, 0.06650920957326889, 0.022786621004343033, -0.07253360748291016, -0.03745080903172493, -0.0001954042527358979, -0.01934131607413292, -0.02398749068379402, 0.012909460812807083, -0.023098066449165344, -0.017747655510902405, -0.05780854821205139, 0.015155158005654812, -0.025655511766672134, 0.008703717030584812, -0.08032619208097458, -0.021732859313488007, -0.0009933856781572104, 0.026288378983736038, 0.02924754098057747, 0.014277382753789425, -0.033227600157260895, 0.0024553267285227776, 0.004537040367722511, 0.04052429273724556, -0.008540773764252663, -0.041367318481206894, 0.022662431001663208, -0.07203122228384018, 0.05426989123225212, 0.0023684026673436165, -0.06066783890128136, -0.03156542032957077, -0.1007847860455513, -0.0013492952566593885, 0.017705779522657394, -0.059448905289173126, 0.01408581342548132, 0.011536301113665104, 0.00962371937930584, 0.03248584270477295, -0.017428936436772346, 0.01796272024512291, 0.012392993085086346, -0.04458101466298103, -0.0059256660751998425, -0.05735057592391968, 0.02679470367729664, -0.02580433338880539, 0.011503998190164566, 0.018761783838272095, 0.07496622204780579, -0.07782572507858276, -0.09141600131988525, 0.04522167518734932, 0.018249517306685448, -0.033098768442869186, -0.0440744124352932, 0.0053725228644907475, 0.03537285700440407, 0.001229126239195466, 0.00099069660063833, 0.1186300590634346, -0.010234913788735867, -0.015913160517811775, -0.059692803770303726, -0.005696467123925686, 0.014530058950185776, -0.012836850248277187, 0.016881616786122322, -0.018826618790626526, -0.06545533984899521, -0.004393543116748333, 0.01875886879861355, -0.025963865220546722, -0.0037148313131183386, 0.050055328756570816, -0.03915268927812576, 0.0041373311541974545, 0.0076453047804534435, 0.01117778941988945, -0.007168265525251627, -0.02088429406285286, 0.039571844041347504, 0.030635826289653778, 0.029674125835299492, -0.033477842807769775, -0.1274336278438568, -0.013282554224133492, 0.014356084167957306, 0.06427296251058578, -0.02764831855893135, -0.029881324619054794, 0.006383832544088364, 0.026260433718562126, -0.03776164725422859, 0.03825170546770096, -0.02134394645690918, -0.048900991678237915, 0.00017095102521125227, -0.0014381940709427, 0.0019105412065982819, 0.033092718571424484, -0.02167079783976078, -0.025685274973511696, 0.026586495339870453, 0.05399183928966522, -0.02654479444026947, 0.00829258281737566, 0.005624230019748211, -0.05588514357805252, -0.013373937457799911, -0.009283551014959812, -0.0028892692644149065, 0.035462114959955215, 0.022900400683283806, -0.07014846056699753, -0.0018379311077296734, -0.013551433570683002, -0.023614659905433655, 0.09646940231323242, 0.010067368857562542, 0.08272136002779007, 0.0017655676929280162, -0.036029327660799026, -0.019519168883562088, 0.06143606826663017, -0.021573342382907867, -0.038281019777059555, -0.04273134097456932, 0.009576793760061264, -0.0006337943486869335, -0.003961917944252491, -0.011780085042119026, 0.10514099895954132, -0.07549508661031723, 0.015239947475492954, 0.007900932803750038, -0.01913868635892868, 0.008720113895833492, 0.048707734793424606, 0.04005781188607216, 0.014850812032818794, -0.03747398406267166, 0.053629133850336075, 0.05313486605882645, -0.008366703055799007, -0.005478503182530403, 0.012247773818671703, 0.0008357368060387671, -0.012601030059158802, -0.00810343399643898, -0.028720857575535774, -0.046422116458415985, 0.029967430979013443, -0.0006773531204089522, 0.02088499255478382, 0.07008828967809677, 0.02291235700249672, -0.02056095004081726, 0.01164355780929327, -0.07234568148851395, 0.010061501525342464, -0.06221684440970421, -0.010966360569000244, 0.02762548066675663, -0.02660837396979332, -0.010144544765353203, 0.0620075985789299, -0.02874893881380558, 0.03663952648639679, 0.001670972676947713, -0.007536287419497967, -0.0504334531724453, -0.022208187729120255, 0.025705920532345772, 0.02173484116792679, 0.0251646526157856, 0.017831800505518913, -0.04742463678121567, 0.021228758618235588, -0.0548521988093853, 0.05991804599761963, 0.01753486692905426, 0.028381090611219406, -0.008369228802621365, 0.030516577884554863, -0.0010715952375903726, 0.006730284076184034, -0.00576621713116765, -0.049050044268369675, 0.05833195149898529, -0.016908816993236542, -0.005008835345506668, 0.03261517360806465, -5.8014334326605593e-33, 0.021786736324429512, -0.08572583645582199, -0.020660648122429848, 0.06738724559545517, -0.059970736503601074, 0.021220140159130096, -0.033888280391693115, -0.02946867048740387, 0.03514230251312256, 0.03797561675310135, -0.009994100779294968, 0.06737557798624039, 0.020477816462516785, 0.019236600026488304, 0.025627370923757553, 0.014210265129804611, 0.006890644785016775, -0.001228898181580007, 0.018298618495464325, 0.058586739003658295, 0.04945429414510727, 0.05706338211894035, 0.0003818551485892385, -0.03601786866784096, -0.05616636946797371, -0.01695222780108452, 0.01949259266257286, -0.016373515129089355, -0.0495963953435421, 0.0071789477951824665, 0.010971485637128353, 0.048851702362298965, -0.015208813361823559, -0.0401766374707222, -0.04995773732662201, -0.0015711613232269883, -0.057020217180252075, 0.02893451228737831, -0.016469905152916908, 0.015216795727610588, -0.053952112793922424, 0.03810737282037735, 0.04248033091425896, -0.0018314719200134277, -0.024463709443807602, -0.008005056530237198, 0.03853943571448326, 0.02150469273328781, -0.03602392598986626, 0.015132148750126362, 0.04414279758930206, 0.028646014630794525, -0.008233973756432533, 0.056581173092126846, 0.030786974355578423, -0.03600996360182762, -0.008788958191871643, 0.016957798972725868, -0.03215362876653671, 0.05547453835606575, -0.06342387944459915, -0.030002368614077568, -0.039283957332372665, 0.03986264020204544, 0.04244207963347435, 0.010717060416936874, 0.04787622019648552, -0.049824416637420654, 0.027880627661943436, 0.05650157481431961, -0.02943459339439869, 0.0828557163476944, 0.00969590526074171, -0.017917001619935036, -0.023317789658904076, -0.07191576808691025, -0.07497622817754745, 0.016096487641334534, 0.04186556115746498, -0.04293571785092354, -0.03226612135767937, -0.015962684527039528, 0.004935746546834707, -0.031348057091236115, 0.0642700269818306, -0.05938676744699478, -0.018748896196484566, 0.01565440185368061, -0.02605592831969261, -0.005033458117395639, 0.001053043408319354, 0.08493270725011826, 0.002313873963430524, -0.06836657226085663, -0.014107397757470608, 0.05525423586368561, 0.009671514853835106, 0.01454237475991249, 0.021506711840629578, -0.01843617856502533, -0.05135649815201759, 0.014297609217464924, -0.08631590753793716, 0.010561238043010235, 0.03819948807358742, -0.010473769158124924, 0.044366080313920975, 0.004601765889674425, -0.009991098195314407, 0.023094138130545616, -0.015095401555299759, 0.008602187968790531, -0.0297828521579504, -0.004694054368883371, 0.0374661386013031, -0.004162121098488569, 0.028534527868032455, 0.06710553914308548, 0.06927354633808136, 0.060758478939533234, -0.02590450458228588, 0.006079694721847773, -0.004794437438249588, -0.007513484917581081, -0.02290646918118, -0.004530389793217182, -0.05153443664312363, 0.01570647582411766, 0.010218448005616665, -0.04716742783784866, 0.0056062061339616776, -0.017786400392651558, 2.9833705639248365e-07, 0.0010147193679586053, 0.048612430691719055, -0.012758013792335987, -0.033004675060510635, 0.0471624918282032, 0.01371160987764597, -0.01359472330659628, 0.04824769124388695, 0.019024645909667015, 0.026285113766789436, 0.012826293706893921, -0.003217234741896391, 0.021622251719236374, 0.024015426635742188, -0.016803478822112083, -0.016341470181941986, -0.08001042902469635, 0.033054646104574203, -0.03547894209623337, 0.039938099682331085, 0.00950049702078104, 0.04081461578607559, 0.0799378901720047, -0.03208713233470917, 0.06164753809571266, -0.031333278864622116, -0.040392763912677765, 0.01829584501683712, 0.006961675360798836, -0.014141969382762909, -0.02471325732767582, 0.04735894501209259, -0.017678186297416687, -0.0008968216134235263, -0.024111345410346985, 0.0032470461446791887, -0.021710889413952827, 0.025102928280830383, -0.011589723639190197, 0.04233546927571297, 0.014205881394445896, -0.04929327592253685, -0.010303180664777756, -0.014806320890784264, 0.027830451726913452, 0.015511561185121536, -0.08109224587678909, -0.028339030221104622, 0.012855316512286663, -0.05251585692167282, 0.07109685987234116, 0.02483491413295269, -0.022089701145887375, -0.003096113447099924, 0.0016854136483743787, -0.05320410430431366, -0.024561230093240738, -0.028091881424188614, -0.0071018291637301445, 0.004623947199434042, -0.01690318062901497, -0.03187736123800278, -0.0016579627990722656, 0.0877966582775116, 0.04584867134690285, 0.04771782457828522, 0.003247934626415372, 2.826661444665689e-34, 0.032128091901540756, 0.03769185394048691, -0.017273617908358574, -0.0036250620614737272, -0.033720098435878754, -0.0425398163497448, -0.01905001513659954, -0.033328160643577576, -0.015725672245025635, -0.03957148268818855, -0.027751963585615158]

['Abdul Ghani Abro', 'Junita Mohamad Saleh']

1204.6250v1

Essentially, motive behind using control system is to generate suitable control signal for yielding desired response of a physical process. Control of synchronous generator has always remained very critical in power system operation and control. For certain well known reasons power generators are normally operated well below their steady state stability limit. This raises demand for efficient and fast controllers. Artificial intelligence has been reported to give revolutionary outcomes in the field of control engineering. Artificial Neural Network (ANN), a branch of artificial intelligence has been used for nonlinear and adaptive control, utilizing its inherent observability. The overall performance of neurocontroller is dependent upon input features too. Selecting optimum features to train a neurocontroller optimally is very critical. Both quality and size of data are of equal importance for better performance. In this work filter technique is employed to select independent factors for ANN training.

Feature Selection for Generator Excitation Neurocontroller Development Using Filter Technique

http://arxiv.org/pdf/1204.6250v1

Title Feature Selection Generator Excitation Neurocontroller Development Using Filter Technique Summary Essentially motive behind using control system generate suitable control signal yielding desired response physical process Control synchronous generator always remained critical power system operation control certain well known reason power generator normally operated well steady state stability limit raise demand efficient fast controller Artificial intelligence reported give revolutionary outcome field control engineering Artificial Neural Network ANN branch artificial intelligence used nonlinear adaptive control utilizing inherent observability overall performance neurocontroller dependent upon input feature Selecting optimum feature train neurocontroller optimally critical quality size data equal importance better performance work filter technique employed select independent factor ANN training Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04758718982338905, -2.2001544493832625e-05, -0.020478885620832443, 0.01696934923529625, 0.03694278374314308, -0.011308496817946434, -0.0033295308239758015, 0.011999501846730709, 0.0006924428744241595, -0.01967509835958481, 0.02159905806183815, 0.05901823565363884, -0.0130363954231143, 0.06964506208896637, 0.08957948535680771, -0.007261874154210091, 0.045164257287979126, 0.06347570568323135, 0.02233579196035862, 0.014186786487698555, -0.023005899041891098, -0.02423611469566822, 0.022607168182730675, 0.06319307535886765, -0.0491238534450531, 0.03604276478290558, -7.191878830781206e-05, -0.015711667016148567, -0.018030894920229912, -0.04326756298542023, -0.017521465197205544, -0.022944455966353416, -0.008081256411969662, 0.020028185099363327, 2.192816282331478e-06, -0.01073160395026207, 0.015211578458547592, -0.002816778374835849, 0.057765088975429535, -0.05104415863752365, 0.007645314559340477, 0.07099253684282303, 0.0172782801091671, 0.02383182756602764, -0.02917131595313549, 0.021280763670802116, 0.02761339396238327, 0.09133478254079819, -0.019604653120040894, 0.05508965998888016, -0.0134042426943779, -0.02845638059079647, -0.011063159443438053, 0.022697387263178825, -0.03695148229598999, 0.03358904644846916, -0.02550858072936535, -0.07720891386270523, 0.003378769150003791, -0.05371217057108879, -0.04715663939714432, 0.031154341995716095, -0.009970666840672493, -0.0652153268456459, 0.034589409828186035, 0.02091618813574314, -0.005381460767239332, -0.008332831785082817, -0.0055995602160692215, -0.009815536439418793, -0.05407979339361191, -0.005263397004455328, 0.042717523872852325, 0.002852214267477393, -0.02071659453213215, -0.0100967176258564, -0.009105531498789787, -0.0035879577044397593, -0.045366134494543076, 0.05651706084609032, -0.004263943526893854, -0.007818242534995079, 0.008442477323114872, -0.006443679332733154, 0.0374436229467392, 0.06228146329522133, -0.04344309866428375, 0.028085140511393547, 0.014517491683363914, -0.0038310878444463015, 0.013652271591126919, 0.008281105197966099, 0.04707926884293556, 0.032030221074819565, -0.0369553342461586, -0.03519243746995926, -0.011637445539236069, -0.05604463443160057, -0.013507122173905373, -0.031242208555340767, -0.00523737445473671, -0.01687649078667164, 0.0551595464348793, -0.024022068828344345, 0.012390957213938236, 0.07769010215997696, -0.03680555149912834, 0.05115385353565216, -0.009302627295255661, 0.02911943569779396, -0.05345984175801277, 0.02221180684864521, -0.00907679833471775, 0.07581160962581635, 0.008450464345514774, -0.004368738736957312, -0.0695275291800499, -0.020856456831097603, 0.004303409717977047, -0.03333422914147377, 0.0189194492995739, 0.026472017168998718, 0.050945818424224854, 0.07124611735343933, -0.013890397734940052, 0.01767292432487011, -0.013315868563950062, 0.00964448694139719, -0.012328957207500935, -0.04399539530277252, 0.007063355762511492, -0.01777546852827072, -0.027347618713974953, 0.03702840209007263, -0.018377797678112984, 0.0434180311858654, 0.02716991864144802, -0.02438810095191002, -0.09886091202497482, 0.022924378514289856, 0.07451080530881882, -0.007352474611252546, -0.01032781321555376, -0.0045887865126132965, -0.006360268220305443, -0.0026458436623215675, -0.019343873485922813, -0.008436879143118858, -0.005032503977417946, 0.002822592156007886, 0.0029686633497476578, 9.733421393320896e-07, -0.009880466386675835, 0.006622239015996456, 0.06402523070573807, -0.03238660469651222, -0.024403145536780357, 0.004256450571119785, 0.06777612119913101, -0.013448100537061691, 0.0013742981245741248, 0.00971447303891182, -0.006644159555435181, -0.03591349348425865, -0.012819286435842514, -0.0278698168694973, -0.028741147369146347, -0.09887830168008804, -0.032396405935287476, -0.014687973074615002, -0.019296282902359962, -0.0060702236369252205, -0.020805751904845238, 0.017581632360816002, 0.027693867683410645, -0.014582844451069832, 0.07341259717941284, 0.06611967086791992, 0.01248014997690916, -0.01869889162480831, -0.004537889733910561, -0.001075955224223435, 0.033274441957473755, 0.04271887615323067, -0.10274019837379456, -0.04970303177833557, 0.010840097442269325, 0.05067390203475952, -0.009184671565890312, -0.06068257614970207, 0.027761975303292274, -0.029173457995057106, 0.009162632748484612, 0.022594626992940903, 0.020810000598430634, 0.09403476864099503, -0.04359551519155502, -0.01013905182480812, 0.023581264540553093, 0.014327581971883774, -0.018589036539196968, -0.016779825091362, 0.035547077655792236, -0.00549386627972126, 0.06940427422523499, -0.01745469681918621, -0.008951626718044281, -0.02111966721713543, -0.05006132647395134, -0.02114756777882576, -0.02385103516280651, -0.01608583889901638, 0.027844201773405075, -0.005719813983887434, -0.014478463679552078, 0.012390726245939732, -0.001947436248883605, 0.029895253479480743, -0.02851293608546257, 0.008761857636272907, -0.0075818314217031, 0.09176593273878098, -0.04650525748729706, 0.009940041229128838, -0.00600490951910615, -0.012855369597673416, 0.0013333880342543125, -0.0072616152465343475, 0.007552215829491615, 0.01525584515184164, 0.016303012147545815, -0.0033484245650470257, 0.01042152475565672, -0.07249508053064346, -0.016796812415122986, -0.0405794195830822, -0.025775980204343796, -0.012154730036854744, -0.00243530236184597, 0.03004511632025242, 0.05073663592338562, -0.022969067096710205, 0.011719861999154091, -0.07267441600561142, 0.012309341691434383, -0.052302028983831406, -0.00830915104597807, -0.03486603870987892, 0.005729021970182657, -0.0054894303902983665, 0.009558544494211674, 0.007738655898720026, 0.0239755567163229, 0.05192429944872856, 0.0045408764854073524, 0.020992036908864975, 0.03905653581023216, 0.041895411908626556, -0.024883517995476723, -0.009884662926197052, 0.10306441783905029, -0.062310174107551575, -0.04366700351238251, 0.012495358474552631, 0.0005638069123961031, 0.04015297070145607, 0.02769509144127369, -0.0033862146083265543, -0.005325592588633299, 0.006984698120504618, -0.03678632155060768, -0.019755234941840172, -0.0013165520504117012, 0.0634576603770256, -0.010283749550580978, -0.04114479199051857, 0.09724681824445724, -0.04913141950964928, -0.07469283789396286, 0.0018789416644722223, 0.017617208883166313, 0.012499122880399227, 0.00555390166118741, 0.019130704924464226, -0.01666729710996151, 0.06169448420405388, 0.062097758054733276, 0.031299930065870285, -0.036659471690654755, 0.03486338630318642, -0.03685138002038002, 0.04846910759806633, -0.003499913029372692, -0.032315611839294434, -0.02049289271235466, -0.002294248901307583, -0.02928197756409645, 0.04405713453888893, 0.07513319700956345, -0.04400767758488655, 0.03808823600411415, 0.052614085376262665, -0.04774808883666992, 0.029549431055784225, -0.04069944843649864, 0.058285124599933624, -0.01634625904262066, 0.07348781079053879, -0.008951259776949883, 0.014087207615375519, 0.0669504925608635, -0.001101758098229766, -0.008957818150520325, 0.014186903834342957, -0.027170348912477493, -0.03197755292057991, -0.011796655133366585, -0.00292943324893713, -0.026846112683415413, -0.00221836706623435, 9.351889457320794e-05, 0.0037964868824929, 0.01976512372493744, 0.021108126267790794, 0.026843762025237083, -0.018969431519508362, -0.03943120315670967, -0.01656182110309601, -0.005471458192914724, 0.019721949473023415, 0.00809900276362896, -0.00013590307207778096, 0.02209422178566456, 0.017387447878718376, -0.001723715104162693, -0.018199246376752853, -0.014655791223049164, -0.027557341381907463, 0.021071946248412132, -0.03959566354751587, -0.008271878585219383, 0.016993770375847816, -0.02790065109729767, -0.021799467504024506, 0.03981928899884224, 0.006157564930617809, 0.04995279014110565, -0.007989929057657719, 0.0475568026304245, -0.038749970495700836, 0.04657786339521408, 0.07622983306646347, -0.09097938239574432, 0.008941926062107086, -0.007766210939735174, -0.001718479092232883, 0.006552431732416153, 0.004747496917843819, 0.003522321814671159, 0.06463287770748138, 0.009762612171471119, 0.0058515346609056, -0.030298449099063873, -0.009080125950276852, -0.10698904097080231, 0.020615145564079285, -0.052543435245752335, -0.0005070979241281748, -0.004553370177745819, 0.012361716479063034, -0.0290458295494318, -0.056221771985292435, 0.04840545728802681, 0.005844801664352417, 0.001928271958604455, -0.027993973344564438, -0.013770584017038345, -0.01581784151494503, -0.0305973868817091, 0.005252706818282604, 0.043302200734615326, 0.06627214699983597, 0.03483159467577934, 0.005575757473707199, 0.02870780974626541, -0.09378786385059357, 0.0001102327078115195, -0.017243659123778343, -0.02332204394042492, -0.01068241149187088, -0.01851210556924343, -0.011950410902500153, -0.04351447522640228, -0.0032825584057718515, -0.01544179953634739, -0.029423965141177177, -0.059008147567510605, 0.04813804477453232, -0.0039032557979226112, -0.0049896240234375, 0.030378984287381172, 0.0368444062769413, -0.014140796847641468, -0.04079654440283775, -0.050755325704813004, -0.011137702502310276, 0.08055181056261063, 0.04009366035461426, 0.004543202463537455, -0.0025974158197641373, -0.028575152158737183, 0.014548507519066334, -0.0027510703075677156, -0.07730916142463684, 0.02814745530486107, 0.08570230007171631, -0.024069422855973244, 0.018278801813721657, 0.04816871136426926, 0.04446902126073837, 0.03325057774782181, -0.03754093125462532, -0.0030390857718884945, -0.05937032029032707, -0.029425328597426414, -0.02546568401157856, -0.005650636740028858, 0.07046357542276382, -0.064357690513134, 0.010325508192181587, -0.004942715633660555, -0.06801634281873703, 0.038632504642009735, -0.008543516509234905, -0.051720116287469864, -0.029508695006370544, -0.0010163192637264729, 0.04589046165347099, -0.06974580883979797, -0.0734763890504837, 0.016659565269947052, -0.020089508965611458, 0.021209556609392166, 0.07775387912988663, 0.058696284890174866, 0.09611734002828598, -0.000332994939526543, 0.013121658936142921, -0.0333302840590477, 0.06638600677251816, -0.018374521285295486, -0.031255222856998444, 0.0013031731359660625, 0.04192553460597992, -0.019211420789361, 0.026064572855830193, -0.025429660454392433, 0.04497019946575165, 0.004918983671814203, 0.03201023116707802, 0.014124312438070774, -0.0005166315822862089, -0.04652516543865204, -0.035472843796014786, -0.008804218843579292, 0.016708364710211754, 0.016610560938715935, -0.01582914963364601, -0.018485097214579582, 0.011197777464985847, 0.014663396403193474, 0.013412361033260822, 0.030817240476608276, -0.017815032973885536, 0.022822313010692596, -0.0028912508860230446, -0.02064668945968151, 0.01647465117275715, -0.014665546827018261, 0.0008866637945175171, 0.020635215565562248, 0.015705443918704987, 0.0009241633815690875, 0.02430492267012596, -0.0785655677318573, -0.01672322489321232, -0.0050809201784431934, 0.042270563542842865, -0.04958505183458328, 0.018878282979130745, -0.022332211956381798, -0.013223402202129364, 0.01924108900129795, -0.05994781106710434, 0.05123995989561081, -0.04049248993396759, 0.006696444936096668, 0.031498849391937256, -0.07634143531322479, 0.036262981593608856, -0.035132911056280136, 0.007529193069785833, 0.01844475045800209, 0.019742131233215332, 0.05337908864021301, -0.017292484641075134, -0.07686635106801987, 0.06154336407780647, 0.005271140951663256, -0.025271782651543617, -0.05475524440407753, 0.016361325979232788, 0.022915547713637352, 0.02068484015762806, -0.0024408772587776184, 0.020111626014113426, 0.02634435147047043, 0.008337238803505898, 0.01460245531052351, -0.006009979639202356, 0.012541605159640312, -0.02641143836081028, 0.02332918904721737, -0.005393995903432369, 0.03865017369389534, -0.009242115542292595, 0.02747446671128273, -0.016424663364887238, -0.04111082851886749, 0.013732463121414185, 0.022237710654735565, -0.03975111246109009, 0.020551828667521477, 0.01833382621407509, -0.012326783500611782, 0.03282332792878151, 0.00630534952506423, -0.05681965500116348, -0.02059148997068405, 0.03474140912294388, -0.014125620014965534, 0.02940390631556511, 0.045246172696352005, -0.027489671483635902, 0.027545182034373283, -0.02555215358734131, 0.08989464491605759, -0.06315948069095612, -0.026631105691194534, -0.011428140103816986, 0.0023426529951393604, -0.02075735107064247, 0.027048984542489052, 0.019634447991847992, -0.08004435151815414, -5.5716378787282335e-33, -0.011270420625805855, -0.04857322573661804, -0.008114066906273365, -0.007817227393388748, -0.06098898872733116, -0.035516221076250076, 0.0013630017638206482, -0.008027000352740288, 0.010061856359243393, -0.041562940925359726, -0.03308545798063278, -0.009569330140948296, -0.037591755390167236, 0.025328336283564568, 0.015599529258906841, -0.022526312619447708, 0.02381032332777977, -0.0030711842700839043, 0.04015713930130005, 0.029621269553899765, 0.07293189316987991, 0.02979704923927784, 0.0414598323404789, -0.0597795769572258, -0.04784991592168808, 0.03410281613469124, 0.00893574021756649, -0.03676323965191841, -0.035975515842437744, -0.02522875741124153, 0.013060878030955791, -0.00126409821677953, 0.009100218303501606, -0.07078301906585693, -0.03859356790781021, -0.022977976128458977, 0.0018785258289426565, -0.05131678655743599, -0.06848762184381485, 0.00420031463727355, -0.05144013091921806, -0.038634393364191055, 0.1017051488161087, -0.04184634983539581, -0.061775755137205124, 0.04175505042076111, 0.033344537019729614, -0.013847735710442066, 0.005537810269743204, -0.026640165597200394, -0.008934893645346165, -0.0035573013592511415, 0.0018159366445615888, 0.0258900448679924, 0.009313782677054405, 0.045659370720386505, -0.0641951709985733, -0.020491143688559532, -0.005418742075562477, 0.04655136168003082, 0.03444137051701546, 0.03016498126089573, -0.057928502559661865, 0.021799221634864807, 0.06946747750043869, 0.0049858372658491135, 0.00956051331013441, -0.023447684943675995, -0.07200565189123154, 0.005024213343858719, -0.012926498427987099, 0.05646987631917, 0.05176784098148346, -0.009413952007889748, 0.02906922996044159, -0.12720128893852234, -0.01553416159003973, 0.05370289459824562, -0.047116801142692566, 0.07199306786060333, 0.02009185217320919, -0.028153952211141586, 0.014030826278030872, 0.016933482140302658, 0.05840030312538147, -0.018084188923239708, -0.010501465760171413, -0.03314461186528206, 0.03294294327497482, -0.03234945237636566, -0.008892257697880268, -0.0372735895216465, -0.044501859694719315, -0.014770292676985264, 0.07868918776512146, 0.06351273506879807, 0.008166195824742317, -0.02493339404463768, 0.05667869374155998, -0.06919868290424347, 0.01786106452345848, -0.017490210011601448, -0.0021539218723773956, -0.03863389790058136, -0.010787312872707844, -0.010663356631994247, -0.05430516600608826, 0.054949045181274414, 0.03968977555632591, 0.02434409037232399, 0.03743710741400719, -0.03764921426773071, 0.0010839725146070123, 0.006444208789616823, -0.02848740667104721, -0.01384555734694004, 0.02070874534547329, 0.018445011228322983, -0.022483093664050102, -0.0012706510024145246, -0.023919707164168358, -0.026979146525263786, 0.033624473959207535, 0.05370883643627167, -0.03535795211791992, -0.006318305153399706, -0.049162499606609344, 0.05450518801808357, -0.05034846439957619, -0.013421401381492615, 0.009078246541321278, 0.01665547862648964, 2.8549345643114066e-07, -0.05633572116494179, 0.009384378790855408, -0.03727440908551216, -0.02468528039753437, 0.017190413549542427, -0.018612682819366455, 0.01546780951321125, 0.021456945687532425, -0.010787340812385082, 0.009479367174208164, -0.00874388124793768, -0.049544572830200195, 0.003389078425243497, 0.016797073185443878, -0.07335394620895386, -0.0338323637843132, 0.024959009140729904, 0.08209972828626633, 0.0031438274309039116, -0.035418301820755005, 0.06815000623464584, 0.009643031284213066, 0.0745886042714119, 0.0003665607364382595, 0.06430238485336304, -0.03243405744433403, 0.007820896804332733, 0.02768765017390251, 0.011025107465684414, -0.021667707711458206, 0.03470843285322189, 0.07433224469423294, 0.017088275402784348, -0.02366112358868122, -0.022341594099998474, 0.0481148324906826, -0.03375418856739998, 0.016040246933698654, 0.003314576344564557, -0.08439874649047852, 0.042189810425043106, 0.03027474693953991, 0.029428893700242043, -0.007373533211648464, -0.007836403325200081, -0.01306474395096302, -0.0322769358754158, 0.018139636144042015, 0.020988542586565018, 0.01326470635831356, -0.013313298113644123, -0.005064437165856361, 0.024811726063489914, -0.050211504101753235, -0.01775858737528324, -0.050773121416568756, -0.014027834869921207, 0.06225629895925522, 0.022158710286021233, -0.02591816708445549, -0.0347735695540905, -0.013081839308142662, -0.03437948226928711, 0.001122063142247498, -0.005088370759040117, 0.05019019916653633, -0.018740681931376457, 2.7848847886971977e-34, -0.024302035570144653, -0.08324350416660309, -0.01129678450524807, 0.021759092807769775, -0.033544037491083145, 0.017819400876760483, -0.0038550503086298704, 0.01588505320250988, -0.007552311290055513, 0.014483924023807049, -0.0233419481664896]

['Konstantinos Chorianopoulos', 'Vassiliki Tsaknaki']

1204.6325v2

We explore the design of a seamless broadcast communication system that brings together the distributed community of remote secondary education schools. In contrast to higher education, primary and secondary education establishments should remain distributed, in order to maintain a balance of urban and rural life in the developing and the developed world. We plan to deploy an ambient and social interactive TV platform (physical installation, authoring tools, interactive content) that supports social communication in a positive way. In particular, we present the physical design and the conceptual model of the system.

CELL: Connecting Everyday Life in an archipeLago

http://arxiv.org/pdf/1204.6325v2

Title CELL Connecting Everyday Life archipeLago Summary explore design seamless broadcast communication system brings together distributed community remote secondary education school contrast higher education primary secondary education establishment remain distributed order maintain balance urban rural life developing developed world plan deploy ambient social interactive TV platform physical installation authoring tool interactive content support social communication positive way particular present physical design conceptual model system Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.04373627156019211, -0.0600912906229496, -0.019045038148760796, -0.024999482557177544, 0.0020238952711224556, -0.01411519292742014, 0.04800533130764961, -0.002904413966462016, 0.005391845013946295, 0.003289593616500497, 0.017858287319540977, 0.03048509918153286, 0.023037288337945938, 0.08501437306404114, -0.0036795393098145723, -0.03989239037036896, -0.04786517471075058, 0.04246770218014717, -0.04256856441497803, 0.03772180899977684, 0.027900144457817078, 0.026250839233398438, 0.018050601705908775, -0.04534653201699257, -0.006746916566044092, -0.015294729731976986, -0.03678775578737259, -0.005878607742488384, 0.031604260206222534, -0.026043636724352837, 0.05540869012475014, 0.025293435901403427, -0.022011861205101013, 0.04320431500673294, 2.2578401512873825e-06, -0.02400812692940235, 0.024738894775509834, -0.0031634310726076365, -0.03881295770406723, 0.04487388953566551, 0.06198965385556221, 0.01976883038878441, -0.00020519460667856038, -0.01905410923063755, -0.0012139359023422003, 0.005987891927361488, 0.04068172723054886, -0.0288253091275692, 0.0033695518504828215, -0.008510085754096508, -0.03588802367448807, -0.03922445327043533, -0.03737613931298256, 0.016919851303100586, -0.013955194503068924, 0.049975670874118805, -0.0033241123892366886, 0.05136123672127724, 0.10372366011142731, 0.0073511735536158085, 0.021219562739133835, 0.0414787195622921, 0.0061281220987439156, -0.009257935918867588, 0.03877106308937073, 0.015540619380772114, -0.008981375023722649, -0.06848887354135513, -0.04023965075612068, -0.00023226792109198868, 0.05277230218052864, -0.012363660149276257, 0.026260513812303543, 0.03532397747039795, -0.01592198759317398, 0.01862798072397709, -0.047450240701436996, -0.03576473519206047, -0.028561381623148918, 0.021318497136235237, -0.06221561133861542, 0.014776043593883514, -0.033564746379852295, 0.02345556579530239, 0.049875784665346146, 0.033019326627254486, 0.0009846034226939082, 0.025819364935159683, -0.08514150977134705, 0.043913569301366806, 0.055850330740213394, -0.0515749491751194, 0.06867452710866928, 0.02914268523454666, 0.04116201400756836, -0.011629072017967701, 0.03313812240958214, -0.05236847698688507, 0.010556180030107498, -0.049911949783563614, -0.007896224036812782, 0.022324595600366592, 0.05371528118848801, 0.013527337461709976, 0.05207827314734459, -0.05553313344717026, -0.023814382031559944, 0.00549675477668643, -0.008942455053329468, 0.06277851015329361, -0.03758592531085014, -0.022086193785071373, -0.011521426029503345, 0.08447505533695221, -0.07631171494722366, -0.021228699013590813, -0.00016784219769760966, 0.061558376997709274, 0.041859958320856094, 0.012067890726029873, 0.016566801816225052, 0.05835613235831261, 0.03373634070158005, -0.03701292350888252, 0.04051290452480316, 0.04786613583564758, -0.04752783849835396, -0.001730716903693974, 0.010111205279827118, -0.04353838041424751, 0.04062551259994507, -0.007296586409211159, 0.013764997012913227, 0.03326164186000824, -0.042506393045186996, -0.013090473599731922, -0.022486262023448944, -0.004575991537421942, 0.025977976620197296, -0.04224946349859238, 0.0063239107839763165, 0.013535606674849987, -0.043957389891147614, -0.05597255751490593, -0.034874461591243744, 0.02165302447974682, -0.017458051443099976, 0.061128612607717514, -0.02878984622657299, -0.04390373453497887, 0.0330912247300148, -0.005621690768748522, -0.014842011034488678, 0.05069555714726448, 0.13477589190006256, 0.07327093929052353, 0.05611057206988335, -0.019383316859602928, 0.020329516381025314, -0.023605864495038986, 0.05332162603735924, 0.017563048750162125, -0.007948538288474083, 0.007794051431119442, -0.028233272954821587, 0.04108599200844765, 0.010610269382596016, -0.010412750765681267, -0.025486694648861885, -0.017956696450710297, -0.07648013532161713, 0.0036422922275960445, -0.026687070727348328, 0.06216976046562195, 0.038286179304122925, 0.002261414425447583, 0.014365817420184612, -0.035708535462617874, -0.07007523626089096, 0.09051740169525146, -0.017498459666967392, -0.045740075409412384, 0.05471653491258621, 0.05679640918970108, -0.0034616300836205482, -0.025845227763056755, -0.02337745763361454, 0.04005786404013634, -0.03515437990427017, -0.008848650380969048, 7.6065143730374984e-06, -0.0017744245706126094, -0.007104580290615559, 0.012209109030663967, 0.003755007404834032, -0.04138810932636261, 0.03348169103264809, 6.185247184475884e-05, 0.020961685106158257, -0.03178790584206581, 0.06036737561225891, -0.0493917316198349, 0.09867004305124283, 0.06753012537956238, -0.01152750849723816, 0.006969325710088015, 0.05991071090102196, 0.00594990374520421, 0.06636835634708405, 0.015015585348010063, 0.04260196536779404, -0.03126230090856552, -0.0407724604010582, 0.0030910915229469538, 0.012075807899236679, 0.061748676002025604, 0.035403862595558167, 0.023269422352313995, -0.06074002757668495, 0.057050302624702454, -0.013075566850602627, 0.07369096577167511, -0.004469006322324276, -0.021172722801566124, 0.007731958758085966, 0.045560259371995926, -0.04591203108429909, 0.029130306094884872, -0.03028106316924095, 0.04516827315092087, 0.038245830684900284, -0.031915340572595596, 0.022593671455979347, -0.020177755504846573, 9.022700396599248e-05, 0.03592239320278168, 0.01896797865629196, 0.04908531531691551, -0.032304536551237106, -0.0431528240442276, 0.049731433391571045, 0.04051676392555237, 0.05136635899543762, 0.023755019530653954, 0.04998769238591194, 0.041843343526124954, 0.06576339155435562, 0.0533197820186615, 0.037754420191049576, -0.00627634022384882, -0.026144040748476982, 0.007098804693669081, -0.005182579159736633, 0.03578215464949608, -0.009120536036789417, -0.061930760741233826, 0.00889245793223381, 0.08193144202232361, -0.02760816365480423, 0.06371554732322693, -0.016649818047881126, -0.030381277203559875, -0.010584622621536255, -0.05175991356372833, 0.036603666841983795, -0.029970521107316017, -0.007803305052220821, -0.04420510679483414, -0.01239028014242649, -0.0380350686609745, 0.010207985527813435, 0.06674502044916153, 0.020879369229078293, -0.02538706734776497, -0.014208965003490448, 0.0022372244857251644, 0.058810584247112274, 0.015534316189587116, -0.037957049906253815, 0.0013838220620527864, 0.01947309635579586, -0.0002658052835613489, -0.0009465525508858263, 0.0066936626099050045, 0.0072016180492937565, 0.047025103121995926, 0.07054392993450165, -0.10589869320392609, -0.044816359877586365, -0.025045717135071754, -0.03519999235868454, -0.06725572794675827, 0.009900598786771297, -0.023110423237085342, 0.019084999337792397, 0.030104225501418114, 0.0038285357877612114, -0.04533056914806366, -0.005991386249661446, -0.026413114741444588, -0.025754539296030998, -0.05845349654555321, -0.01027587428689003, -0.00154634821228683, -0.01699310727417469, 0.03143100440502167, -0.00935631524771452, -0.0012556281872093678, -0.01319094654172659, -0.05278971791267395, 0.003639064496383071, 0.04928828403353691, 0.009658568538725376, 0.03623031824827194, -0.015031842514872551, 0.009908468462526798, -0.046256326138973236, -0.03584371879696846, 0.004048880189657211, 0.03884069621562958, 0.0071490611881017685, 0.015506893396377563, -0.024130888283252716, 0.042452286928892136, -0.001809960580430925, -0.030411098152399063, -0.0494244322180748, -0.00603099912405014, 0.028167694807052612, -0.07640007883310318, 0.03955885022878647, -0.026556849479675293, -0.04765855893492699, -0.0012505451450124383, -0.01872960850596428, 0.011788355186581612, -0.02914331667125225, -0.06508757919073105, -0.02730146422982216, -0.06328888237476349, -0.030728787183761597, -0.046128030866384506, 0.005933066830039024, 0.055341750383377075, -0.033805422484874725, -0.04386338219046593, -0.018723279237747192, 0.03079238161444664, 0.04799151420593262, 0.015808243304491043, 0.02628254145383835, -0.001562431687489152, -0.0017130840569734573, 0.006138508208096027, 0.0062353420071303844, 0.051373425871133804, -0.058013688772916794, 0.0033583485055714846, -0.0610983707010746, 0.052046988159418106, -0.025949127972126007, 0.01207229495048523, -0.00011519914551172405, -0.01130449678748846, 0.02275196462869644, 0.03067542053759098, 0.04778335243463516, 0.04344431683421135, -0.08055340498685837, -0.03829722851514816, 0.10176126658916473, 0.012108536437153816, 0.033825188875198364, 0.01827733963727951, -0.003395903157070279, -0.05928569287061691, -0.018235649913549423, -0.03164706379175186, -0.03418659791350365, -0.016995415091514587, 0.016264788806438446, -0.06348444521427155, 0.0479167215526104, -0.004736799281090498, -0.008245589211583138, -0.009788270108401775, -0.014130016788840294, -0.035183411091566086, 0.011052779853343964, 0.00048295879969373345, 0.02329600416123867, 0.012740288861095905, -0.0017703069606795907, 0.02487485110759735, -0.02418224699795246, 0.03712169826030731, -0.02875697985291481, 0.01714390143752098, 0.016088396310806274, 0.008470715954899788, 0.02889038249850273, -0.08850809186697006, -0.005684451200067997, -0.004264698829501867, -0.042348235845565796, 0.04678450897336006, 0.010583647526800632, 0.025867169722914696, -0.014546945691108704, -0.050935689359903336, -0.04026973992586136, 0.011047719977796078, -0.005220285151153803, -0.01160004734992981, -0.04577003791928291, 0.019874606281518936, -0.016760092228651047, -0.05273761972784996, -0.00023253900872077793, 0.014565643854439259, -0.017337754368782043, 0.022009264677762985, 0.04109566658735275, 0.011836803518235683, 0.00984677579253912, -0.0032415904570370913, 0.04325952008366585, 0.06970561295747757, -0.037496741861104965, -0.06339650601148605, -0.03416765481233597, 0.008816712535917759, 0.010316302999854088, -0.028170058503746986, 0.015450306236743927, -0.05377887561917305, -0.009138110093772411, 0.006431400775909424, -0.09667793661355972, -0.027547042816877365, 0.012421172112226486, -0.014925823546946049, 0.06018336862325668, 0.030398236587643623, -0.012900500558316708, 0.010146565735340118, 0.01355711743235588, 0.028758596628904343, -0.08545792102813721, 0.021703070029616356, -0.00511005986481905, -0.03239572048187256, 0.007272989023476839, -0.08466940373182297, -0.05213514715433121, 0.00268190517090261, -0.053629741072654724, -0.018738558515906334, -0.003087438875809312, 0.03148046135902405, 0.0010769652435556054, 0.03892447054386139, -0.0247020460665226, 0.004381854087114334, -0.004622561391443014, 0.0038594892248511314, 0.003466624766588211, -0.011550202034413815, 0.03839405998587608, -0.04670294374227524, 0.014879747293889523, 0.005264206789433956, -0.013873634859919548, 0.0018589528044685721, 0.0019151298329234123, 0.01022233534604311, -0.03274502977728844, -0.04478434473276138, 0.010199940763413906, 0.002378574339672923, -0.000595432473346591, -0.021512892097234726, 0.014668463729321957, -0.07691515237092972, 0.014054665341973305, 0.002874558325856924, -0.021018650382757187, 0.012580008246004581, -0.008077265694737434, -0.036315832287073135, -0.02153134159743786, 0.009777908213436604, 0.024370022118091583, 0.036749217659235, 0.004344598390161991, 0.017451440915465355, -0.004439986776560545, 0.028549913316965103, -0.03724023699760437, -0.04647515341639519, -0.015707675367593765, 0.043649494647979736, 0.01600378192961216, 0.02882673405110836, -0.024300627410411835, 0.014736686833202839, -0.03495188057422638, 0.02854066714644432, 0.02007097192108631, -0.04864536225795746, 0.0671267956495285, 0.02026611939072609, 0.07835058867931366, -0.023088131099939346, -0.01380552165210247, 0.08634088188409805, -0.039759766310453415, 0.07128508388996124, -0.011090190149843693, 0.0039781914092600346, 0.006895406171679497, -0.04461191967129707, -0.0038846598472446203, -0.05102292448282242, -0.07393257319927216, -0.010878519155085087, 0.03870857134461403, 0.0005868648295290768, 0.01312987320125103, -0.05154838785529137, -0.01018191035836935, -0.06906355172395706, 0.018623625859618187, -0.044417623430490494, -0.00643940782174468, 0.09104683995246887, 0.030940411612391472, 0.009560180827975273, -0.05435063689947128, 0.033046264201402664, -0.06444279104471207, 0.006274830549955368, 0.002611525123938918, 0.0005094431689940393, 0.01588560827076435, -0.016701918095350266, 0.036830537021160126, -0.005513806361705065, 0.011582981795072556, 0.013835613615810871, -0.0038741386961191893, 0.007367097306996584, -0.06508126854896545, 0.024164771661162376, 0.013858923688530922, -6.902543235646782e-33, -0.00043047292274422944, -0.022184746339917183, 0.014485666528344154, 0.005583321675658226, -0.04635187238454819, -0.010385510511696339, -0.012079793028533459, 0.01709938794374466, -0.025354662910103798, -0.021592890843749046, -0.014039585366845131, 0.03948034346103668, 0.012331783771514893, -0.0032703205943107605, 0.0068780044093728065, -0.02423146739602089, 0.010163058526813984, 0.02388748899102211, -0.029196463525295258, -0.058301590383052826, 0.031161746010184288, 0.02680683135986328, -0.02381882816553116, -0.042769599705934525, -0.037965077906847, -0.041754454374313354, -0.025736840441823006, -0.017425715923309326, 0.030391566455364227, -0.031050464138388634, -0.026644369587302208, 0.02130972221493721, -0.007236395962536335, 0.02954917773604393, 0.012758481316268444, 0.109890416264534, -0.05058623477816582, 0.00711858831346035, -0.04066434130072594, 0.044770367443561554, -0.03312075510621071, -0.009118187241256237, -0.008185112848877907, -0.017761873081326485, -0.0634441077709198, 0.02561614103615284, 0.01088772900402546, 0.012945170514285564, -0.016362681984901428, 0.0508597195148468, -0.0030113409738987684, -0.011777689680457115, 0.006008954718708992, 0.004714777693152428, -0.03948332369327545, -0.051067255437374115, -0.003939829301089048, -0.017812950536608696, -0.03935391828417778, 0.032781682908535004, -0.011333378031849861, 0.010061806067824364, -0.01405471470206976, -0.029701581224799156, 0.0065130190923810005, -0.009365457110106945, -0.033771611750125885, -0.06808236241340637, -0.04208690673112869, -0.010163337923586369, -0.006860238034278154, 0.00998781993985176, 0.05846139043569565, -0.0037443535402417183, -0.04966627061367035, -0.08216826617717743, -0.0418216735124588, -0.037746332585811615, 0.021853569895029068, -0.044212665408849716, -0.05322323739528656, 0.014233913272619247, 0.012745815329253674, -0.0003517793957144022, 0.07147485762834549, -0.02186572551727295, -0.016976501792669296, -0.04428083449602127, -0.005768321454524994, 0.023138025775551796, 0.011259699240326881, 0.029795318841934204, -0.009189629927277565, 0.007820053957402706, -6.000582743581617e-06, -0.0037362047005444765, 0.03643538057804108, 0.014397655613720417, 0.0186323095113039, 0.002523551695048809, -0.022353336215019226, 0.004554654471576214, -0.04076575115323067, 0.0679640993475914, -0.037405844777822495, 0.02747863344848156, -0.02391451969742775, 0.06563672423362732, 0.01274101436138153, 0.011601065285503864, 0.04325614497065544, -0.006148687098175287, 0.051180120557546616, -0.020976684987545013, -0.02906198427081108, -0.036232903599739075, 0.010736535303294659, 0.015907075256109238, -0.0052545517683029175, -0.03171909600496292, 0.017619451507925987, -0.03621809557080269, -0.04904349148273468, -0.04082489013671875, -0.0238486360758543, 0.02279018610715866, -0.08125029504299164, 0.06674885004758835, 0.049565695226192474, -0.0015341691905632615, 0.0027183762285858393, -0.03286710008978844, 2.987296454648458e-07, -0.022386394441127777, 0.029097171500325203, -0.015486545860767365, -0.04138676077127457, 0.023258786648511887, -0.04364113137125969, 0.00914086401462555, 0.057378966361284256, 0.015440337359905243, -0.019338788464665413, -0.02443566545844078, -0.029218437150120735, 0.052694253623485565, 0.011951332911849022, -0.09567411988973618, -0.027157122269272804, -0.03305995464324951, 0.008186258375644684, 0.009580438956618309, 0.00010952232696581632, 0.07733933627605438, -0.020049264654517174, 0.06284566223621368, 0.03785619139671326, 0.007121525704860687, 0.009584860876202583, 0.004816355649381876, -0.006415584124624729, 0.018357155844569206, -0.018694661557674408, -0.02506614848971367, -0.025557098910212517, -0.018436474725604057, -0.016683999449014664, -0.019857339560985565, -0.04165391996502876, -0.002487919060513377, 0.05517388880252838, -0.013375962153077126, 0.06371445208787918, -0.02472461760044098, -0.0793544352054596, 0.004285645671188831, -0.02845194563269615, 0.02705700322985649, -0.04013896733522415, -0.01005085464566946, 0.09304127097129822, 0.002380477264523506, -0.06528300046920776, -0.053623881191015244, 0.031079519540071487, -0.014224202372133732, -0.041821300983428955, -0.023643458262085915, -0.006457807030528784, -0.0018254590686410666, 0.004227029625326395, 0.05601910129189491, -0.011197376996278763, 0.027752885594964027, -0.06228828430175781, -0.04974205791950226, 0.02308482676744461, 0.030230090022087097, -0.0012525992933660746, 0.006318678613752127, 2.2617493949629702e-34, -0.01618664152920246, 0.02813420258462429, -0.009883912280201912, -0.051101069897413254, -0.012922484427690506, -0.012915514409542084, 0.02706817537546158, -0.033836327493190765, 0.042149219661951065, -0.01648142747581005, -0.0031665381975471973]

['Jia Zeng', 'Xiao-Qin Cao', 'Zhi-Qiang Liu']

1204.6610v1

Fast convergence speed is a desired property for training latent Dirichlet allocation (LDA), especially in online and parallel topic modeling for massive data sets. This paper presents a novel residual belief propagation (RBP) algorithm to accelerate the convergence speed for training LDA. The proposed RBP uses an informed scheduling scheme for asynchronous message passing, which passes fast-convergent messages with a higher priority to influence those slow-convergent messages at each learning iteration. Extensive empirical studies confirm that RBP significantly reduces the training time until convergence while achieves a much lower predictive perplexity than other state-of-the-art training algorithms for LDA, including variational Bayes (VB), collapsed Gibbs sampling (GS), loopy belief propagation (BP), and residual VB (RVB).

Residual Belief Propagation for Topic Modeling

http://arxiv.org/pdf/1204.6610v1

Title Residual Belief Propagation Topic Modeling Summary Fast convergence speed desired property training latent Dirichlet allocation LDA especially online parallel topic modeling massive data set paper present novel residual belief propagation RBP algorithm accelerate convergence speed training LDA proposed RBP us informed scheduling scheme asynchronous message passing pass fastconvergent message higher priority influence slowconvergent message learning iteration Extensive empirical study confirm RBP significantly reduces training time convergence achieves much lower predictive perplexity stateoftheart training algorithm LDA including variational Bayes VB collapsed Gibbs sampling GS loopy belief propagation BP residual VB RVB Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.019131580367684364, 0.040033970028162, 0.022219564765691757, 0.0017610195791348815, -0.04361964017152786, 0.028305072337388992, -0.00770682143047452, -0.007572125177830458, -0.03259881213307381, -0.03659398481249809, 0.02954399585723877, 0.009200505912303925, -0.021230826154351234, 0.01625032350420952, -0.037759870290756226, -0.04889560118317604, 0.02662874199450016, 0.005470664706081152, 0.04250328242778778, -0.03168891742825508, 0.01438450999557972, 0.006471772212535143, -0.01161082461476326, -0.013675394468009472, -0.035209834575653076, -0.02668008953332901, -0.03971168026328087, -0.04001527279615402, -0.0021284082904458046, -0.03852882608771324, -0.006760724354535341, 0.041667938232421875, 0.04649389535188675, -0.021802609786391258, 2.1572334389929892e-06, -0.013984667137265205, -0.042867667973041534, -0.012877910397946835, 0.04907417297363281, 0.03311864659190178, 0.04928998649120331, -0.00022141488443594426, 0.024099543690681458, 0.029938701540231705, -0.0346861407160759, -0.004758264869451523, 0.02924163267016411, 0.15093576908111572, 0.006325162947177887, 0.06354057043790817, -0.03133729472756386, -0.0582234226167202, 0.05437638238072395, -0.025799335911870003, 0.0548599474132061, -0.08775073289871216, 0.05010315403342247, 0.05144709721207619, -0.0287346038967371, 0.03240612894296646, -0.02286570705473423, 0.009655793197453022, -0.005378731060773134, 0.021153312176465988, -0.011293875984847546, 0.016603296622633934, 0.06187204644083977, -0.03450416773557663, -0.0408509187400341, 0.03901809826493263, 0.0539374053478241, -0.05401214212179184, -0.001838680705986917, 0.01858367957174778, -0.07137511670589447, 0.07166597247123718, -0.034489743411540985, 0.02132616937160492, -0.036569397896528244, 0.06337148696184158, 0.038915496319532394, -0.03051752783358097, 0.022141998633742332, -0.022386103868484497, -0.007038877811282873, 0.08995286375284195, 0.013993783853948116, -0.04200928658246994, -0.006103838328272104, 0.020520314574241638, -0.046433836221694946, -0.03324007987976074, 0.035168688744306564, -0.017928967252373695, -0.00588741572573781, 0.020930929109454155, -0.0033017080277204514, -0.08290096372365952, 0.010808179154992104, -0.015190978534519672, -0.055784184485673904, -0.023201461881399155, -0.004104568623006344, 0.03623759374022484, 0.004190774634480476, -0.014065378345549107, -0.03314334899187088, -0.024018224328756332, 0.003767482005059719, -0.008996536955237389, -0.06032519415020943, 0.012933218851685524, 0.0004745741025544703, 0.050827570259571075, 0.035799290984869, -0.01801910065114498, -0.0426313653588295, 0.02650729939341545, -0.022343389689922333, -0.03820070996880531, 0.009809404611587524, 0.015483830124139786, -0.04124679043889046, 0.009474295191466808, -0.010511752218008041, 0.04419437795877457, -0.022582583129405975, 0.03245456889271736, -0.05874292925000191, 0.04936224967241287, 0.03553443029522896, -0.007192482706159353, 0.0113031892105937, 0.07260534912347794, 0.015010826289653778, -0.005704179406166077, -0.02261381596326828, -0.0008513549691997468, -0.08422450721263885, 0.05411308631300926, 0.00031591334845870733, -0.029710598289966583, -0.008169280365109444, -0.0924016460776329, -0.014515780843794346, 0.013004070147871971, -0.016340812668204308, 0.04035842791199684, 0.005206701345741749, -0.0023472101893275976, -0.028463520109653473, 0.08188842982053757, -0.06651066243648529, 0.01993231102824211, 0.08971027284860611, 0.007679545320570469, 0.04544692859053612, 0.10907323658466339, -0.03305010125041008, 0.023508919402956963, 0.024044105783104897, 0.026318209245800972, -0.02723108045756817, -0.029942676424980164, 0.007887640967965126, 0.036407649517059326, -0.04296879470348358, 0.013438279740512371, 0.004067490808665752, 0.006473214831203222, 0.023948514834046364, 0.0154268192127347, -0.018656229600310326, 0.014957007952034473, -0.003468320472165942, 0.05675000697374344, -0.017600087448954582, 0.025880979374051094, 0.0002819167566485703, 0.03302251175045967, -0.004216859117150307, 0.013222592882812023, 0.02748197689652443, -0.0042437841184437275, 0.01988249085843563, -0.055293530225753784, 0.015846384689211845, 0.0006183972582221031, -0.04454922303557396, 0.0027662436477839947, 0.010110790841281414, 0.008688785135746002, -0.018090996891260147, -0.03623809665441513, 0.09308066219091415, -0.009192937053740025, 0.007613713387399912, -0.009764677844941616, 0.0623437725007534, 0.02246411330997944, -0.05364585295319557, -0.02000250667333603, 0.03373859077692032, -0.009116295725107193, 0.03165389597415924, -0.05637029930949211, -0.027208639308810234, -0.004003974609076977, 0.037676263600587845, -0.023842712864279747, -0.005383884999901056, -0.009721813723444939, -0.05540924519300461, -0.025848517194390297, 0.02210123836994171, 0.03801786154508591, 0.02870149165391922, 0.04855383187532425, -0.0014814083697274327, 0.014579187147319317, -0.020494243130087852, -0.0034469414968043566, 0.024461230263113976, 0.03785357251763344, -0.0009184497757814825, 0.038281120359897614, 0.025560084730386734, -0.0105562349781394, 0.057839490473270416, 0.027051780372858047, 0.013801077380776405, -0.03344214707612991, 0.04510422423481941, 0.003853745525702834, -0.06973027437925339, -0.02112133800983429, 0.006673118099570274, -0.07025598734617233, 0.030483167618513107, -0.056674543768167496, 0.013873902149498463, 0.03827669098973274, -0.0029405553359538317, -0.012390058487653732, 0.015564142726361752, -0.018956035375595093, 0.041048359125852585, -0.03665963187813759, 0.03510428965091705, -0.0435277484357357, -0.009167266078293324, -0.0247983168810606, 0.028447410091757774, -0.025898031890392303, 0.03636183589696884, -0.0017727324739098549, -0.0047589996829628944, 0.038514237850904465, -0.005347722675651312, 0.011618999764323235, -0.015189259313046932, 0.0026898644864559174, 0.0020792868454009295, -0.005304882302880287, -0.004302708897739649, 0.0034672096371650696, 0.008227210491895676, -0.08534342050552368, 0.004613265860825777, -0.02069677785038948, -0.02684793993830681, 0.023886825889348984, -0.016360409557819366, 0.018230585381388664, -0.0003652733576018363, -0.012548688799142838, 0.07752572000026703, -0.01911863312125206, 0.027438106015324593, -0.0002993709349539131, 0.0022517507895827293, 0.010594747960567474, 0.002111857058480382, -0.007012226618826389, -0.020721858367323875, 0.03283549100160599, 0.029745670035481453, -0.02927151508629322, -0.05927741900086403, -0.003317213384434581, -0.029571998864412308, 0.019580954685807228, -0.018202586099505424, -0.022475549951195717, -0.007977105677127838, -0.03171344846487045, 0.08132090419530869, -0.041452884674072266, 0.006161951459944248, 0.02426772005856037, 0.043151989579200745, 0.020724792033433914, -0.021857235580682755, 0.0018989014206454158, -0.07227155566215515, 0.01210498996078968, -0.0011127045145258307, -0.024089191108942032, 0.005807888228446245, 0.026080433279275894, 0.041871577501297, 0.010975069366395473, -0.0029103257693350315, -0.027294276282191277, 0.001831257832236588, -0.013998335227370262, -0.0374581553041935, -0.0011967876926064491, 0.00763683533295989, 0.027178779244422913, -0.01680177077651024, -0.041462987661361694, 0.06190897896885872, 0.017439326271414757, 0.032397668808698654, -0.09860538691282272, -0.03792678564786911, -0.003976939711719751, -0.01334359310567379, -0.010945865884423256, 0.006183309014886618, -0.040840018540620804, -0.02184862457215786, -0.0019268831238150597, 0.03677719086408615, 0.030484316870570183, 0.002972128102555871, 0.06338022649288177, 0.02746693417429924, 0.03794645145535469, 0.014116579666733742, 0.02415563352406025, -0.026558883488178253, -0.06811710447072983, 0.011129209771752357, -0.018641607835888863, 0.015488019213080406, -0.032405149191617966, -0.03011449985206127, 0.04563350975513458, 0.022101441398262978, -0.004843626171350479, -0.033059269189834595, -0.0343952402472496, 0.02875320054590702, 0.0057951644994318485, 0.03499825298786163, -0.08961734175682068, -0.010405704379081726, -0.0037416107952594757, 0.02255840227007866, 0.04988463968038559, 0.033015020191669464, -0.02784326672554016, -0.05633167922496796, -0.010977888479828835, -0.0017280479660257697, -0.014155302196741104, -0.02470540627837181, -0.007859748788177967, 0.01969764195382595, 0.00013289270282257348, 0.02550588920712471, 0.0696287751197815, 0.02341487817466259, -0.14745670557022095, -0.021039126440882683, -0.0208501648157835, -0.002532027428969741, 0.00943880993872881, 0.023777343332767487, -0.04247790575027466, -0.0008201921591535211, -0.01375421043485403, 0.017202187329530716, 0.015887808054685593, -0.052771348506212234, -0.020131981000304222, -0.02497773803770542, 0.07135103642940521, -0.03168988972902298, -0.01068123709410429, -0.041707511991262436, -0.15184147655963898, 0.004919963888823986, 0.011608387343585491, -0.005135869607329369, 0.025369003415107727, -0.003506558947265148, -0.015210583806037903, 0.009593240916728973, -0.04782142862677574, 0.00011963400174863636, -0.005040798801928759, -0.03916630148887634, 0.006312125828117132, -0.02559700980782509, 0.04165491461753845, -0.0039866468869149685, -0.020692195743322372, -0.03303401917219162, -0.028210775926709175, -0.02630358561873436, -0.04269110783934593, 0.05622611567378044, -0.013053893111646175, 0.0012485182378441095, -0.0169744323939085, 0.006419002544134855, -0.035096172243356705, -0.015425086952745914, 0.030333368107676506, 0.07256628572940826, -0.03364735096693039, 0.0038724644109606743, -0.022906659170985222, 0.011025083251297474, 0.01247323490679264, 0.021527091041207314, -0.008037400431931019, -0.03866685926914215, 1.5739344235043973e-05, 0.017439279705286026, 0.001515658339485526, 0.06607353687286377, 0.05166153609752655, -0.04285098984837532, -0.09386111795902252, -0.10151240229606628, -0.07917580753564835, 0.021977921947836876, 0.005944719072431326, 0.06019500270485878, 0.014490828849375248, 0.035235803574323654, -0.002081645419821143, -0.010667674243450165, -0.06387807428836823, -0.035330478101968765, 0.016669489443302155, -0.027263766154646873, -0.03317765146493912, -0.01896408386528492, 0.045336607843637466, -0.023961974307894707, -0.002685938961803913, -0.07001924514770508, -0.08061729371547699, -0.04836777597665787, 0.004600307438522577, -0.028857922181487083, 0.0008623484172858298, 0.0372922308743, -0.028137018904089928, -0.0505683533847332, -0.030906865373253822, 0.013003355823457241, -0.01860678941011429, 0.03252959996461868, 0.01640627719461918, 0.02203587256371975, 0.03570454940199852, 0.019764000549912453, -0.01502245757728815, 0.06164015084505081, -0.022835129871964455, -0.03377198055386543, -0.05373798683285713, 0.003492365824058652, 0.00774775817990303, 0.03202734515070915, 0.08606583625078201, 0.014532074332237244, -0.030318517237901688, -0.037043310701847076, 0.009522449225187302, -0.019237669184803963, -0.00527107622474432, -0.024003971368074417, 0.04645473510026932, 0.022550880908966064, 0.018639730289578438, -0.03968116641044617, -0.025095831602811813, 0.010477762669324875, -0.007449017837643623, -0.02468183822929859, 0.014297636225819588, -0.009778277948498726, 0.0184148121625185, 0.0060157934203743935, 0.020266929641366005, 0.0039432900957763195, -0.0487837977707386, 0.021376922726631165, -0.004965178668498993, -0.012710653245449066, 0.046039026230573654, 0.01798022724688053, -0.026380077004432678, -0.030222155153751373, -0.02031370997428894, -0.05955836549401283, -0.03307260572910309, -0.007203567307442427, 0.07204741984605789, 0.08345331251621246, 0.044014714658260345, 0.017775781452655792, -0.037189729511737823, 0.008007388561964035, -0.009977662935853004, 0.049852922558784485, -0.032418955117464066, 0.011399162001907825, 0.03252618387341499, -0.0018652873113751411, -0.02124287188053131, 0.08593085408210754, 0.07030318677425385, 0.0375344417989254, -0.0002478276437614113, 0.015995066612958908, -0.04307134822010994, -0.03150938078761101, 0.04238513857126236, 0.040163975208997726, 0.05899005010724068, -0.006874672137200832, 0.022989068180322647, 0.030858274549245834, -0.01786230318248272, 0.0375959612429142, -0.05621643364429474, -0.004586270544677973, -0.014915834181010723, 0.012720483355224133, 0.09108737111091614, -0.019272109493613243, 0.0341080017387867, -0.07190700620412827, 0.02130325883626938, -0.007245028391480446, -0.01695871166884899, 0.008870177902281284, -6.356622353289803e-33, 0.012754252180457115, -0.057481344789266586, -0.016714653000235558, 0.02076873555779457, -0.015784384682774544, 0.018337570130825043, -0.00579105643555522, -0.0028568804264068604, 0.048764195293188095, 0.03332601860165596, -0.025445131585001945, 0.04300623759627342, 0.00034661893732845783, -0.02487528696656227, 0.022048193961381912, -0.0006153835565783083, 0.03710443526506424, 0.0028224128764122725, 0.04592728242278099, 0.022780580446124077, 0.0421241894364357, 0.07508919388055801, 0.050824977457523346, -0.0393369160592556, -0.051620110869407654, -0.001178677543066442, -0.022969026118516922, 0.01575515791773796, 0.06844779849052429, -0.006551204714924097, -0.021247854456305504, 0.014018422923982143, 0.030610404908657074, -0.06439072638750076, -0.0001644455041969195, 0.014989049173891544, -0.016650481149554253, -0.05413740873336792, -0.02932693064212799, 0.013006279245018959, -0.00014342917711474001, 0.05058407038450241, 0.003926663193851709, 0.029048031195998192, 0.01716325618326664, 0.04691731557250023, 0.05763743445277214, -0.01812964491546154, -0.0262601375579834, -0.025680173188447952, -0.006872400175780058, 0.03149824216961861, 0.01434320118278265, 0.06197052821516991, -0.010003605857491493, -0.06889799237251282, -0.030258499085903168, 0.05328620597720146, -0.015858251601457596, 0.012689938768744469, 0.02700674906373024, 0.03241391479969025, -0.016703974455595016, -0.010024222545325756, 0.029414581134915352, 0.03941497951745987, 0.025099171325564384, 0.0064598573371768, -0.026183027774095535, -0.003691035555675626, 0.005998184438794851, 0.03113996982574463, 0.005485944449901581, 0.032669708132743835, 0.07507830858230591, 0.013822759501636028, -0.08132344484329224, 0.031706493347883224, 0.037218254059553146, 0.02521701529622078, 0.03615717962384224, 0.03246491774916649, -0.04199647530913353, -0.020668843761086464, 0.0017450277227908373, 0.04542912542819977, -0.014722706750035286, -0.0397910512983799, -0.015139184892177582, 0.016459520906209946, -0.030595513060688972, 0.018282746896147728, -0.006433528382331133, -0.04737098142504692, -0.023227104917168617, 0.02283957041800022, -0.009537359699606895, 0.02397751249372959, -0.009879697114229202, -0.017838405445218086, -0.11005396395921707, -0.020757080987095833, -0.016963157802820206, -0.007848244160413742, -0.02116963639855385, -0.00034857334685511887, -0.008341395296156406, -0.022751325741410255, -0.046650487929582596, -0.038774289190769196, 0.007726882118731737, -0.053242143243551254, 0.026759712025523186, 0.07567712664604187, 0.018407408148050308, -0.047522976994514465, 0.005289074499160051, 0.07882025092840195, 0.0729638934135437, 0.012854034081101418, 0.017995145171880722, -0.009493570774793625, 0.00018244460807181895, 0.011141659691929817, -0.04708416759967804, -0.014827451668679714, -0.023299088701605797, -0.03851761668920517, 0.005833691917359829, -0.09320762008428574, -0.036504920572042465, 0.008728286251425743, 2.8004654950564145e-07, -0.004794848617166281, 0.04809202253818512, -0.04716286063194275, -0.012536713853478432, 0.028944222256541252, 0.0031731247436255217, -0.004497095942497253, -0.003828165354207158, 0.030338626354932785, -0.011854907497763634, 0.034048616886138916, 0.010925255715847015, -0.005129348952323198, 0.046882808208465576, -0.09941035509109497, -0.04009810835123062, -0.027106430381536484, 0.03689894825220108, -0.008405033499002457, 0.001938874484039843, 0.006251090206205845, 0.06658570468425751, 0.05489009618759155, -0.007942751981317997, 0.020307574421167374, 0.049815673381090164, 0.057827603071928024, 0.010530711151659489, -0.03595556691288948, 0.03745374083518982, 0.028491349890828133, 0.016168484464287758, -0.0012069365475326777, 0.012937065213918686, -0.03070482797920704, 0.017856474965810776, -0.00039034592919051647, 0.0299222469329834, -0.042210936546325684, -0.011644444428384304, 0.04075303673744202, -0.008371039293706417, -0.013864761218428612, -0.03310219198465347, 0.05050121992826462, -0.03055112436413765, -0.050502341240644455, -0.02957739681005478, -0.03605892136693001, 0.01329194288700819, 0.007990460842847824, 0.002986413659527898, -0.005439599044620991, -0.009674496948719025, -0.02838950604200363, -0.031320881098508835, -0.04506586119532585, -0.04145604744553566, 0.03500167652964592, 0.031363602727651596, -0.0457734540104866, -0.0673273429274559, -7.018164615146816e-05, -0.023271363228559494, 0.06884138286113739, -0.041762907058000565, 0.03812294453382492, 2.8849758367823115e-34, 0.06837736070156097, -0.024324925616383553, -0.05259384959936142, 0.0583810992538929, -0.05320778861641884, -0.025143006816506386, 0.005867311730980873, -0.006568762939423323, 0.003924535121768713, -0.06877562403678894, 0.0035720092710107565]

['L. Chekina', 'D. Mimran', 'L. Rokach', 'Y. Elovici', 'B. Shapira']

1208.0564v2

In this paper a novel system for detecting meaningful deviations in a mobile application's network behavior is proposed. The main goal of the proposed system is to protect mobile device users and cellular infrastructure companies from malicious applications. The new system is capable of: (1) identifying malicious attacks or masquerading applications installed on a mobile device, and (2) identifying republishing of popular applications injected with a malicious code. The detection is performed based on the application's network traffic patterns only. For each application two types of models are learned. The first model, local, represents the personal traffic pattern for each user using an application and is learned on the device. The second model, collaborative, represents traffic patterns of numerous users using an application and is learned on the system server. Machine-learning methods are used for learning and detection purposes. This paper focuses on methods utilized for local (i.e., on mobile device) learning and detection of deviations from the normal application's behavior. These methods were implemented and evaluated on Android devices. The evaluation experiments demonstrate that: (1) various applications have specific network traffic patterns and certain application categories can be distinguishable by their network patterns, (2) different levels of deviations from normal behavior can be detected accurately, and (3) local learning is feasible and has a low performance overhead on mobile devices.

Detection of Deviations in Mobile Applications Network Behavior

http://arxiv.org/pdf/1208.0564v2

Title Detection Deviations Mobile Applications Network Behavior Summary paper novel system detecting meaningful deviation mobile application network behavior proposed main goal proposed system protect mobile device user cellular infrastructure company malicious application new system capable 1 identifying malicious attack masquerading application installed mobile device 2 identifying republishing popular application injected malicious code detection performed based application network traffic pattern application two type model learned first model local represents personal traffic pattern user using application learned device second model collaborative represents traffic pattern numerous user using application learned system server Machinelearning method used learning detection purpose paper focus method utilized local ie mobile device learning detection deviation normal application behavior method implemented evaluated Android device evaluation experiment demonstrate 1 various application specific network traffic pattern certain application category distinguishable network pattern 2 different level deviation normal behavior detected accurately 3 local learning feasible low performance overhead mobile device Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.053822051733732224, -0.02677486091852188, -0.039546020328998566, -0.006948825903236866, -0.040933649986982346, -0.027852840721607208, 0.02057725191116333, -0.00654739560559392, -0.019901372492313385, -0.07932005077600479, 0.05333175137639046, 0.011258108541369438, 0.015124429948627949, 0.027059223502874374, 0.00879895780235529, 0.011433766223490238, 0.03846542909741402, 0.012348795309662819, -0.009557021781802177, 0.06829281151294708, 0.04382636398077011, -0.009723920375108719, 0.06808475404977798, 0.017047787085175514, -0.00945985410362482, -0.024461979046463966, -0.007859532721340656, 0.025363991037011147, 0.012761012651026249, -0.06984253972768784, 0.06446106731891632, -0.010539690963923931, -0.008605421520769596, 0.025748053565621376, 1.9044583723371034e-06, -0.0033276428002864122, -0.015368591994047165, -0.011462518945336342, 0.03586716949939728, 0.012929080985486507, 0.011971558444201946, 0.03684861585497856, -0.0036332185845822096, 0.05003882572054863, -0.02051319181919098, 0.016501232981681824, -0.011647981591522694, 0.024789215996861458, 0.05288025736808777, 0.053478747606277466, -0.003018546849489212, -0.004536958411335945, -0.0025458307936787605, 0.053635358810424805, 0.038204483687877655, 0.007483886554837227, 0.0057065775617957115, 0.020317798480391502, 0.018677374348044395, -0.028382612392306328, 0.005355869885534048, -0.09688036888837814, -0.004199694376438856, 0.005059403833001852, 0.008832682855427265, -0.013228029944002628, 0.008589857257902622, -0.005284307058900595, -0.03361804410815239, 0.013411257416009903, -0.06311621516942978, -0.023658566176891327, 0.022157618775963783, 0.0165147315710783, -0.03715341538190842, 0.013704833574593067, 0.03880755603313446, -0.004856782965362072, -0.04615224525332451, 0.0063256449066102505, 0.006003169808536768, 0.032479263842105865, 0.015771357342600822, -0.013068145141005516, -0.05913805589079857, -0.06498154252767563, -0.019829487428069115, -0.028543101623654366, -0.03627779707312584, -0.027184942737221718, 0.047949738800525665, -0.017586320638656616, 0.06692425161600113, 0.007001176476478577, -0.04591267183423042, -0.014678677543997765, -0.023537375032901764, -0.055794961750507355, 0.027930647134780884, -0.05873390659689903, -0.004422526806592941, -0.025869369506835938, -0.007243702188134193, -0.04680027440190315, -0.006699804216623306, 0.02053205668926239, 0.006997474003583193, 0.004762968048453331, -0.00028234111960045993, 0.042529016733169556, -0.02785665914416313, 0.027413804084062576, 0.01104352530092001, 0.06925641000270844, 0.02501155063509941, 0.0085563063621521, -0.0590498261153698, 0.03783910721540451, -0.0178187545388937, 0.001956953201442957, -0.023283980786800385, 0.02127479575574398, 0.018647048622369766, 0.0001609659375390038, 0.03721242398023605, -0.07879108935594559, -0.046963293105363846, 0.014871438033878803, -0.018071511760354042, -0.009987037628889084, 0.016764314845204353, -0.028184931725263596, -0.015687471255660057, 0.0007808403461240232, -0.017267022281885147, 0.024140143766999245, 0.045629847794771194, 0.01425760705024004, -0.08058282732963562, -0.06193693354725838, 0.05306631326675415, 0.00033918776898644865, -0.045350082218647, -0.05838862806558609, -0.07204687595367432, -0.027408776804804802, 0.014625837095081806, 0.015652146190404892, -0.03416693955659866, -0.03938350826501846, -0.007102879695594311, -0.0076430682092905045, 0.03346996381878853, 0.014327027834951878, 0.039511438459157944, 0.01647922769188881, 0.004890173673629761, -0.027180051431059837, -0.02833525463938713, 0.03944946452975273, 0.03451058641076088, -0.03787486255168915, 0.026429176330566406, -0.013610290363430977, -0.00553889898583293, -0.030007317662239075, 0.008481889963150024, -0.02926238253712654, 0.007910762913525105, -0.07839316129684448, -0.05057824030518532, 0.0008641845197416842, 0.03408563509583473, 0.00481839757412672, 0.017758317291736603, 0.01176952850073576, 0.017584223300218582, 0.0022955373860895634, -0.002333025448024273, 0.052722930908203125, -0.05606388300657272, 0.025939449667930603, 0.0291743241250515, -0.00612129969522357, -0.08464930951595306, -0.030951138585805893, -0.00930904783308506, 0.0431043915450573, -0.01753564551472664, 0.004372810013592243, 0.0013801997993141413, -0.042326416820287704, -0.01577647402882576, -0.004309460986405611, 0.034655019640922546, 0.013505486771464348, 0.05326976254582405, -0.03659818321466446, 0.017457829788327217, 0.05631277710199356, -0.03821054473519325, -0.05835236236453056, 0.07335920631885529, 0.017093436792492867, -0.015638262033462524, -0.0015252280281856656, -0.012819076888263226, 0.003028890583664179, -0.06412266939878464, -0.0755900889635086, -0.0017848402494564652, -0.03049102984368801, -0.020247720181941986, -0.010826772078871727, 0.011980067007243633, 0.03745799511671066, 0.0593683160841465, -0.057624150067567825, -0.0393734872341156, 0.05877126008272171, 0.0449882373213768, -0.010709777474403381, -0.02545752003788948, 0.021357635036110878, 0.042706914246082306, 0.015274496749043465, 0.05683375895023346, 0.05099908635020256, 0.04217491298913956, -0.011846661567687988, 0.04956845939159393, -0.016338374465703964, 0.01570105366408825, 0.0013883945066481829, 0.03177154064178467, 0.020382629707455635, 0.0425729975104332, 0.016952119767665863, -0.00415784539654851, 0.005426615942269564, 0.03670156002044678, 0.06428253650665283, -0.0037968545220792294, -0.01971936970949173, 0.04186895862221718, -0.03199273720383644, 0.009322404861450195, 0.005330202169716358, 0.03569359704852104, -0.014922058209776878, 0.05452222749590874, -0.02200600877404213, 0.016391674056649208, 0.0660250335931778, 0.0067757596261799335, 0.00030616758158430457, 0.002362316008657217, 0.007651542779058218, 0.03851492702960968, 0.018761932849884033, -0.06576500833034515, -0.06549438834190369, 0.06469731032848358, -0.011937691830098629, -0.004870194010436535, 0.031088242307305336, 0.017473263666033745, 0.03125816956162453, 0.07058277726173401, -0.05840383097529411, -0.0017411039443686604, 0.06098000705242157, 0.07842771708965302, 0.011954911053180695, -0.048564571887254715, -0.01171974465250969, 0.030736926943063736, 0.023457596078515053, -0.031200015917420387, 0.031976502388715744, -0.020240988582372665, -0.011855443939566612, 0.005821571685373783, 0.0029835104942321777, -0.04820551350712776, 0.03857792913913727, 0.03225218504667282, -0.03137146681547165, -0.02869286760687828, -0.04765376076102257, -0.013349359855055809, -0.03035876154899597, 0.00845734216272831, -0.045937273651361465, -0.0032126985024660826, 0.003915873356163502, -0.0176771841943264, 0.042585715651512146, 0.023219818249344826, 0.008867142722010612, -0.007191197946667671, 0.016598399728536606, -0.04159596562385559, -0.00399613194167614, 0.0214995127171278, -0.0025389771908521652, -0.028138700872659683, -0.04558568447828293, 0.03240581601858139, 0.061074208468198776, 0.048853132873773575, 0.02358497865498066, 0.027299191802740097, 0.0003683828981593251, -0.018869545310735703, 0.01680481992661953, -0.03260014206171036, 0.049929454922676086, -0.043508585542440414, -0.0179264098405838, 0.009754667058587074, -0.01637430302798748, 0.047762151807546616, 0.06647761166095734, 0.060020361095666885, -0.030735308304429054, -0.06928759068250656, 0.03974280133843422, -0.02659662440419197, -0.013825161382555962, 0.0546252615749836, -0.0029122252017259598, -0.0543205589056015, 0.03722434118390083, 0.005700270179659128, 0.03658322989940643, -0.05527672544121742, -0.017048915848135948, -0.038384854793548584, -0.0603342279791832, 0.022677483037114143, -0.0052044447511434555, -0.03643708676099777, -0.05874312296509743, 0.017376234754920006, -0.0540759339928627, -0.019416948780417442, -0.0048570651561021805, -0.003749328199774027, 0.03383401408791542, -0.04426585137844086, 0.007594228256493807, 0.003198622027412057, -0.020869821310043335, 0.01471028570085764, 0.025367949157953262, -0.005967463366687298, -0.0594804510474205, -0.048488590866327286, 0.015135838650166988, 0.02757684700191021, 0.02187376283109188, -0.016419483348727226, 0.003123509930446744, -0.05691163241863251, 0.06675825268030167, -0.022915683686733246, -0.05654982849955559, -0.012067223899066448, 0.09251020848751068, 0.03518885746598244, -0.03684629499912262, 0.0033328281715512276, 0.003150446340441704, 0.05925549566745758, -0.05513595789670944, -0.01632671244442463, -0.024065429344773293, -0.028711747378110886, 0.034329671412706375, 0.022608373314142227, -0.02608245052397251, -0.013264698907732964, -0.03852665796875954, 0.00460820784792304, -0.013961976394057274, 0.015475832857191563, 0.016379542648792267, -0.006426624953746796, -0.024057485163211823, 0.04065530374646187, -0.024446794763207436, 0.0005386090488173068, -0.049443285912275314, -0.0069003235548734665, 0.0026474781334400177, 0.016275612637400627, -0.02450709231197834, 0.02157152257859707, 0.0014359245542436838, 0.02602030709385872, -0.08174998313188553, -0.03959943354129791, 0.018871301785111427, -0.06869067251682281, 0.030193081125617027, 0.0050152260810136795, -0.012258914299309254, 0.0006313110352493823, 0.020990749821066856, -0.015385864302515984, -0.013422937132418156, 0.007378122303634882, 0.01949487440288067, 0.01055865827947855, 0.026841184124350548, 0.00729865487664938, -0.02929680235683918, 0.04323038086295128, -0.029502110555768013, 0.0038697239942848682, 0.03877157345414162, 0.05972137674689293, -0.03754432499408722, -0.026787620037794113, -0.06058128923177719, -0.015864664688706398, 0.05385959893465042, -0.019055373966693878, 0.0019918407779186964, -0.05886034667491913, -0.042386069893836975, -0.015439637005329132, -0.014079262502491474, 0.012757664546370506, 0.01282850094139576, 0.035778407007455826, -0.0012670301366597414, -0.06870334595441818, -0.04300633817911148, 0.028577925637364388, -0.06876163929700851, 0.03261534869670868, 0.06005147472023964, 0.037007298320531845, -0.005581252742558718, -0.004319674801081419, -0.00360832829028368, -0.09544646739959717, 0.07289819419384003, 0.04935397207736969, -0.024937424808740616, 0.048586029559373856, 0.007890735752880573, -0.020734217017889023, -0.04800038039684296, -0.07987771928310394, -0.004458869341760874, -0.04142293706536293, -0.010589202865958214, -0.0015523142646998167, 0.016515139490365982, 0.0258710328489542, -0.08364111185073853, 0.01197079662233591, -0.022852975875139236, -0.009468547999858856, -0.017739571630954742, -0.04003613069653511, 0.039234697818756104, -0.0742553099989891, -0.027078503742814064, -0.016902565956115723, -0.018337516114115715, 0.022291578352451324, 0.022847939282655716, -0.06132175773382187, -0.10658465325832367, 0.019604729488492012, 0.03623387962579727, -0.004591906908899546, 0.050461940467357635, 0.043386202305555344, -0.037073519080877304, 0.008159576915204525, -0.011313844472169876, 0.06192485988140106, -0.008435094729065895, 0.0485413558781147, -0.037394918501377106, 0.03598589450120926, 0.003539003897458315, 0.023339908570051193, -0.008341660723090172, 0.009038836695253849, -0.08890974521636963, 0.015528379939496517, 0.003109942190349102, 0.03284488990902901, 0.08369564265012741, -0.025251038372516632, -0.001355169340968132, -0.007018023170530796, -0.023942988365888596, 0.06157956272363663, 0.06829781830310822, -0.0652315765619278, -0.026712579652667046, -0.0520639643073082, -0.007053376641124487, -0.03332854434847832, -0.002323022810742259, 0.02062372863292694, 0.06165317818522453, 0.03988197073340416, 0.022832252085208893, 0.0199410542845726, -0.0028018977027386427, -0.02424509823322296, -0.008377864956855774, 0.0354364849627018, -0.025801897048950195, 0.025378169491887093, -0.07853294909000397, -0.0005034577916376293, 0.00572587177157402, -0.024079862982034683, -0.021136466413736343, 0.025036124512553215, 0.0159040205180645, 0.019419832155108452, -0.02146773226559162, -0.004770633764564991, -0.08439951390028, -0.04790220409631729, 0.07818293571472168, 0.05923791229724884, 0.02697504498064518, -0.03032929077744484, 0.013229546137154102, -0.018104391172528267, -0.0074337804690003395, -0.023721041157841682, -0.02291090227663517, 0.07356736809015274, 0.02328948676586151, -0.0005146564799360931, 0.06448148190975189, -0.03173038735985756, 0.03412648290395737, -0.06062138080596924, -0.04232770577073097, -0.04073350876569748, 0.04398238658905029, -0.03709070011973381, -4.817161155990349e-33, 0.03634864091873169, 0.015094930306077003, -0.056310735642910004, -0.042011674493551254, 0.008267531171441078, 0.00537723395973444, 0.010233007371425629, 0.006164082791656256, 0.0333709754049778, -0.04454724118113518, -0.02275608666241169, 0.021873803809285164, -0.005110893398523331, -0.02897212654352188, 0.0020720656029880047, 0.03218667954206467, 0.04529880732297897, 0.011279791593551636, 0.004984844941645861, 0.028821129351854324, 0.016356108710169792, 0.01441675703972578, 0.004310648422688246, -0.049805015325546265, -0.03897995501756668, -0.030529379844665527, 0.016440602019429207, -0.053753286600112915, -0.04780089855194092, 0.033237092196941376, 0.02255827561020851, -0.0009648582781665027, 0.019565952941775322, -0.003365884069353342, -0.0585859976708889, 0.02046971209347248, 0.008790852501988411, -0.02709287963807583, 0.00814412347972393, 0.052345193922519684, 0.01713653653860092, -0.050622835755348206, 0.0861438661813736, 0.013828994706273079, -0.04880828782916069, 0.028803279623389244, 0.05639024078845978, -0.030578168109059334, -0.0628882497549057, 0.03870463743805885, 0.008949571289122105, -0.02455398626625538, -0.02285218983888626, 0.026977911591529846, -0.005584154278039932, -0.010373841039836407, -0.058328282088041306, -0.00870122853666544, -0.02747729979455471, 0.0031341889407485723, -0.04726327583193779, -0.0015753107145428658, -0.058137401938438416, 0.027126522734761238, 0.017159095034003258, 0.016140228137373924, -0.012738100253045559, -0.015043738298118114, 0.02815803326666355, -0.0031600617803633213, -0.011054638773202896, 0.06132570654153824, 0.00024642416974529624, 0.026977337896823883, 0.07395917177200317, -0.09539801627397537, -0.03702276572585106, 0.046036675572395325, 0.0535624697804451, -0.030652521178126335, 0.007788154762238264, -0.05380350351333618, -0.04023675620555878, -0.0026814667508006096, 0.046066805720329285, 0.009246284142136574, -0.009464026428759098, -0.057945553213357925, 0.0010341309243813157, 0.015965331345796585, -0.042950090020895004, -0.0036396903451532125, -0.036796506494283676, -0.07195783406496048, 0.005030448082834482, -0.03505578637123108, 0.013262534514069557, -0.00691643264144659, -0.0032172584906220436, -0.02678513340651989, -0.0204372089356184, -0.03297819569706917, -0.03311870992183685, -0.015882784500718117, 0.04786808043718338, 0.012808023020625114, 0.03162195160984993, 0.03180435299873352, -0.01572604477405548, -0.005034955218434334, 0.009771224111318588, -0.02132405899465084, -0.046676188707351685, 0.03611868619918823, 0.010247153230011463, -0.00753521965816617, -0.015044464729726315, 0.0642317533493042, -0.03762750327587128, -0.019470442086458206, -0.01542151253670454, -0.04397105798125267, 0.014190010726451874, 0.006567211356014013, -0.0861576497554779, -0.013873331248760223, -0.07203372567892075, 0.03321484848856926, 0.022273937240242958, 0.004542244598269463, -0.008653456345200539, -0.026656318455934525, 2.569898356341582e-07, -0.07011100649833679, 0.0065962146036326885, 0.0033704261295497417, -0.019457243382930756, 0.009411373175680637, 0.02843932807445526, -0.020924119278788567, 0.051926836371421814, 0.02446596510708332, -0.014104736037552357, 0.007399701979011297, -0.09830787777900696, 0.02527480386197567, 0.05947154387831688, -0.004521732684224844, 0.036449071019887924, -0.04148533567786217, 0.05583205446600914, -0.06500789523124695, 0.044577375054359436, 0.058396946638822556, 0.08189891278743744, 0.04613180458545685, -0.022333592176437378, 0.09503509849309921, 0.0007642309064976871, -0.024287523701786995, 0.028192467987537384, 0.0054184249602258205, -0.0149850994348526, 0.015718048438429832, 0.06729774177074432, 0.022989755496382713, 0.039354100823402405, -0.0659828707575798, -0.005821123719215393, -0.05943230539560318, 0.02439173497259617, -0.010761294513940811, 0.06083100661635399, -0.0026849948335438967, -0.06712143123149872, 0.03756740689277649, -0.025131354108452797, 0.037740640342235565, 0.05694442614912987, -0.04280445724725723, 0.022274097427725792, 0.0218315739184618, -0.03457021340727806, -0.006397359073162079, 0.043198708444833755, -0.0035175455268472433, 0.0042111994698643684, 0.037835314869880676, 0.019894732162356377, 0.014973752200603485, -0.037981025874614716, 0.027338175103068352, -0.00018113001715391874, 0.0323578417301178, 0.0012288277503103018, 0.01809815876185894, 0.03974059224128723, 0.07243165373802185, 0.035841722041368484, 0.04548190161585808, 2.1913448597771482e-34, 0.007292394060641527, 0.00011637569696176797, 0.04265457019209862, 0.013540144078433514, -0.04203823208808899, 0.008357732556760311, 0.017407497391104698, -0.0167995635420084, 0.055759914219379425, 0.04763033613562584, 0.015945101156830788]

['Shang Shang', 'Sanjeev R. Kulkarni', 'Paul W. Cuff', 'Pan Hui']

1208.0787v2

Collaborative filtering (CF) is one of the most popular approaches to build a recommendation system. In this paper, we propose a hybrid collaborative filtering model based on a Makovian random walk to address the data sparsity and cold start problems in recommendation systems. More precisely, we construct a directed graph whose nodes consist of items and users, together with item content, user profile and social network information. We incorporate user's ratings into edge settings in the graph model. The model provides personalized recommendations and predictions to individuals and groups. The proposed algorithms are evaluated on MovieLens and Epinions datasets. Experimental results show that the proposed methods perform well compared with other graph-based methods, especially in the cold start case.

A Random Walk Based Model Incorporating Social Information for Recommendations

http://arxiv.org/pdf/1208.0787v2

Title Random Walk Based Model Incorporating Social Information Recommendations Summary Collaborative filtering CF one popular approach build recommendation system paper propose hybrid collaborative filtering model based Makovian random walk address data sparsity cold start problem recommendation system precisely construct directed graph whose node consist item user together item content user profile social network information incorporate user rating edge setting graph model model provides personalized recommendation prediction individual group proposed algorithm evaluated MovieLens Epinions datasets Experimental result show proposed method perform well compared graphbased method especially cold start case Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03977284952998161, -0.013768618926405907, 0.0045171258971095085, -0.03113686479628086, -0.018398769199848175, -0.028498470783233643, -0.012127713300287724, -0.020074328407645226, 0.035360053181648254, -0.011577989906072617, 0.0033016095403581858, 0.02054073102772236, 0.0011517773382365704, 0.06180737912654877, -0.00864762905985117, -0.042128533124923706, -0.008423957042396069, -0.0216683279722929, 0.006171657703816891, -0.03676502779126167, 0.00663144513964653, -0.0036108188796788454, 0.04386536031961441, -0.004772226791828871, 0.03656008094549179, 0.027742525562644005, -0.0023480630479753017, 0.01431065984070301, -0.003509208094328642, -0.07847082614898682, -0.010965525172650814, 0.027089372277259827, 0.005084848962724209, 0.03609773889183998, 2.0712093373731477e-06, -0.017891494557261467, -0.007207729388028383, -0.03233953192830086, 0.06360301375389099, -0.013298152014613152, 0.036799799650907516, 0.09048707038164139, 0.03718169778585434, 0.024537550285458565, -0.0488448329269886, 0.025839710608124733, 0.01306356955319643, 0.04171309620141983, -0.023870432749390602, -0.007055455818772316, -0.01645045168697834, -0.05338909849524498, -0.011744420044124126, -0.03342379629611969, 0.023861229419708252, -0.01044528465718031, 0.03641326725482941, 0.02427518554031849, 0.01767478510737419, -0.0040167756378650665, -0.015832075849175453, -0.051666125655174255, -0.025898339226841927, -0.001546156476251781, 0.07836579531431198, 0.0019307660404592752, -0.002021587686613202, -0.02940664254128933, -0.0033416198566555977, 0.06825419515371323, 0.03865262120962143, -0.012628313153982162, 0.02702729031443596, 0.021276181563735008, 0.016377344727516174, 0.06089388579130173, -0.03163418546319008, 0.006798545829951763, -0.014156205579638481, 0.029551686719059944, -0.03629317507147789, 0.05757501348853111, 0.044134169816970825, 0.01609172858297825, 0.06446262449026108, 0.0820903405547142, 0.02549411728978157, 0.03090941533446312, 0.009394224733114243, -0.01155279204249382, 0.061323974281549454, -0.045701753348112106, 0.05918886512517929, 0.01101769506931305, 0.006518114823848009, -0.011218191124498844, -0.009872264228761196, 0.03420329838991165, 0.03858695179224014, -0.027754763141274452, 0.021617110818624496, -0.042056888341903687, 0.04989758878946304, 0.029272878542542458, 0.03361792862415314, -0.05050677806138992, -0.005767947994172573, 0.007131130900233984, 0.03738901764154434, 0.031032798811793327, -0.015237061306834221, 0.018439192324876785, 0.0153491897508502, 0.06326235085725784, -0.018170233815908432, -0.05132296308875084, -0.06026451662182808, 0.031451087445020676, -0.026535693556070328, 0.008282964117825031, 0.05647243559360504, 0.06153085455298424, 0.04850742965936661, 0.0380546860396862, -0.05232328549027443, -0.027602382004261017, -0.06308383494615555, 0.022977028042078018, 0.00781784113496542, 0.08032972365617752, 0.05489769205451012, -0.028912337496876717, 0.0417252816259861, -0.006617949344217777, 0.004107333719730377, 0.027860127389431, 0.06081823632121086, -0.03915062174201012, -0.032615624368190765, -0.02580736018717289, 0.027324171736836433, -0.012304301373660564, -0.06775271147489548, -0.08537889271974564, 0.034282151609659195, 0.031180549412965775, 0.0009402703726664186, 0.023511692881584167, 0.02128627710044384, -0.02813793160021305, -0.068203866481781, 0.002949757967144251, 0.04218960553407669, 0.0033454494550824165, 0.019455887377262115, 0.003819603705778718, 0.04254450649023056, -0.059582170099020004, -0.018965184688568115, 0.04255019500851631, 0.05586080998182297, 0.024469828233122826, -0.01254427433013916, 0.020818624645471573, -0.02377481944859028, 0.007972787134349346, 0.05499012768268585, 0.003744489513337612, -0.048287395387887955, -0.008073121309280396, -0.034809671342372894, 0.050802119076251984, -0.024845950305461884, -0.01911679282784462, 0.004911771509796381, -0.007926760241389275, -0.009928569197654724, 0.06376150250434875, 0.052728984504938126, 0.05012821406126022, -0.03660820424556732, -0.027134427800774574, 0.037648603320121765, 0.07627428323030472, -0.04305301606655121, -0.02928772009909153, 0.03163670003414154, 0.027212349697947502, -0.03689929097890854, 0.039543040096759796, 0.04638217017054558, -0.0086215790361166, 0.11583036929368973, -0.01641988195478916, 0.040845077484846115, 0.0022820301819592714, -0.034634627401828766, -0.04455142095685005, 0.04628794640302658, -0.013337453827261925, -0.014064664952456951, 0.019353345036506653, 0.036748018115758896, 0.0750470757484436, 0.01752350851893425, 0.019381897523999214, 0.020333969965577126, -0.010820284485816956, -0.02515975758433342, -0.11388292163610458, 0.05200718343257904, -0.03173311427235603, -0.061844851821660995, -0.057444144040346146, -0.035904817283153534, 0.08527328819036484, -0.013041796162724495, 0.03562876209616661, -0.024653218686580658, 0.030327292159199715, 0.009083016775548458, 0.014678001403808594, -0.014837154187262058, -0.014491498470306396, -0.01793753169476986, 0.047746170312166214, 0.020515965297818184, -0.019443834200501442, 0.037940941751003265, 0.04543595016002655, 0.06426462531089783, -0.023793330416083336, 0.031713902950286865, 0.01764802634716034, -0.04632187262177467, 0.0012045446783304214, 0.04795556887984276, 0.022776488214731216, 0.005165683571249247, -0.022497810423374176, 0.06304393708705902, 0.06302741169929504, 0.027969123795628548, -0.034481827169656754, 0.03142834082245827, -0.008092332631349564, 0.0034687132574617863, 0.03517752140760422, 0.01091890037059784, 0.01747649349272251, 0.036707401275634766, -0.005559532903134823, 0.04156336933374405, -0.010794826783239841, 0.024519845843315125, -0.016291609033942223, -0.012443196028470993, 0.025066042318940163, -0.06347259134054184, 0.01554636750370264, -0.015415097586810589, 0.02996019460260868, -0.007821576669812202, 0.03691333532333374, -0.02870590053498745, 0.0011480634566396475, -0.0101845758035779, -0.00698807742446661, -0.015508021228015423, -0.001300371834076941, 0.0028221472166478634, -0.005956532433629036, 0.010899403132498264, 0.003182800021022558, -0.03639537841081619, -0.030042635276913643, 0.03396055847406387, -0.02548227645456791, -0.03225529566407204, -0.015888765454292297, 0.023607904091477394, -0.011890691705048084, -0.016145529225468636, -0.044393423944711685, -0.030463295057415962, 0.0011230622185394168, 0.02200726419687271, -0.051530033349990845, -0.0028869675006717443, -0.010326053947210312, -0.06453720480203629, -0.028670936822891235, -0.02383013814687729, 0.021129148080945015, -0.046186670660972595, -0.00380183313973248, -0.001334557426162064, -0.046418704092502594, -0.005541425663977861, 0.0068962606601417065, 0.014066768810153008, -0.022517159581184387, 0.014653815887868404, -0.021301615983247757, -0.010618896223604679, 0.05819982662796974, -0.026331504806876183, -0.047138653695583344, -0.008865746669471264, -0.06926652044057846, 0.02514752559363842, -0.004999796859920025, -0.03294423222541809, -0.004181801341474056, -0.0037360836286097765, 0.047801196575164795, 0.005751215387135744, -0.01372728031128645, -0.007633714471012354, 0.014082747511565685, 0.021113982424139977, 0.041576456278562546, 0.04523279145359993, 0.01941564492881298, 0.03119610995054245, -0.002586636459454894, -0.06426388770341873, 0.020936746150255203, 0.003765171393752098, 0.04628309607505798, 0.017960969358682632, -0.07412631064653397, 0.0029767858795821667, 0.0033359751105308533, -0.011109772138297558, 0.07513874024152756, -0.024247735738754272, -0.045836735516786575, 0.09026017040014267, -0.00837356224656105, 0.032051291316747665, 0.04342207685112953, 0.013777115382254124, -0.08641345053911209, -0.050899047404527664, -0.01495192851871252, -0.007042569573968649, -0.051085323095321655, 0.05151323601603508, -0.0356302484869957, -0.043798889964818954, 0.009834745898842812, -0.02782619185745716, -0.0036590266972780228, 0.03555542603135109, 0.027660086750984192, 0.0181498434394598, -0.10029570013284683, -0.029317686334252357, 0.02002168446779251, 0.04556892067193985, 0.045581668615341187, -0.004757522605359554, -0.04027332365512848, -0.06568457186222076, -0.007736897096037865, 0.0063136424869298935, 0.016841355711221695, -0.029813140630722046, 0.04086698964238167, -0.0010353690013289452, 0.005879204720258713, 0.048820845782756805, 0.02012110874056816, 0.031641531735658646, -0.06916143000125885, -0.0047340067103505135, -0.012883071787655354, 0.02667653001844883, 0.04958139732480049, 0.05063023045659065, -0.015094203874468803, 0.002949236426502466, -0.005090875085443258, 0.034266889095306396, 0.00948585756123066, -0.05287749692797661, 0.02600790001451969, -0.023171011358499527, 0.054698191583156586, 0.00948003027588129, -0.017098626121878624, 0.02510479837656021, -0.06113226339221001, -0.004510162863880396, -0.01721350848674774, -0.06844372302293777, 0.008721647784113884, -0.027302082628011703, 0.005049698054790497, 0.0063467142172157764, -0.026606082916259766, 0.014506995677947998, 0.093553826212883, -0.035666223615407944, 0.06624534726142883, 0.013545642606914043, 0.01995498687028885, -0.04625516012310982, -0.05058271437883377, -0.043380316346883774, 0.05382714048027992, -0.013819513842463493, 0.005626338999718428, 0.02921486087143421, -0.0006054430268704891, 0.03356483206152916, -0.07029904425144196, 0.022166991606354713, -0.012190188281238079, -0.03859718516469002, -0.008734269998967648, 0.05898790806531906, -0.03392038121819496, -0.05845267325639725, -0.026462797075510025, 0.04846152290701866, 0.004944689571857452, 0.004377729259431362, -0.04537107050418854, -0.022888464853167534, 0.010495644994080067, -0.013127901591360569, 0.0008739875629544258, 0.02369195967912674, -0.019558222964406013, 0.0033437805250287056, -0.02039054036140442, -0.009632202796638012, -0.050999805331230164, -0.027198949828743935, -0.044139742851257324, 0.045442257076501846, -0.007008585147559643, 0.030215095728635788, 0.00899859145283699, -0.05348113179206848, 0.03743256628513336, -0.029255719855427742, 0.03349534422159195, 0.023913271725177765, -0.022192731499671936, 0.0008352082222700119, -0.014843527227640152, -0.05016602203249931, -0.013959837146103382, -0.04566512629389763, -0.05759545415639877, -0.05282329022884369, -0.04153985157608986, 0.06994658708572388, 0.013381262309849262, 0.0037271585315465927, -0.0515982024371624, -0.02705506980419159, 0.008623306639492512, -0.07604455202817917, 0.002998596988618374, -0.008462410420179367, -0.01175323873758316, 0.0036783020477741957, -0.01987534761428833, 0.012323425151407719, -0.03151572123169899, -0.012768851593136787, -0.050833560526371, -0.005695848260074854, -0.07620783895254135, -0.04643113166093826, -0.03032531961798668, -0.004527132026851177, -0.002607645932585001, 0.025592433288693428, 0.04484523832798004, 0.0028820219449698925, 9.72332782112062e-05, -0.0030539999715983868, -0.01912442222237587, -0.018718233332037926, -0.021930264309048653, 0.04813215881586075, -0.03011484257876873, -0.02468094974756241, -0.04187994450330734, -0.026998426765203476, 0.0039826943539083, -0.0006166408420540392, 0.007942522875964642, -0.0032569151371717453, -0.012011534534394741, 0.0032305836211889982, 0.01554881688207388, 0.03438403084874153, -0.019714662805199623, 0.025763047859072685, 0.028809791430830956, -0.02419811300933361, 0.015365065075457096, -0.049722012132406235, -0.00632998114451766, -0.006065741181373596, -0.006965851876884699, 0.004904831759631634, -0.004532051272690296, 0.0022662398405373096, 0.03837985172867775, -0.011706136167049408, -0.02044162154197693, 0.008770494721829891, -0.020583702251315117, 0.011943546123802662, -0.0398402139544487, -0.0046907938085496426, -0.06687206774950027, -0.028684528544545174, 0.03416094556450844, 0.04111082851886749, 0.012980512343347073, 0.1031700000166893, 0.050194427371025085, 0.02031581848859787, -0.07923667877912521, 0.01637422852218151, -0.11147666722536087, 0.0008208680083043873, 0.047103408724069595, 0.01384257897734642, 0.08756162226200104, -0.05094467103481293, -0.020160429179668427, -0.0025280159898102283, -0.02527051419019699, 0.025638895109295845, -0.01791989989578724, 0.05590943619608879, -0.03884293511509895, 0.03945573419332504, 0.005870964378118515, -0.021630313247442245, 0.044651977717876434, -0.07174234837293625, -0.02608729712665081, 0.018693553283810616, 0.010078884661197662, -0.03319551795721054, -6.39717837776111e-33, 0.03628900647163391, -0.042773135006427765, 0.0007251604693010449, 0.07275433838367462, -0.022761685773730278, -0.05987566336989403, 0.00843867938965559, 0.024296969175338745, 0.048186980187892914, 0.03194228559732437, 0.015342293307185173, 0.014902791939675808, 0.00259268912486732, 0.008916693739593029, 0.0067464690655469894, -0.011989085003733635, -0.006626027636229992, 0.026890413835644722, 0.05200377479195595, -0.021540625020861626, 0.032497089356184006, 0.03218628093600273, -0.03868493065237999, -0.07071730494499207, -0.006096229888498783, -0.056431498378515244, 0.013122880831360817, -0.04312317445874214, 0.023341234773397446, 0.0062506599351763725, 0.017187321558594704, -0.008007151074707508, -0.009976116009056568, -0.003461659885942936, 0.010303390212357044, -0.027379704639315605, -0.07957729697227478, 0.0004867645038757473, -0.03063727542757988, 0.019688576459884644, -0.007994121871888638, 0.030736779794096947, 0.014428731985390186, 0.0015828482573851943, -0.0017182494048029184, 0.023565949872136116, 0.053791340440511703, 0.01158952061086893, -0.06332014501094818, 0.01837475411593914, 0.048668272793293, 0.027935653924942017, -0.006784314755350351, 0.016727278009057045, -0.024036819115281105, -0.010395814664661884, -0.037175267934799194, 0.03814610466361046, -0.02771838568150997, 0.019195666536688805, -0.0822712779045105, -0.013635626994073391, -0.0475790798664093, -0.027775529772043228, 0.004718311131000519, 0.00952677708119154, -0.03486089035868645, -0.03334275260567665, 0.034787021577358246, -0.0007984503172338009, -0.06934204697608948, 0.06028420105576515, -0.01108034048229456, 0.033044759184122086, -0.057136982679367065, -0.055419567972421646, -0.04980279505252838, 0.04168837517499924, 0.025993777438998222, -0.024042589589953423, 0.045882340520620346, -0.002171377884224057, 0.006526703480631113, 0.0007518810452893376, 0.05064556375145912, -0.07191682606935501, -0.024698559194803238, -0.06031877174973488, -0.023384016007184982, 0.03331806883215904, -0.017202012240886688, -0.005148660391569138, -0.029154639691114426, -0.03638205677270889, -0.05142652988433838, -0.0016130807343870401, -0.02947888895869255, 0.01454834919422865, -0.0105038583278656, -0.005153475794941187, -0.013012454845011234, 0.013652931898832321, -0.05885430797934532, -0.0695435032248497, -0.045892082154750824, 0.0004553184553515166, 0.014504904858767986, 0.03594524785876274, -0.005133356433361769, -0.03497718647122383, 0.04895266145467758, -0.03654748573899269, -0.0114394910633564, 0.0018850464839488268, -0.0010760563891381025, 0.025131557136774063, -0.03206595033407211, 0.09591028094291687, 0.0317842997610569, 0.08669082820415497, 0.016559012234210968, -0.06076439097523689, 0.012956691905856133, -0.03460896015167236, -0.016374273225665092, -0.02467968501150608, -0.040239062160253525, 0.040896207094192505, 0.03281555697321892, -0.040965255349874496, -0.011256816796958447, -0.028961120173335075, 2.7138497671330697e-07, -0.003302615834400058, 0.02124345861375332, -0.05923421308398247, -0.01626499369740486, 0.006058862432837486, 0.0013856859877705574, 0.009922447614371777, 0.04376368224620819, 0.02844383381307125, -0.001991149503737688, 0.011456375010311604, 0.002016851445659995, -0.0299509447067976, 0.009674645960330963, -0.044628068804740906, -0.0010614743223413825, -0.053470026701688766, -0.01303287222981453, -0.026222500950098038, -0.023219257593154907, -0.07984934747219086, 0.06582873314619064, 0.1183353066444397, 0.018593885004520416, -0.021507252007722855, 0.013524865731596947, 0.034236542880535126, 0.01064648013561964, -0.05415946617722511, -0.07068581134080887, 0.021506603807210922, -0.026976658031344414, -0.03383759781718254, 0.028995443135499954, -0.03818581998348236, 0.008366379886865616, 0.017934193834662437, -0.027526894584298134, -0.04864928126335144, -0.001469865208491683, 0.016589391976594925, -0.012212804518640041, 0.006140104029327631, 0.0028525409288704395, 0.02005169913172722, 0.08040442317724228, -0.04970330372452736, 0.016756635159254074, -0.0260170791298151, 0.007292619906365871, 0.030241936445236206, 0.026475315913558006, -0.00794302485883236, 0.005583987105637789, 0.02509203925728798, -0.014110216870903969, 0.0042549301870167255, -0.018496589735150337, 0.03567363694310188, -0.05145208537578583, 0.015897130593657494, -0.029152164235711098, 0.03345580771565437, 0.015157235786318779, -0.012406189925968647, 0.025339260697364807, 0.020884016528725624, 2.2736916828833554e-34, 0.05703587830066681, 0.047219906002283096, -0.03193427622318268, -0.11178423464298248, -0.0159559715539217, -0.04526146128773689, -0.04640340432524681, 0.0039972541853785515, 0.06975293904542923, -0.04291987419128418, -0.041918713599443436]

['Peter Sarlin']

1208.1819v1

This paper adopts and adapts Kohonen's standard Self-Organizing Map (SOM) for exploratory temporal structure analysis. The Self-Organizing Time Map (SOTM) implements SOM-type learning to one-dimensional arrays for individual time units, preserves the orientation with short-term memory and arranges the arrays in an ascending order of time. The two-dimensional representation of the SOTM attempts thus twofold topology preservation, where the horizontal direction preserves time topology and the vertical direction data topology. This enables discovering the occurrence and exploring the properties of temporal structural changes in data. For representing qualities and properties of SOTMs, we adapt measures and visualizations from the standard SOM paradigm, as well as introduce a measure of temporal structural changes. The functioning of the SOTM, and its visualizations and quality and property measures, are illustrated on artificial toy data. The usefulness of the SOTM in a real-world setting is shown on poverty, welfare and development indicators.

Self-Organizing Time Map: An Abstraction of Temporal Multivariate Patterns

http://arxiv.org/pdf/1208.1819v1

Title SelfOrganizing Time Map Abstraction Temporal Multivariate Patterns Summary paper adopts adapts Kohonens standard SelfOrganizing Map SOM exploratory temporal structure analysis SelfOrganizing Time Map SOTM implement SOMtype learning onedimensional array individual time unit preserve orientation shortterm memory arranges array ascending order time twodimensional representation SOTM attempt thus twofold topology preservation horizontal direction preserve time topology vertical direction data topology enables discovering occurrence exploring property temporal structural change data representing quality property SOTMs adapt measure visualization standard SOM paradigm well introduce measure temporal structural change functioning SOTM visualization quality property measure illustrated artificial toy data usefulness SOTM realworld setting shown poverty welfare development indicator Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.046924907714128494, 0.0448126383125782, -0.056186188012361526, -0.016106417402625084, -0.02442609705030918, -0.003573003225028515, 0.06771527975797653, -0.0052459524013102055, -0.008492781780660152, 0.014870432205498219, 0.04684275761246681, 0.0687222108244896, 0.012016016989946365, 0.09537918120622635, -0.022091597318649292, -0.08556254208087921, 0.034976426512002945, 0.010203917510807514, -0.06006123870611191, 0.03167816996574402, -0.0013592781033366919, -0.025441382080316544, -0.043425340205430984, 0.013162820599973202, -0.010520314797759056, -0.037865716964006424, -0.04744894802570343, -0.043740976601839066, 0.012686965987086296, -0.06421349197626114, 0.008713257499039173, -0.002765612443909049, 0.008383328095078468, 0.005051556974649429, 2.3875568331277464e-06, -0.004229144658893347, -0.0472085066139698, -0.01060656551271677, 0.042894408106803894, 0.05402994900941849, 0.021051649004220963, -0.01579601690173149, -0.006192774511873722, -0.03847114369273186, -0.0365341380238533, -0.004646314308047295, 0.01546569261699915, -0.004286409355700016, 0.062201447784900665, -0.020157938823103905, -0.006735625676810741, -0.015102224424481392, 0.01768692210316658, 0.009963437914848328, 0.0010687726316973567, 0.03965640068054199, -0.013372781686484814, -0.0014874875778332353, 0.05621175840497017, -0.01626228168606758, -0.01120120007544756, 0.01491722371429205, 0.0011839235667139292, -0.012722996063530445, 0.10543762147426605, 0.03267398849129677, 0.03548824042081833, 0.006644777487963438, -0.036139123141765594, 0.03579661250114441, 0.03997094929218292, 0.007894341833889484, 0.058481376618146896, 0.014005757868289948, -0.03907664865255356, 0.028091976419091225, -0.04026893526315689, -0.033074889332056046, 0.003125215182080865, -0.005817136261612177, -0.0039342353120446205, 0.10837339609861374, -0.03905162960290909, -0.008521378971636295, -0.011654045432806015, 0.041318852454423904, -0.016981137916445732, -0.018970387056469917, -0.08479288220405579, -0.0640571117401123, 0.07100421190261841, -0.0014080690452829003, 0.04513203352689743, 0.05666719377040863, 0.009600239805877209, -0.030619872733950615, 0.03224670886993408, -0.038020793348550797, 0.041966475546360016, -0.0748385339975357, 0.0651346817612648, 0.0247610192745924, -0.002122222911566496, 0.03198666498064995, 0.026124928146600723, 0.03746847063302994, -0.041008394211530685, -0.02765120193362236, -0.025482377037405968, 0.046932850033044815, -0.04508509486913681, 0.00387744908221066, -0.0045661041513085365, 0.04760365188121796, 0.00997055135667324, 0.04149258881807327, -0.05156400799751282, 0.0467490591108799, 0.0014304175274446607, -0.04280484467744827, -0.022498616948723793, -0.000875825178809464, 0.022164102643728256, 0.016805971041321754, -0.05139615386724472, -0.011307714506983757, -0.08121968805789948, -0.004092813469469547, -0.05439382418990135, 0.021163351833820343, 0.02673882618546486, -0.012477591633796692, 0.016787981614470482, 0.007599566597491503, -0.048553965985774994, 0.044845856726169586, 0.007875739596784115, 0.019636819139122963, -0.1112060546875, -0.047929976135492325, -0.006845505442470312, 0.017399704083800316, 0.007071392610669136, -0.04966612532734871, -0.01678464747965336, -0.03827943280339241, -0.025921586900949478, 0.09288011491298676, -0.019107311964035034, -0.007195715792477131, -0.03396272286772728, 0.050854481756687164, 0.017534779384732246, 0.05808607488870621, 0.041742902249097824, -1.6868927559698932e-05, 0.051409073173999786, -0.024238530546426773, 0.04286743700504303, -0.028949074447155, 0.004806071519851685, -0.05134065821766853, 0.0075590419583022594, -0.01967673748731613, -0.02157975360751152, -0.015498341992497444, -0.0582575723528862, 0.014574270695447922, -0.0339273102581501, -0.006919948849827051, -0.009246432222425938, -0.027196472510695457, -0.007217925973236561, 0.017076220363378525, 0.017955712974071503, 0.042897533625364304, 0.0407419390976429, 0.05199313536286354, 0.005895642563700676, 0.020898059010505676, 0.002377268625423312, -0.02047133259475231, 0.034788571298122406, 0.07865472882986069, 0.023365717381238937, -0.02896156720817089, -0.08231808990240097, 0.01840180903673172, -0.019204802811145782, -0.04282834753394127, 0.02848139964044094, 0.015140758827328682, 0.0231037400662899, -0.05847411975264549, 0.02810111828148365, -0.005105788353830576, 0.03267243131995201, 0.0007146575953811407, 0.012453863397240639, 0.01626100018620491, -0.05379118770360947, -0.037737127393484116, 0.06266340613365173, 0.03186308592557907, 0.00021016213577240705, -0.05739926919341087, -0.006441995035856962, 0.0050993855111300945, 0.04605180397629738, -0.041144222021102905, 0.06323446333408356, 0.013267716392874718, -0.026072243228554726, 0.0023706492502242327, -0.010627138428390026, 0.052126143127679825, -0.011617770418524742, 0.02049376256763935, -0.040069010108709335, 0.05418022722005844, -0.018460342660546303, 0.007067730184644461, 0.03335796669125557, -0.005335625261068344, -0.0006899380823597312, 0.020485559478402138, 0.02811395563185215, 0.02817656844854355, 0.0005408906727097929, 0.038673534989356995, 0.029840152710676193, -0.01756923273205757, 0.061689671128988266, -0.02599858120083809, 0.013503138907253742, 0.05727202072739601, -0.050235480070114136, 0.018328964710235596, -0.011633726768195629, -0.00031547952676191926, -0.010842157527804375, 0.024476654827594757, 0.0014451321912929416, -0.0413798987865448, 0.07868574559688568, -0.004351987969130278, 0.03859406337141991, -0.01737602986395359, 0.028166016563773155, 0.008936041966080666, 0.04246750846505165, -0.010369587689638138, 0.0404568612575531, -0.010475912131369114, -0.03752085566520691, -0.06188225373625755, 0.03131202608346939, 0.016582312062382698, 0.007766125723719597, 0.07122941315174103, -0.006011627148836851, -0.05030521750450134, -0.0447738878428936, -0.009613845497369766, 0.008763130754232407, -0.030146341770887375, 0.005592769477516413, -0.026742415502667427, -0.05915425345301628, 0.042957596480846405, 0.00831046886742115, -0.007412829902023077, -0.012890014797449112, -0.003253895090892911, -0.015479816123843193, 0.018224934116005898, 0.03751470893621445, -0.022776195779442787, -0.03774244710803032, 0.07712101191282272, -0.023232383653521538, -0.044369008392095566, 0.002115017967298627, 0.0013797010760754347, -0.056510910391807556, 0.013732261024415493, 0.04283939301967621, -0.07208295911550522, 0.0013013406423851848, -0.061230480670928955, 0.01778228022158146, -0.03696371614933014, -0.006066581234335899, -0.025023415684700012, -0.014956621453166008, -0.005678647197782993, 0.06543236970901489, 0.013325413689017296, 0.033081620931625366, 0.04757443815469742, 0.03075994923710823, -0.05625860020518303, -0.024694934487342834, 0.037202563136816025, -0.010449188761413097, 0.08654533326625824, 0.07006800919771194, -0.011576163582503796, 0.025259288027882576, 0.022584518417716026, 0.03950702026486397, 0.020946037024259567, 0.006861165165901184, 0.011339129880070686, -0.03022129274904728, 0.031885724514722824, -0.05515242740511894, -0.0022359599824994802, -0.026676394045352936, -0.0058894031681120396, -0.023544760420918465, -0.022316306829452515, -0.014271248131990433, 0.05132562667131424, 0.0020617693662643433, 0.035484131425619125, -0.043205756694078445, -0.049417492002248764, 0.0352826826274395, -0.03748970106244087, 0.005012722220271826, 0.01655895821750164, -0.03776371851563454, 0.03222225233912468, -0.012238942086696625, -0.01415498461574316, -0.03150700777769089, -0.03620317578315735, -0.059495944529771805, -0.0076858531683683395, 0.02351321093738079, -0.019565749913454056, -0.03383173048496246, -0.03706489875912666, 0.06805419921875, -0.04508271440863609, -0.03442147374153137, -0.012116774916648865, 0.01313219778239727, 0.05512776970863342, -0.004185204394161701, 0.021889491006731987, 0.006812535226345062, -0.050615184009075165, 0.017537368461489677, 0.023755671456456184, -0.022321566939353943, -0.004015805199742317, -0.04971476271748543, 0.006644128821790218, 0.03219768777489662, -0.010971500538289547, 0.017495447769761086, -0.005793444812297821, -0.06407767534255981, 0.05171788111329079, -0.030160630121827126, -0.0012957045109942555, -0.0012432157527655363, 0.001529300701804459, -0.0194273442029953, -0.025710372254252434, 0.025066116824746132, 0.030715657398104668, 0.022849641740322113, -0.02384796179831028, 0.022331399843096733, -0.013148358091711998, -0.04242405295372009, -0.010674471035599709, 0.007087151985615492, -0.005209664814174175, 0.05892211198806763, -0.047468628734350204, -0.0009785613510757685, -0.051465682685375214, -0.03306389972567558, -0.018996132537722588, -0.023940924555063248, 0.026513459160923958, 0.014079916290938854, -0.07289449125528336, -0.029913578182458878, -0.005671713035553694, -0.026478534564375877, -0.011106482706964016, -0.07656490802764893, 0.009278074838221073, -0.015425527468323708, -0.01714164949953556, 0.0510086715221405, -0.12776827812194824, 0.025003958493471146, 0.024690205231308937, -0.0012214008020237088, 0.03343456983566284, 0.017307396978139877, 0.06194233149290085, -0.04182997718453407, -0.03814265877008438, -0.009568789042532444, 0.07064931094646454, 0.03534003719687462, -0.04881337285041809, 0.027621129527688026, 0.0587591752409935, 8.894146594684571e-05, -0.00863953959196806, 0.05391092225909233, -0.012980570085346699, 0.030691565945744514, 0.029520535841584206, 0.09530852735042572, -0.008910357020795345, 0.02427774667739868, -0.08134086430072784, -0.043195806443691254, -0.0008781151846051216, -0.04320743307471275, -0.02627844735980034, 0.009628450497984886, -0.014744943007826805, 0.015390056185424328, -0.006709147710353136, -0.03170303255319595, -0.06673702597618103, -0.022219395264983177, -0.014632186852395535, 0.013952714391052723, -0.029112782329320908, -0.025258582085371017, -0.04950937256217003, 0.05451524257659912, -0.009088253602385521, -0.02896103635430336, 0.03755447268486023, -0.028378453105688095, -0.050516486167907715, -0.07066065073013306, 0.031198950484395027, 0.0061500463634729385, -0.007029727101325989, -0.01866547204554081, -0.01695682853460312, 0.034543830901384354, 0.006307708565145731, -0.04812804237008095, -0.0330057330429554, -0.014046978205442429, 0.0593876950442791, 0.021311677992343903, 0.010911553166806698, -0.04264665022492409, 0.010445335879921913, 0.07157059013843536, 0.09036862105131149, 4.304121830500662e-05, 0.016918474808335304, -0.026275666430592537, -0.05036718770861626, 0.00727394875138998, -0.008589236065745354, -0.005558070261031389, 0.044718436896800995, 0.06790957599878311, -0.04577530547976494, -0.031201275065541267, -0.042461927980184555, 0.08953404426574707, -0.016238050535321236, -0.048870671540498734, 0.09931255131959915, 0.08822675049304962, -0.016183558851480484, -0.018948212265968323, 2.420997952867765e-05, -0.06236021965742111, -0.004623040556907654, -0.0007772527751512825, 0.002413724781945348, 0.008777112700045109, 0.0058035897091031075, -0.04985837638378143, 0.014548971317708492, 0.025019749999046326, -0.04204387217760086, -0.002037925412878394, 0.03646812215447426, -0.0442512109875679, 0.008195657283067703, -0.05902541056275368, 0.05669042468070984, 0.016832485795021057, 0.016485687345266342, -0.014336333610117435, 0.021775847300887108, 0.027496933937072754, 0.005452240351587534, -0.014178616926074028, 0.041532594710588455, 0.0024408167228102684, -0.0149711724370718, 0.017923031002283096, -0.012415398843586445, 0.012358295731246471, -0.046671461313962936, 0.024538258090615273, -0.02768583409488201, 0.02390444092452526, -0.011243540793657303, 0.013794784434139729, 0.019921723753213882, 0.028111781924962997, -0.03296607360243797, 0.0518348254263401, 0.020165329799056053, -0.026397371664643288, -0.028864793479442596, -0.0403788797557354, 0.02695879340171814, 0.03471456468105316, -0.022402187809348106, -0.03314715996384621, -0.019381212070584297, -0.05374715104699135, 0.051301803439855576, 0.010054231621325016, -0.042605768889188766, -0.023063508793711662, -0.031705163419246674, -0.05408577248454094, 0.004370945040136576, 0.02055829018354416, -0.0017487452132627368, 0.04208334535360336, 0.0021131187677383423, -0.0010002522030845284, -0.012588228099048138, 0.0018114610575139523, 0.016478799283504486, -0.006240752525627613, -0.0003671147278510034, -0.018243934959173203, -0.06141119822859764, -0.024761071428656578, -6.943169055095169e-33, -0.029473012313246727, -0.07326748222112656, 0.01632540673017502, -0.029853425920009613, -0.03339935094118118, -0.00847734697163105, 0.0020290433894842863, 0.015210943296551704, 0.004077867139130831, -0.037432845681905746, 0.0017986968159675598, 0.01392418798059225, 0.012631895020604134, -0.019021742045879364, 0.07845588028430939, 0.06292899698019028, 0.006805657874792814, -0.03217851370573044, 0.008470580913126469, -0.02604944445192814, 0.026377251371741295, 0.015547648072242737, 0.024949360638856888, -0.043600890785455704, -0.026010144501924515, 0.023675603792071342, -0.013629800640046597, 0.001561083015985787, 0.045655615627765656, 0.011845609173178673, -0.021610764786601067, -0.03330983594059944, 0.012802154757082462, 0.013573378324508667, -0.029705053195357323, 0.01403080951422453, -0.08508993685245514, -0.07865364849567413, -0.06421301513910294, 0.0240964125841856, -0.02605110965669155, -0.02478834055364132, 0.029793204739689827, 0.020912159234285355, -0.018575672060251236, 0.021733585745096207, 0.038357991725206375, -0.008428354747593403, -0.000768299272749573, 0.03204518184065819, -0.004265706520527601, 0.057158201932907104, -0.04739163815975189, 0.014477105811238289, 0.025811664760112762, 0.01807933859527111, 0.0019362552557140589, -0.031278129667043686, -0.033049795776605606, 0.07125154882669449, 0.0018211057176813483, -0.016983527690172195, 0.006301990244537592, 0.003386442782357335, 0.0754532665014267, -0.00016286929894704372, -0.011928914114832878, 0.008359061554074287, 0.021791893988847733, 0.010482941754162312, 0.013714991509914398, 0.00021239431225694716, -0.033833250403404236, -0.029199009761214256, 0.07665081322193146, -0.03447103127837181, -0.019475659355521202, 0.04441678151488304, -0.00031034465064294636, -0.011277640238404274, -0.03824648633599281, 0.0198566485196352, -0.02051185443997383, 0.01904052123427391, 0.04717398062348366, 0.025595368817448616, -0.01436636596918106, 0.002365422435104847, 0.03066619113087654, -0.017708899453282356, 0.006286116316914558, 0.043889645487070084, -0.03744642436504364, -0.006353367120027542, -0.014047120697796345, -0.042078886181116104, -0.0014615365071222186, 0.011291701346635818, 0.02601322904229164, -0.016376951709389687, -0.061024077236652374, -0.03546997904777527, -0.043934229761362076, 0.024357670918107033, 0.02831117995083332, 0.00311464536935091, -0.01258732657879591, 0.04579177871346474, -0.04693190008401871, -0.00499710300937295, 0.0523783378303051, -0.050837546586990356, 0.026423698291182518, -0.0999954417347908, 0.017295803874731064, -0.06615643948316574, -0.0013889314141124487, 0.08473514765501022, 0.05388676002621651, 0.005966260097920895, -0.054311081767082214, 0.002780826296657324, -0.023421114310622215, 0.021430647000670433, 0.026740971952676773, -0.009750771336257458, -0.04873374104499817, -0.007625973783433437, 0.037007126957178116, -0.029370270669460297, -0.01411013025790453, -0.005097880959510803, 3.0651253268842993e-07, -0.025646936148405075, 0.08245843648910522, 0.026822449639439583, 0.031609050929546356, 0.04868260398507118, -0.0116643151268363, -0.03661300614476204, 0.041079044342041016, -0.08600179851055145, 0.04514350742101669, 0.07630665600299835, -0.021992195397615433, 0.044058315455913544, 0.043240826576948166, 0.031291939318180084, -0.034377727657556534, -0.02186601608991623, 0.008659840561449528, -0.0849643275141716, 0.006417113821953535, 0.07280465215444565, 0.007793831638991833, 0.05374300852417946, 0.019668133929371834, -0.005042795091867447, 0.002830639248713851, 0.04904738441109657, 0.012396018952131271, 0.014203748665750027, -0.02371741645038128, -0.047090351581573486, -0.021223876625299454, -0.047698136419057846, -0.057089708745479584, -0.016120094805955887, 0.006965769920498133, -0.05240796133875847, 0.0033084119204431772, 0.0008757019531913102, -0.0022473966237157583, 0.06527804583311081, -0.03045012429356575, 0.00611781096085906, 0.0027999121230095625, 0.04394391179084778, -0.023302413523197174, -0.028959956020116806, 0.010178101249039173, 0.01245145220309496, 0.08767061680555344, 0.054646868258714676, 0.03502792492508888, -0.05285688117146492, 0.008517690002918243, -0.0024833756033331156, -0.03160089626908302, 0.02189439721405506, 0.00656186742708087, 0.03119618073105812, 0.03651051223278046, 0.0033321359660476446, 0.00126375793479383, -0.03121163323521614, 0.03567211329936981, 0.020899521186947823, 0.025695225223898888, -0.02879698947072029, 3.24243264860783e-34, -0.006829173304140568, 0.0016837011789903045, -0.0348084382712841, -0.03437760844826698, -0.014623663388192654, 0.011076348833739758, 0.00453203683719039, 0.00936493556946516, 0.03426024690270424, -0.009102512151002884, -0.01933370903134346]

['Sahand Negahban', 'Benjamin I. P. Rubinstein', 'Jim Gemmell']

1208.1860v1

We consider a serious, previously-unexplored challenge facing almost all approaches to scaling up entity resolution (ER) to multiple data sources: the prohibitive cost of labeling training data for supervised learning of similarity scores for each pair of sources. While there exists a rich literature describing almost all aspects of pairwise ER, this new challenge is arising now due to the unprecedented ability to acquire and store data from online sources, features driven by ER such as enriched search verticals, and the uniqueness of noisy and missing data characteristics for each source. We show on real-world and synthetic data that for state-of-the-art techniques, the reality of heterogeneous sources means that the number of labeled training data must scale quadratically in the number of sources, just to maintain constant precision/recall. We address this challenge with a brand new transfer learning algorithm which requires far less training data (or equivalently, achieves superior accuracy with the same data) and is trained using fast convex optimization. The intuition behind our approach is to adaptively share structure learned about one scoring problem with all other scoring problems sharing a data source in common. We demonstrate that our theoretically motivated approach incurs no runtime cost while it can maintain constant precision/recall with the cost of labeling increasing only linearly with the number of sources.

Scaling Multiple-Source Entity Resolution using Statistically Efficient Transfer Learning

http://arxiv.org/pdf/1208.1860v1

Title Scaling MultipleSource Entity Resolution using Statistically Efficient Transfer Learning Summary consider serious previouslyunexplored challenge facing almost approach scaling entity resolution ER multiple data source prohibitive cost labeling training data supervised learning similarity score pair source exists rich literature describing almost aspect pairwise ER new challenge arising due unprecedented ability acquire store data online source feature driven ER enriched search vertical uniqueness noisy missing data characteristic source show realworld synthetic data stateoftheart technique reality heterogeneous source mean number labeled training data must scale quadratically number source maintain constant precisionrecall address challenge brand new transfer learning algorithm requires far le training data equivalently achieves superior accuracy data trained using fast convex optimization intuition behind approach adaptively share structure learned one scoring problem scoring problem sharing data source common demonstrate theoretically motivated approach incurs runtime cost maintain constant precisionrecall cost labeling increasing linearly number source Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.015625394880771637, 0.011896106414496899, 0.021129591390490532, -0.022104967385530472, 0.026374321430921555, 0.04109823331236839, 0.030849527567625046, 0.041065700352191925, 0.004682623781263828, -0.004581865854561329, -0.04604577273130417, -0.0012872660299763083, -0.01217725221067667, 0.01691576838493347, -0.013616117648780346, -0.054090797901153564, 0.028173014521598816, 0.04697643965482712, -0.011703538708388805, -0.017905570566654205, -0.0009337048977613449, 0.023391034454107285, 0.0124612832441926, -0.013698602095246315, -0.03743799403309822, 0.018629668280482292, 0.007934732362627983, -0.0025845596101135015, 0.0411231629550457, -0.02097448520362377, 0.026878152042627335, 0.005255811847746372, 0.006509131286293268, -0.016936706379055977, 2.07781772587623e-06, -0.026565341278910637, -0.06884939968585968, -0.0014421631349250674, 0.012689978815615177, -0.028674853965640068, 0.011916269548237324, -0.06046438589692116, 0.03369683027267456, 0.006453540176153183, -0.021200798451900482, -0.06315743178129196, 0.06039542704820633, 0.05310274288058281, 0.06157507002353668, 0.027590548619627953, -0.04809543117880821, -0.08224522322416306, -0.00014765842934139073, -0.0012019866844639182, -0.02492378279566765, -0.06570682674646378, 0.052478138357400894, 0.04609581083059311, -0.002211060142144561, 0.008026421070098877, -0.0009459755383431911, 0.05274498090147972, -0.03178254887461662, 0.005843267310410738, 0.018314817920327187, 0.03871197625994682, 0.0229592677205801, 0.03132665902376175, 0.021564412862062454, 0.06315094977617264, -0.016680825501680374, 0.03146863356232643, 0.05391542240977287, 0.01978369802236557, -0.011568667367100716, -0.006331456359475851, -0.01244261022657156, -0.04443957656621933, -0.0175307784229517, 0.024703962728381157, -0.07204123586416245, 0.007162656635046005, -0.019778285175561905, 0.002190191298723221, -0.06251055002212524, -0.008822144009172916, -0.002976394724100828, 0.02489742822945118, 0.005054392386227846, 0.006656519137322903, -0.0008167920168489218, -0.017124809324741364, 0.05146504566073418, 0.049421630799770355, -0.06348395347595215, 0.0220407135784626, -0.03640793636441231, -0.059502072632312775, 0.021303245797753334, -0.04609131067991257, 0.0075220465660095215, -0.040979042649269104, 0.008008284494280815, 0.04307897388935089, -0.03995231166481972, 0.0076917316764593124, -0.035296905785799026, 0.0339324027299881, -0.004269882570952177, -0.05605033412575722, -0.07441699504852295, 0.021531030535697937, -0.04358382150530815, 0.07854221016168594, -0.025108864530920982, 0.00446656160056591, -0.06652411073446274, -0.04040597751736641, -0.03084218129515648, 0.01040785200893879, 0.0035116681829094887, 0.00339470524340868, 0.011228618212044239, -0.04170932248234749, -0.029675230383872986, 0.06987706571817398, -0.06273362785577774, 0.004262825008481741, -0.04739272594451904, 0.007550704758614302, 0.04464779794216156, -0.0046721771359443665, 0.06682967394590378, -0.019626254215836525, 0.03904057294130325, 0.0066349501721560955, 0.004196877591311932, -0.010362230241298676, -0.09894964098930359, -0.026713894680142403, -0.005726702976971865, -0.0223349928855896, -0.05686879903078079, -0.0532069094479084, 0.060971830040216446, -0.024525882676243782, -0.02671010047197342, -0.045109283179044724, -0.013479344546794891, -0.01156901940703392, -0.08506307750940323, 0.09145507216453552, -0.055207137018442154, 0.05071775242686272, 0.06397627294063568, -0.024314897134900093, 0.031660158187150955, 0.016796661540865898, 0.03197174519300461, -0.028173290193080902, 0.002901463070884347, -0.010077299550175667, -0.01268627680838108, 0.007507359143346548, 0.03811321035027504, -0.02977844700217247, 0.023830272257328033, 0.0050236983224749565, 0.022775115445256233, 0.040249720215797424, 0.018549831584095955, 0.06444275379180908, 0.03141292557120323, -0.06436166167259216, 0.03317078948020935, 0.01042971108108759, -0.01930883340537548, 0.004374375566840172, -0.00897097960114479, 0.011319277808070183, -0.029501082375645638, -0.006537154782563448, 0.025620967149734497, 0.046407464891672134, 0.007175799459218979, -0.05323386192321777, 0.04405033588409424, 0.030915584415197372, -0.05011731758713722, 0.012470465153455734, 0.02424704097211361, 0.012629124335944653, -0.05597982183098793, -0.0005439767264761031, 0.06485722959041595, 0.02158660814166069, -0.008156421594321728, 0.038945119827985764, 0.01888967677950859, 0.020146667957305908, -0.01741146109998226, 0.006152460817247629, -0.040862876921892166, -0.0037530683912336826, -0.005990562494844198, -0.03886660560965538, -0.01844955049455166, -0.019251404330134392, 0.01602103002369404, -0.004379395395517349, 0.03795662149786949, -0.016014359891414642, 0.005135172978043556, -0.03190239146351814, -0.029568025842308998, 0.06638956069946289, -0.030883166939020157, 0.019322583451867104, 0.01866494119167328, 0.03823544457554817, 0.03465596213936806, -0.02978562004864216, 0.011362968944013119, 0.02026468701660633, -0.027601586654782295, 0.03914593532681465, 0.02728811837732792, 0.05341232195496559, -0.024301912635564804, 0.034318339079618454, -0.017405899241566658, -0.04022928327322006, 0.024567024782299995, -0.029603932052850723, -0.028269808739423752, -0.02179572731256485, 0.021963639184832573, -0.000522540183737874, 0.02038009837269783, -0.015862973406910896, -0.0021156396251171827, -0.002765798009932041, -0.01835460774600506, -0.03400438651442528, -0.060455843806266785, -0.023147612810134888, -0.02377535216510296, -0.0026217682752758265, 0.054865606129169464, 0.009165508672595024, 0.037777241319417953, -0.05687094107270241, 0.08705504238605499, 0.015105973929166794, 0.040162429213523865, -0.005270808469504118, -0.04009115323424339, 0.03794983774423599, -0.014702669344842434, 0.003758340375497937, -0.003754954319447279, -0.022768903523683548, -0.005665838252753019, 0.0038703421596437693, -0.04312347620725632, -0.05432708561420441, 0.018750928342342377, 0.005387592129409313, -0.003712873673066497, 0.04457880184054375, 0.02879064530134201, 0.004948431625962257, 0.033909596502780914, 0.02704092301428318, -0.010389079339802265, -0.02602500095963478, 0.0040014972910285, 0.018159804865717888, 0.013408211059868336, 0.06462247669696808, 0.010966304689645767, -0.04789343476295471, 0.03029762953519821, -0.01864103600382805, -0.03004176914691925, 0.03063596412539482, 0.03288014233112335, -0.07477130740880966, -0.046613551676273346, 0.05412992089986801, -0.08840179443359375, 0.012678186409175396, 0.03470005467534065, 0.03924524784088135, -0.031680651009082794, -0.00784496683627367, -0.027229752391576767, -0.011028271168470383, 0.00896872952580452, -0.0274746622890234, 0.006304950453341007, -0.0009053030516952276, -0.06002381816506386, 0.01901465281844139, 0.009465590119361877, 0.01737019419670105, 0.023890096694231033, -0.013515574857592583, 0.009981495328247547, -0.010208693332970142, -0.0015644605737179518, -0.01942623034119606, -0.037028998136520386, 0.00542127899825573, 0.008616193197667599, 0.011822274886071682, -0.04887250065803528, 0.03877872973680496, 0.017488982528448105, 0.03420468792319298, -0.03111138753592968, 0.0339088998734951, 0.046299684792757034, 0.02206539548933506, 0.018072927370667458, 0.012128163129091263, -0.016400421038269997, -0.008664015680551529, 0.04998736456036568, -0.0012505869381129742, 0.061731670051813126, -0.006484766956418753, -0.04797367379069328, -0.012035831809043884, 0.007068553939461708, 0.02394578792154789, -0.021161671727895737, 0.05680771917104721, 0.015984216704964638, 0.05712025240063667, -0.011363915167748928, -0.041214633733034134, -0.03917338699102402, 0.02275279350578785, 0.028402509167790413, -0.0007278784178197384, -0.00451176380738616, -0.00916508212685585, -0.07847218960523605, 0.04123620688915253, 0.015414342284202576, 0.039198487997055054, 0.026899339631199837, -0.038375500589609146, -0.0028709922917187214, 0.059549178928136826, -0.0024069922510534525, 0.004370194394141436, 0.0048124296590685844, -0.014500917866826057, -0.005367486272007227, 0.05697295442223549, -0.007956702262163162, 0.0025810336228460073, -0.011376149021089077, -0.01256771944463253, 0.013066187500953674, -0.07265651971101761, 0.023814009502530098, -0.029897406697273254, 0.022226225584745407, -0.01044800877571106, 0.017022186890244484, 0.04806366562843323, 0.02229274995625019, -0.009068300016224384, -0.025795506313443184, 0.023438047617673874, -0.0006362640997394919, 0.03356833755970001, 0.03422864153981209, -0.06881723552942276, 0.014873904176056385, -0.01858719252049923, -0.007518583443015814, 0.018924426287412643, -0.12967437505722046, -0.009258883073925972, -0.10573142766952515, 0.00019921647617593408, -0.02107764221727848, -0.07053463906049728, -0.06532435864210129, -0.057095956057310104, 0.03735600784420967, -0.005502061452716589, -0.023367201909422874, 0.025224467739462852, -0.048688266426324844, -0.06143981218338013, 0.0163438580930233, 0.01746995374560356, 0.027798965573310852, 0.007123304530978203, -0.12162306904792786, 0.04074907302856445, -0.015913112089037895, 0.06494218111038208, 0.003721236251294613, -0.033827923238277435, -0.043137721717357635, -0.009713871404528618, -0.056961048394441605, -0.024891475215554237, 0.09586675465106964, -0.011682059615850449, -0.02678913250565529, -0.01745060831308365, 0.009935610927641392, -0.014455834403634071, 0.021361833438277245, 0.018368178978562355, 0.06518501043319702, 0.02762971818447113, -0.003485226770862937, -0.0024327512364834547, -0.00822106096893549, 0.0006678301142528653, 0.02618347480893135, -0.007558181881904602, -0.013658644631505013, 0.009802097454667091, 0.02433084510266781, 0.01947798579931259, 0.021633682772517204, 0.005837680771946907, 0.07599061727523804, -0.12161913514137268, -0.04457487538456917, -0.07260129600763321, -0.005488265305757523, 0.06317989528179169, 0.0412975512444973, 0.021382944658398628, 0.004706777166575193, 0.027576223015785217, 0.0009109494858421385, -0.031367458403110504, -0.0434877909719944, -0.045776329934597015, 0.03543630242347717, -0.034447893500328064, 0.051688630133867264, 0.0405447781085968, 0.00982777401804924, -0.0425046905875206, -0.04390854015946388, -0.01896601915359497, -0.05820950120687485, -0.02400784380733967, -0.015937337651848793, 0.002425123006105423, -0.0010620420798659325, -0.025648292154073715, -0.014293879270553589, -0.009720941074192524, 0.03492320328950882, -0.031766779720783234, -0.022892804816365242, -0.022370491176843643, -0.0072982641868293285, -0.019606254994869232, 0.042831096798181534, -0.02946607396006584, 0.06366556137800217, 0.0011494726641103625, 0.018981803208589554, -0.03065153956413269, -0.05072011426091194, 0.009410926140844822, 0.08278776705265045, -0.010726900771260262, 0.03567156568169594, -0.03833043575286865, -0.038091275840997696, 0.007583968807011843, -0.004058595281094313, -0.000437640817835927, -0.009983483701944351, 0.003663844196125865, 0.009009690023958683, 0.030449016019701958, -0.012229254469275475, 0.008012400008738041, 0.03253333270549774, -0.02419944480061531, -0.013235306367278099, -0.0071772318333387375, -0.07574504613876343, 0.022234436124563217, 0.004380673170089722, -0.028877075761556625, -0.0076623340137302876, 0.021009963005781174, 0.07983481884002686, 0.08940062671899796, -0.052342820912599564, -0.025873752310872078, 0.04978765919804573, 0.05823366343975067, -0.048033542931079865, -0.042770300060510635, 0.0148420175537467, -0.01362689770758152, -0.04897134006023407, 0.030615350231528282, 0.03962027654051781, 0.023787230253219604, 0.07315778732299805, 0.01545802317559719, -0.011253045871853828, 0.007146844640374184, 0.015998875722289085, -0.007348234765231609, 0.007428591139614582, 0.005369266029447317, -0.009160714223980904, 0.027531838044524193, 0.03425515070557594, 0.04484042525291443, -0.046488936990499496, 0.024250682443380356, -0.015350040048360825, -0.06640825420618057, -0.025051217526197433, -0.019992277026176453, -0.025522101670503616, -0.04698742553591728, 0.009157436899840832, -0.01017842534929514, -0.008562450297176838, -0.015841864049434662, -0.004004120826721191, -0.02591792494058609, -0.033307034522295, 0.00910541508346796, 0.010931403376162052, -0.027799906209111214, 0.0583878830075264, 0.015745852142572403, -5.834911280544475e-05, -0.036070093512535095, 0.04305499792098999, -0.042089641094207764, 0.024908071383833885, -5.603817403923978e-33, -0.026199214160442352, -0.05638299509882927, -0.012597087770700455, -0.04826228693127632, -0.023268623277544975, -0.0021463956218212843, 0.011096270754933357, -0.018598761409521103, -0.029452776536345482, -0.017081862315535545, -0.019768238067626953, -0.008017389103770256, 0.04572758451104164, 0.009871823713183403, 0.020463092252612114, -0.004852576181292534, 0.017112093046307564, -0.0005269645480439067, 0.01764662191271782, 0.02507644146680832, 0.034920383244752884, 0.05705777928233147, 0.06813953816890717, -0.10201184451580048, -0.01282054278999567, 0.06948447972536087, -0.02116529643535614, 0.05038558691740036, 0.07343418151140213, 0.033595237880945206, 0.008865077048540115, 0.006439067889004946, 0.02955407276749611, -0.08409170806407928, -0.03167370334267616, -0.0325494222342968, -0.14830419421195984, 0.0012990828836336732, -0.0565674714744091, 0.036710578948259354, 0.03248802199959755, 0.02202918380498886, 0.056721027940511703, -0.01911257952451706, 0.06586893647909164, -0.02860681153833866, 0.0701088160276413, -0.052839942276477814, -0.01735302247107029, -0.029530487954616547, -0.012493285350501537, 0.036176443099975586, 0.02377406693994999, 0.038289617747068405, 0.04743185639381409, -0.0015990084502846003, 0.0053424169309437275, -0.0020531429909169674, -0.0830003172159195, 0.014787633903324604, -0.007002800703048706, -0.008484463207423687, -0.006303653586655855, 0.028068169951438904, -0.024126755073666573, 0.017368655651807785, 0.050268080085515976, -0.019638903439044952, -0.0036165909841656685, -0.041521668434143066, -0.014279047027230263, 0.04820616543292999, -0.027236245572566986, 0.028358198702335358, 0.018241990357637405, -0.03960780054330826, -0.08451095223426819, 0.07370615750551224, -0.020451340824365616, -0.004572846926748753, -0.033569447696208954, -0.02749369665980339, -0.01391309779137373, -0.011916061863303185, 0.005625427700579166, 0.0423298254609108, -0.02878686413168907, -0.01931636594235897, 0.006720345932990313, -0.0007843818166293204, -0.023422034457325935, 0.05559120699763298, 0.006649630144238472, -0.04592793062329292, -0.10060857981443405, -0.030079500749707222, 0.03763303905725479, 0.0316697433590889, -0.011164702475070953, -0.01905662752687931, 0.009635046124458313, -0.04641295596957207, 0.0008263294002972543, -0.020658912137150764, 0.00811544805765152, 0.008773376233875751, 0.03994864597916603, -0.06623001396656036, -0.07651671767234802, 0.02078738994896412, 0.03193580359220505, -0.028855519369244576, -0.02775142341852188, -0.02551017887890339, -0.01854037307202816, -0.020343145355582237, 0.03427090868353844, 0.021022019907832146, 0.06688553094863892, -0.012882120907306671, 0.016596579924225807, 0.004290830343961716, 0.06285971403121948, 0.03488876298069954, -0.027100257575511932, 0.03977075219154358, -0.05450230836868286, -0.057844702154397964, 0.0570441298186779, -0.021730920299887657, -0.02315729483962059, 0.01171057391911745, 2.6553470888757147e-07, 0.0480826161801815, -0.019691988825798035, 0.03645401820540428, 0.011230040341615677, -0.04549822211265564, 0.011623945087194443, 0.036037951707839966, 0.06752589344978333, -0.01495344378054142, 0.0049471016973257065, 0.030577175319194794, 0.0029817346949130297, 0.019339516758918762, 0.04768100008368492, -0.07553249597549438, -0.07249364256858826, -0.005069202743470669, -0.017499009147286415, -0.06463142484426498, 0.007319855038076639, 0.016742797568440437, 0.01432925183326006, 0.04350466653704643, -0.023271212354302406, 0.019267065450549126, 0.02466992288827896, 0.0026971250772476196, -0.005516926757991314, 0.03910641744732857, 0.0527891144156456, 0.005060238763689995, -0.005489767994731665, -0.0010949134593829513, 0.04679470136761665, 0.009179596789181232, 0.01178908534348011, 0.06631001085042953, 0.048685088753700256, 0.0030134425032883883, 0.06191268563270569, 0.017054177820682526, -0.04292608052492142, 0.0009689878206700087, -0.004206967540085316, 0.03698047623038292, -0.04694720730185509, -0.017560407519340515, 0.05494144558906555, -0.004708315711468458, -0.002341030165553093, -0.011546236462891102, 0.019960645586252213, -0.009843659587204456, 0.016644800081849098, 0.03384324908256531, -0.007855136878788471, -0.023856837302446365, -0.04833986237645149, 0.06388044357299805, 0.06182484328746796, 0.004060664214193821, -0.010737443342804909, 0.037674758583307266, -0.029773488640785217, 0.018372975289821625, -0.028932882472872734, -0.006889966316521168, 2.4558244306386915e-34, -0.03353884443640709, 0.03979264944791794, 0.008940553292632103, -6.930494419066235e-05, 0.005938686430454254, -0.024876045063138008, -0.03497648984193802, 0.0030130527447909117, -0.013080568984150887, -0.035597097128629684, 0.011980718933045864]

['Sudarshan Nandy', 'Partha Pratim Sarkar', 'Achintya Das']

1208.2808v1

The growth of world-wide-web (WWW) spreads its wings from an intangible quantities of web-pages to a gigantic hub of web information which gradually increases the complexity of crawling process in a search engine. A search engine handles a lot of queries from various parts of this world, and the answers of it solely depend on the knowledge that it gathers by means of crawling. The information sharing becomes a most common habit of the society, and it is done by means of publishing structured, semi-structured and unstructured resources on the web. This social practice leads to an exponential growth of web-resource, and hence it became essential to crawl for continuous updating of web-knowledge and modification of several existing resources in any situation. In this paper one statistical hypothesis based learning mechanism is incorporated for learning the behavior of crawling speed in different environment of network, and for intelligently control of the speed of crawler. The scaling technique is used to compare the performance proposed method with the standard crawler. The high speed performance is observed after scaling, and the retrieval of relevant web-resource in such a high speed is analyzed.

Analysis of a Statistical Hypothesis Based Learning Mechanism for Faster crawling

http://arxiv.org/pdf/1208.2808v1

Title Analysis Statistical Hypothesis Based Learning Mechanism Faster crawling Summary growth worldwideweb WWW spread wing intangible quantity webpage gigantic hub web information gradually increase complexity crawling process search engine search engine handle lot query various part world answer solely depend knowledge gather mean crawling information sharing becomes common habit society done mean publishing structured semistructured unstructured resource web social practice lead exponential growth webresource hence became essential crawl continuous updating webknowledge modification several existing resource situation paper one statistical hypothesis based learning mechanism incorporated learning behavior crawling speed different environment network intelligently control speed crawler scaling technique used compare performance proposed method standard crawler high speed performance observed scaling retrieval relevant webresource high speed analyzed Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.056844018399715424, -0.029567649587988853, -0.03742828592658043, -0.041210878640413284, -0.054200056940317154, -0.04358135536313057, 0.03534575551748276, 0.027581045404076576, 0.03494608402252197, -0.04034874215722084, 0.015665195882320404, 0.006236433517187834, -0.021418705582618713, 0.04168194904923439, -0.00444395188242197, -0.01798722706735134, 0.020336706191301346, 0.025846371427178383, -0.01959671452641487, -0.020006980746984482, 0.021734466776251793, -0.04782374948263168, 0.02528366632759571, 0.01414547860622406, 0.05970136821269989, 0.025535453110933304, -0.03414655104279518, 0.0016546075930818915, -0.030461184680461884, -0.07641623914241791, 0.020824510604143143, 0.01484435610473156, 0.00854517426341772, 0.08404279500246048, 2.045339897449594e-06, -0.059480492025613785, -0.05810089036822319, -0.015477020293474197, 0.025788314640522003, 0.03141959011554718, 0.05714957043528557, 0.003522681538015604, -0.0045648240484297276, 0.05901654437184334, 0.012592277489602566, -0.01575591415166855, 0.012255349196493626, 0.034041330218315125, -0.01981545425951481, 0.01492493599653244, 0.01273911353200674, -0.03589077293872833, -0.010550925508141518, 0.005757017061114311, -0.001482312218286097, -0.017431849613785744, 0.041233740746974945, 0.03525802120566368, 0.02789054811000824, 0.0038504197727888823, -0.03131452202796936, 0.010819007642567158, -0.020084692165255547, -0.029188066720962524, 0.05114543065428734, 0.03994125500321388, 0.002492324449121952, -0.006097666919231415, 0.04123131185770035, 0.022702595219016075, 0.009392344392836094, -0.008285467512905598, 0.03058268502354622, 0.014319437555968761, -0.04880468174815178, 0.08781306445598602, -0.052934106439352036, 0.04066499322652817, -0.013754977844655514, 0.006798155605792999, -0.05467621609568596, 0.028284965083003044, 0.009625738486647606, 0.010555141605436802, -0.021492820233106613, 0.012802435085177422, -0.011250659823417664, -0.04171011969447136, 0.02237876132130623, -0.013029372319579124, 0.11750872433185577, -0.033558279275894165, 0.04282381013035774, 0.018065402284264565, -0.0005605300539173186, -0.001978409243747592, 0.054845862090587616, -0.05012162774801254, 0.09923044592142105, -0.037362582981586456, -0.004754229448735714, -0.01659499481320381, -0.009460320696234703, 0.04307415708899498, -0.0005090564955025911, -0.0007206813315860927, -0.019911032170057297, -0.020415350794792175, 0.01563076674938202, 0.051719654351472855, -0.054561398923397064, -0.02170061692595482, 0.007428811397403479, 0.05155860632658005, 0.03435640409588814, -0.033806052058935165, -0.017008744180202484, 0.042795103043317795, 0.041826024651527405, -0.012069512158632278, -0.03331005945801735, -0.005136458668857813, -0.0023846302647143602, 0.03427358716726303, -0.01804615743458271, -0.011833984404802322, -0.04543130472302437, 0.029061581939458847, -0.007109445985406637, -0.006090634502470493, 0.024079572409391403, 0.005369726102799177, 0.09393787384033203, 0.02307962253689766, 0.019845910370349884, 0.0262935571372509, 0.01731090433895588, 0.023898132145404816, -0.09361293166875839, -0.06254330277442932, 0.04595731571316719, 0.045070815831422806, -0.047981005162000656, -0.07362745702266693, -0.02651883475482464, -0.013954857364296913, -0.008262524381279945, 0.052226971834897995, -0.03431568667292595, 8.570360660087317e-05, -0.04367687180638313, 0.002272463170811534, -0.044189564883708954, 0.009783872403204441, 0.05863700062036514, 0.0034462311305105686, 0.017432713881134987, 0.04141518846154213, -0.04738694056868553, 0.0772637352347374, 0.0509689524769783, 0.011410153470933437, 0.003980043809860945, -0.02199350856244564, -0.004325491841882467, -0.0051539745181798935, 0.09544704109430313, 0.008318353444337845, 0.024118179455399513, -0.020931106060743332, -0.03606496378779411, 0.040001582354307175, -0.03853839263319969, -0.00011630092194536701, 0.03234277665615082, 0.06485594809055328, 0.03820958733558655, 0.02539166435599327, -0.012984112836420536, 0.055154770612716675, 0.040736302733421326, 0.01576029136776924, 0.00987052172422409, -0.002295961370691657, -0.04343853145837784, -0.010457269847393036, 0.013516902923583984, 0.03479060158133507, -0.027322014793753624, 0.004681068938225508, -0.013091279193758965, 0.02626124396920204, 0.017082789912819862, -0.01583798974752426, 0.04721338674426079, 0.01133565604686737, -0.006026127375662327, -0.08311225473880768, 0.020260322839021683, 0.010779798962175846, -0.002433601301163435, -0.03938698768615723, -0.0364970862865448, 0.04076774790883064, 0.04159484803676605, -0.03593115881085396, 0.0014514506328850985, 0.004309523850679398, 0.012109081260859966, 0.0025736582465469837, 0.002674642950296402, -0.004935452248901129, -0.0655679926276207, -0.020057929679751396, -0.042219337075948715, 0.047339797019958496, -0.011019144207239151, -0.009972594678401947, 0.006317134015262127, 0.0410984568297863, 0.023953355848789215, -0.01921740733087063, -0.029565416276454926, 0.01654040813446045, -0.005207404028624296, 0.061376024037599564, -0.0022532353177666664, -0.0011314642615616322, -0.015518086962401867, -0.015830224379897118, -3.1035571737447754e-05, -0.012327011674642563, 0.023128893226385117, 0.048219453543424606, -0.07270997762680054, 0.007509212475270033, 0.09691489487886429, 0.03922917693853378, 0.01499831024557352, -0.04872001335024834, 0.0820172131061554, 0.032494742423295975, 0.06022362411022186, -0.007312894333153963, 0.0008077564416453242, -0.07178737968206406, 0.0449519045650959, 0.02196306549012661, 0.010555804707109928, -0.07029112428426743, 0.03916803374886513, -0.057683974504470825, 0.03748105838894844, 0.041039980947971344, 0.007513875141739845, -0.0037024947814643383, -0.016364967450499535, 0.03751193359494209, -0.015713578090071678, 0.009538399055600166, -0.022432368248701096, -0.02996746636927128, 0.032493069767951965, 0.07206761837005615, -0.021278392523527145, -0.06696397811174393, 0.0071830167435109615, -0.021142464131116867, -0.0053067877888679504, -0.012565393932163715, 0.014379894360899925, 0.004498268011957407, -0.01802070438861847, 0.014182530343532562, -0.021354107186198235, -0.01635480858385563, 0.027417514473199844, -0.020675580948591232, 0.0048502543941140175, 0.018526559695601463, 0.004198357928544283, -0.03315940871834755, -0.04020603001117706, -0.0322880819439888, -0.042256273329257965, 0.0028011836111545563, 0.10184143483638763, -0.03524176776409149, -0.00836201012134552, 0.05048905685544014, -0.020083783194422722, -0.02605297788977623, -0.031645145267248154, -0.0579671636223793, -0.030403345823287964, -0.0545930415391922, -0.01946873776614666, 0.03217582404613495, 0.028194505721330643, 0.02430609054863453, 0.06430472433567047, 0.018026741221547127, -0.059379007667303085, -0.0318869948387146, -0.04413319751620293, 0.015143042430281639, -0.014880784787237644, -0.04245169460773468, 0.05759021267294884, -0.014512418769299984, 0.03586132079362869, -0.011215210892260075, 0.010360585525631905, -0.01713920198380947, -0.0283746849745512, -0.002310205949470401, -0.03571030870079994, 0.02663719281554222, -0.004582192283123732, 0.05499710515141487, 0.03465466946363449, -0.007573303300887346, 0.021978290751576424, 0.02905551716685295, 0.056734997779130936, -0.054222602397203445, -0.023153312504291534, 0.012434148229658604, 0.019606847316026688, 0.02044839970767498, 0.032568223774433136, -0.0001529231230961159, -0.02120017074048519, 0.006776966154575348, 0.05065896734595299, 0.09323283284902573, -0.03727099299430847, -0.060793064534664154, 0.06336743384599686, 0.011036998592317104, -0.000906849920284003, -0.018446600064635277, -0.018311789259314537, -0.037482500076293945, 0.04667214676737785, -0.004268522374331951, 0.03391255438327789, -0.05651504546403885, -0.01932668685913086, 0.012647944502532482, 0.050740256905555725, 0.009364992380142212, -0.009271429851651192, -0.060414452105760574, 0.014659455046057701, 0.002263909438624978, -0.009206932038068771, -0.03503508120775223, -0.004140810575336218, 0.0325448252260685, 0.00816799234598875, 0.045525334775447845, 0.030888613313436508, 0.00308095826767385, -0.02582980878651142, -0.0016103399684652686, 0.03265246003866196, -0.08506517857313156, -0.020665861666202545, 0.009973233565688133, -0.0796661525964737, -0.027733774855732918, 0.0603337436914444, 0.03432208672165871, 0.04011854529380798, -0.058106765151023865, -0.045967865735292435, -0.04889038950204849, -0.03930693492293358, 0.021867062896490097, 0.036585837602615356, -0.026824332773685455, 0.05613214150071144, 0.006400167942047119, 0.02341471239924431, -0.05351242795586586, -0.06601723283529282, 0.02763729728758335, -0.06098450347781181, 0.03075534664094448, -0.049434613436460495, -0.0391206219792366, 0.026314230635762215, -0.12301444262266159, 0.009638786315917969, 0.011938435025513172, -0.0797671526670456, 0.06339102238416672, -0.03946984186768532, 0.011808247305452824, 0.05017906054854393, -0.0659676045179367, -0.021308952942490578, -0.00406954251229763, -0.05872916802763939, -0.0067493123933672905, -0.00769807118922472, 0.02046196535229683, -0.06028009578585625, 0.01804642751812935, -0.005287844687700272, 0.01318269968032837, -0.0012985446956008673, -0.04535801708698273, 0.06546485424041748, -0.0009644367382861674, 0.02224821038544178, -0.014898106455802917, -0.024689702317118645, 0.010568861849606037, 0.050258852541446686, 0.04790293052792549, 0.047596901655197144, -0.001939593581482768, -0.001994731370359659, -0.0641932412981987, 0.009334138594567776, -0.03595706820487976, -0.0015714719193056226, 0.010870500467717648, -0.0017252408433705568, 0.00241309916600585, -0.015263487584888935, 0.006612455006688833, 0.023484405130147934, -0.015700511634349823, 0.0073713576421141624, -0.056099142879247665, -0.036010824143886566, -0.08500292897224426, -0.010556482709944248, -0.011969978921115398, 0.05717252567410469, 0.03559379279613495, 0.012058603577315807, 0.007617519702762365, 0.010485305450856686, -0.09370215237140656, -0.09995196014642715, 0.04041166603565216, -0.006700829602777958, -0.02384461835026741, 0.006029186304658651, 0.06935355812311172, -0.02363663539290428, -0.0237592663615942, -0.09174350649118423, -0.006627135910093784, -0.035337019711732864, -0.010756617411971092, -0.013987736776471138, 0.021534135565161705, -0.01944867894053459, -0.030808648094534874, -0.0625588670372963, 0.00383357354439795, -0.01712227240204811, -0.024287598207592964, -0.03423687443137169, 0.01964639313519001, -0.04797210544347763, -0.006350758485496044, -0.004926273599267006, -0.030066341161727905, 0.016668520867824554, -0.020400336012244225, -0.025531312450766563, -0.050638336688280106, -0.007273797411471605, 0.019641758874058723, 0.07217039167881012, 0.028220999985933304, 0.028332041576504707, -0.04242461919784546, 0.02748163416981697, -0.00959461648017168, -0.005762774497270584, 0.004288245923817158, 0.03934447839856148, -0.0016829298110678792, 0.03347364813089371, 0.015776704996824265, 0.02678869478404522, 0.09365462511777878, 0.028476860374212265, -0.041989557445049286, -0.017530174925923347, 0.041441455483436584, -0.046657297760248184, 0.03579976409673691, -0.00036820670356974006, 0.012926283292472363, -0.004648938309401274, -0.09626179188489914, 0.05498539283871651, 0.06775061786174774, 0.0045294854789972305, -0.0077660223469138145, 0.008118896745145321, -0.03589901700615883, -0.02771667204797268, 0.027987655252218246, -0.057776547968387604, -0.06262676417827606, 2.69230567937484e-05, -0.01080742571502924, -0.00853660237044096, 0.03359397500753403, -0.005684167146682739, -0.013920116238296032, 0.008010982535779476, 0.0034636170603334904, 0.013486520387232304, -0.025064680725336075, 0.0008022898691706359, 0.006160739343613386, -0.0051383632235229015, -0.006972465664148331, 0.045041073113679886, 0.043727319687604904, 0.02570614404976368, -0.06186029687523842, -0.03371630981564522, -0.03313556686043739, -0.0007922101067379117, 0.03391006588935852, 0.01975587196648121, 0.06902425736188889, -0.003084389725700021, -0.044983215630054474, -0.005409847479313612, 0.0048123691231012344, -0.009487886913120747, 0.02187812700867653, 0.08063054084777832, -0.0055167898535728455, 0.04065488651394844, 0.06802740693092346, 0.023374738171696663, 0.006311808247119188, -0.05265114828944206, -0.0018347257282584906, -0.015135092660784721, 0.02047770284116268, 0.015680471435189247, -6.536158544226768e-33, 0.06382753700017929, -0.03225141391158104, 0.013950152322649956, 0.006067485082894564, -0.007442481815814972, -0.006574688944965601, -0.00795661099255085, -0.0034999120980501175, -0.04095026105642319, -0.0364023819565773, -0.024374239146709442, 0.016747834160923958, 0.015714360401034355, -0.01856691762804985, 0.030006738379597664, 0.02177342213690281, 0.01296261977404356, 0.019163580611348152, -0.041314948350191116, -0.005910659208893776, 0.04192252457141876, 0.017355920746922493, 0.018090032041072845, -0.025253139436244965, -0.02754242718219757, 0.007012983784079552, 0.02137070707976818, -0.007058685179799795, 0.06763790547847748, 0.007847536355257034, -0.00040767790051177144, -0.012118659913539886, 0.014686374925076962, -0.06555777043104172, 0.0179235078394413, -0.048722557723522186, -0.07147647440433502, -0.027623405680060387, -0.011481471359729767, 0.0385211780667305, 0.018096255138516426, 0.028315097093582153, 0.04528430104255676, -0.020850343629717827, -0.019889090210199356, 0.02323635295033455, 0.07389521598815918, 0.011077874340116978, -0.04612736031413078, -0.025739174336194992, -0.008148767054080963, 0.027773011475801468, -0.026180217042565346, 0.0670723095536232, 0.01832444965839386, 0.008367656730115414, -0.009245005436241627, 0.03974480181932449, -0.009002907201647758, 0.03088114596903324, -0.009815871715545654, 0.03639325872063637, 0.008726035244762897, 0.03423912823200226, 0.016479581594467163, 0.056850042194128036, 0.00384051026776433, 0.013793496415019035, 0.011268489994108677, -0.01981484517455101, 0.04274726286530495, -0.018641367554664612, -0.023105992004275322, 0.013527917675673962, 0.0244313832372427, -0.05513858050107956, -0.022396065294742584, 0.05733994394540787, 0.09216762334108353, -0.005442293360829353, 0.007875734008848667, -0.007455334533005953, -0.051050812005996704, -0.02084747701883316, 0.018377380445599556, 0.033547673374414444, -0.013300193473696709, -0.05213756114244461, -0.00034054458956234157, 0.013683565892279148, -0.06110694259405136, -0.0009498006547801197, -0.02942265197634697, -0.044773899018764496, -0.03694315254688263, 0.01608462817966938, -0.009825010783970356, 0.06044476106762886, -0.029536690562963486, -0.08511464297771454, -0.03747439384460449, -0.0005833828472532332, -0.05045401304960251, 0.035615935921669006, -0.0030541447922587395, -0.028509432449936867, -0.032005030661821365, -0.010599183849990368, -0.0439513698220253, -0.014519711956381798, 0.0073079196736216545, -0.07061208784580231, 0.025618182495236397, -0.06159389764070511, -0.02484070137143135, -0.007490937132388353, 0.021056916564702988, -0.007046983111649752, 0.07956089824438095, 0.010985536500811577, -0.04537985846400261, 0.005977895576506853, -0.010462608188390732, -0.026881583034992218, -0.036030061542987823, -0.008074332028627396, -0.0413677953183651, 0.03449898585677147, -0.009350505657494068, -0.06248549371957779, -0.0010700657730922103, -0.0021363713312894106, 2.753963315171859e-07, 0.03402775526046753, 0.050094787031412125, -0.029181722551584244, 0.012153002433478832, 0.014261409640312195, -0.020980261266231537, 0.0074135004542768, 0.0059560672380030155, -0.017528686672449112, 0.03298139199614525, -0.0016996765043586493, -0.013229742646217346, -0.018995342776179314, 0.024625146761536598, -0.06940896809101105, -0.05405149608850479, -0.0015340364770963788, -0.03063330240547657, -0.00744303222745657, 0.008457048796117306, 0.005042815115302801, 0.012215211056172848, 0.01475955918431282, 0.002516457810997963, 0.01368669606745243, -0.06627141684293747, -0.024880578741431236, 0.012234624475240707, 0.05744180083274841, 0.05078473687171936, 0.006633342709392309, 0.05530998110771179, -0.01739053800702095, -0.009321455843746662, -0.018724236637353897, -0.003754254663363099, -0.030338341370224953, -0.03181001543998718, 0.02515917643904686, 0.08376221358776093, 0.033640965819358826, -0.09344550967216492, 0.023957334458827972, -0.06190657615661621, 0.0455828458070755, 0.07130374759435654, -0.028689615428447723, 0.04661965370178223, -0.024322010576725006, -0.037625424563884735, -0.007613376714289188, -0.037557248026132584, -0.039135660976171494, 0.020507236942648888, -0.061139948666095734, -0.015171261504292488, 0.01395619660615921, -0.0383375808596611, 0.03499419987201691, 0.006737997289747, -0.010041886940598488, -0.07585038989782333, 0.003609613049775362, 0.008426648564636707, 0.0015375359216704965, 0.017443619668483734, 0.029440654441714287, 2.716968306691036e-34, 0.033043697476387024, -0.002624544082209468, 0.01315648015588522, 0.000912494957447052, -0.054893411695957184, 0.012157490476965904, 0.0035262624733150005, -0.012222575955092907, 0.013889510184526443, -0.035677049309015274, -0.011032085865736008]

['Stijn van Dongen', 'Anton J. Enright']

1208.3145v1

We investigate two classes of transformations of cosine similarity and Pearson and Spearman correlations into metric distances, utilising the simple tool of metric-preserving functions. The first class puts anti-correlated objects maximally far apart. Previously known transforms fall within this class. The second class collates correlated and anti-correlated objects. An example of such a transformation that yields a metric distance is the sine function when applied to centered data.

Metric distances derived from cosine similarity and Pearson and Spearman correlations

http://arxiv.org/pdf/1208.3145v1

Title Metric distance derived cosine similarity Pearson Spearman correlation Summary investigate two class transformation cosine similarity Pearson Spearman correlation metric distance utilising simple tool metricpreserving function first class put anticorrelated object maximally far apart Previously known transforms fall within class second class collates correlated anticorrelated object example transformation yield metric distance sine function applied centered data Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0017239461885765195, 0.0016298789996653795, -0.007444172631949186, 0.0016079026972875, -0.04940096288919449, -0.001021405216306448, 0.05335332080721855, 0.042682912200689316, -0.03660762682557106, 0.009122248739004135, -0.011908885091543198, 0.04535027593374252, 0.036613091826438904, -0.01772318221628666, -0.040480177849531174, -0.07210513949394226, 0.009204551577568054, 0.021906118839979172, -0.04544513300061226, -0.005711952690035105, -0.018893493339419365, -0.04633219540119171, -0.00958870630711317, -0.012712644413113594, -0.013395354151725769, -0.017009783536195755, -0.013209971599280834, 0.01373755931854248, 0.04993599280714989, -0.010824506171047688, 0.054049301892519, 0.04215000569820404, -0.03982015326619148, 0.04647769406437874, 2.294667410751572e-06, -0.052590444684028625, -0.005465083755552769, -0.0021029463969171047, 0.04012132063508034, -0.024333246052265167, -0.005141397938132286, 0.010117361322045326, 0.039173416793346405, -0.05377458035945892, -0.015933867543935776, 0.022246502339839935, 0.020771963521838188, 0.039513688534498215, 0.006568571552634239, 0.03624141961336136, -0.009276170283555984, -0.0057416497729718685, -0.013714226894080639, -0.04747585952281952, 0.04069286584854126, 0.023361174389719963, -0.017221150919795036, 0.045259419828653336, -0.019392821937799454, 0.038652606308460236, -0.07269902527332306, 0.015336656011641026, -0.017940158024430275, 0.0632215291261673, 0.0391983687877655, -0.004320419393479824, -0.040676869451999664, -0.0021488890051841736, 0.02958676405251026, 0.052930403500795364, -0.04806246981024742, -0.0404173769056797, 0.03614190220832825, 0.03717489540576935, -0.049000099301338196, 0.03793703392148018, -0.05581815540790558, -0.0379510261118412, 0.018481550738215446, -0.020223164930939674, -0.03441784530878067, 0.11477623879909515, -0.03650590032339096, -0.04212207347154617, -0.03405730426311493, -0.04061935096979141, 0.019420450553297997, -0.02238284796476364, -0.04319069907069206, -0.03486192971467972, 0.009073135443031788, 0.009691189974546432, 0.013524153269827366, -0.011020134203135967, -0.0286727137863636, -0.05538124591112137, 0.05571192875504494, -0.059334076941013336, 0.06118955835700035, -0.002639543265104294, 0.03785642609000206, -0.01017941813915968, 0.0024317309726029634, 0.054111335426568985, -0.06983651220798492, 0.07835616916418076, -0.03305143490433693, 0.03796236217021942, -0.019942332059144974, 0.030688371509313583, -0.08429721742868423, 0.022136172279715538, 0.04678219184279442, -0.021076641976833344, 0.05913974344730377, -0.011175015941262245, -0.038381077349185944, -0.01799478754401207, 0.004893441218882799, 0.018832549452781677, 0.016241535544395447, 0.02542634680867195, 0.0146144088357687, -0.006171329412609339, 0.018035130575299263, 0.052221473306417465, 0.0032889461144804955, 0.01805700734257698, -0.005406441632658243, 0.040688928216695786, 0.03457222878932953, 0.05415699630975723, 0.0003091152757406235, -0.0210854634642601, 0.0039107003249228, 0.03911057114601135, 8.775982132647187e-05, -0.01145268976688385, 0.03743639960885048, 0.01642576977610588, -0.022216398268938065, 0.025461815297603607, 0.022172925993800163, -0.06160394847393036, 0.03084496222436428, 0.01646486669778824, -0.015047913417220116, 0.005456350278109312, 0.019553033635020256, -0.0349339097738266, -0.02317499928176403, 0.08137201517820358, 0.009101170115172863, 0.009204244241118431, 0.05957545340061188, 0.03160954266786575, 0.036682404577732086, -0.02667856402695179, 0.011919310316443443, -0.021074771881103516, 0.04954541102051735, -0.04598186910152435, 0.013373956084251404, -0.04900800436735153, -0.06127587705850601, -0.05059674754738808, -0.04879928007721901, 0.012377600185573101, -0.004754799883812666, 0.022122519090771675, 0.0014281633775681257, 0.01042739674448967, 0.012533585540950298, -0.02195821888744831, 0.038476333022117615, 0.022619200870394707, 0.055326808243989944, -0.008306751027703285, -0.019059456884860992, -0.00748589588329196, -0.03433525562286377, -0.0324188657104969, -0.00929910596460104, 0.054910656064748764, -0.02131415531039238, 0.009620574302971363, -0.06566587835550308, 0.029902258887887, 0.0005892289336770773, -0.033696942031383514, 0.0007831474649719894, -0.04085377976298332, -0.04212778061628342, -0.0539625883102417, 0.019746633246541023, 0.0309868473559618, 0.019643139094114304, -0.06425444036722183, -0.04442724958062172, -0.05480894818902016, -0.04749474301934242, 0.017147794365882874, 0.0064019327983260155, -0.051274385303258896, -0.019481396302580833, -0.05970771238207817, -0.024123763665556908, -0.00018546232604421675, 0.0020532419439405203, 0.00022907124366611242, -0.0047686113975942135, 0.03835451975464821, -0.03643744811415672, -0.03097296506166458, -0.006563358008861542, 0.06136181205511093, -0.018750794231891632, -0.05192511901259422, 0.007447705138474703, 0.05217843875288963, 0.038899946957826614, -0.01647843047976494, 0.04780293628573418, -0.017238730564713478, -0.005639385897666216, 0.024788780137896538, 0.03695722296833992, 0.031087640672922134, -0.009969018399715424, -0.004114797804504633, 0.033731136471033096, 0.010691543109714985, 0.03929677605628967, -0.04611847177147865, -0.03961227461695671, 0.04683840274810791, 0.024130642414093018, 0.003546330612152815, -0.008077160455286503, -0.04232923313975334, 0.026293408125638962, -0.0031347405165433884, 0.013407168909907341, -0.009693318977952003, 0.025600513443350792, 0.03711798042058945, 0.036909885704517365, 0.0007426693919114769, 0.055534109473228455, -0.007631824817508459, 0.01415597926825285, -0.07309757173061371, 0.008574572391808033, 0.009793587028980255, 0.04039277508854866, -0.03517870232462883, -0.049197081476449966, 0.053801778703927994, 0.03859689459204674, 0.04939521849155426, -0.008688465692102909, 0.007928834296762943, -0.01723010651767254, 0.011348070576786995, 0.01946423202753067, -0.02175924740731716, -0.07945776730775833, 0.06539834290742874, -0.016904586926102638, 0.02805442363023758, -0.006463911384344101, 0.05649959295988083, -0.03268970549106598, 0.011590340174734592, -0.0229524876922369, -0.003216691082343459, 0.02214575558900833, -0.030677536502480507, -0.025316091254353523, 0.0648714229464531, -0.05912424623966217, -0.06567779928445816, -0.05155196785926819, 0.013440345413982868, 0.013635697774589062, 0.05411667376756668, 0.012945998460054398, 0.0024105741176754236, 0.01908387616276741, 0.021890930831432343, -0.002945484360679984, -0.022380005568265915, 0.008017301559448242, -0.01681935414671898, -0.019809290766716003, -0.025159867480397224, 0.031106529757380486, 0.08838848769664764, 0.055425114929676056, -0.016153020784258842, 0.01539280079305172, 0.03345133364200592, -0.00411193585023284, -0.029094746336340904, -0.05841311439871788, 0.0414188988506794, 0.0410560742020607, -0.02386932261288166, 0.041590455919504166, 0.03591900318861008, 0.020133260637521744, -0.02060779184103012, 0.021194076165556908, -0.0417383648455143, 0.006298137828707695, 0.020484188571572304, -0.03814532607793808, -0.02583814039826393, 0.009836803190410137, -0.004301886539906263, -0.020098134875297546, -0.0036040456034243107, -0.028434760868549347, 0.0003571775450836867, 0.03883618861436844, -0.019330527633428574, -0.004788592923432589, 0.03806190565228462, 0.008658811450004578, 0.014799576252698898, 0.016814930364489555, -0.06649331003427505, -0.011995119974017143, -0.03454647213220596, 0.025449814274907112, 0.03309112787246704, -0.03874417394399643, -0.07444032281637192, -0.007749570533633232, -0.018364660441875458, 0.01255742646753788, -0.002012420678511262, -0.0378144234418869, 0.04602283611893654, 0.06112267076969147, -0.007991379126906395, -0.038308002054691315, -0.06375021487474442, 0.025219080969691277, -0.0018504828913137317, -0.004952336195856333, 0.034310098737478256, 0.00823125708848238, -0.02268851548433304, -0.021369587630033493, 3.291968459961936e-05, 0.00808513630181551, -0.006264794617891312, -0.03592624142765999, -0.010109341703355312, 0.01647774688899517, -0.00029471999732777476, -0.012940294109284878, -0.0031361859291791916, -0.05287930369377136, -0.014380527660250664, -0.018908029422163963, 0.003676073858514428, -0.03967712074518204, -0.04040060192346573, 0.024579647928476334, 0.04569622129201889, 0.0120990676805377, 0.03511430695652962, 0.03177244961261749, -0.04347016662359238, 0.00593755254521966, -0.02461273968219757, -0.03502459079027176, 0.04438917711377144, -0.03369811922311783, 0.0357530303299427, 0.026999739930033684, 0.0039643095806241035, -0.005508095491677523, -0.010001510381698608, -0.03212931379675865, 0.02303651161491871, -0.016844775527715683, -0.06383904069662094, 0.0017203305615112185, -0.023253388702869415, -0.07553388923406601, -0.035915765911340714, 0.012608211487531662, -0.0033383904956281185, -0.06930182874202728, 0.00789064634591341, -0.012430303730070591, 0.013060612604022026, 0.006837827153503895, -0.07677233964204788, 0.05110008269548416, 0.006271068938076496, -0.04247218370437622, -0.05509074404835701, -0.017821092158555984, 0.047031983733177185, -0.007662668824195862, -0.09674861282110214, -0.0037187745328992605, -0.015254752710461617, 0.06669249385595322, 0.006574177648872137, 0.018850477412343025, 0.06798873096704483, -0.009152174927294254, -0.0006467947969213128, 0.025253869593143463, -0.011490646749734879, -0.018508167937397957, 0.02125752717256546, 0.02481173910200596, 0.019154518842697144, 0.020164169371128082, -0.021702753379940987, 0.027404960244894028, -0.004732009954750538, 0.02213270589709282, 0.01729429140686989, -0.011218337342143059, -0.024944968521595, 0.025650333613157272, 0.04594208672642708, 0.05663057789206505, 0.00735207786783576, -0.05284304916858673, -0.02697295881807804, 0.0027365696150809526, -0.08750533312559128, 0.0464043989777565, -0.044592034071683884, 0.05085108429193497, 0.03469420224428177, -0.04337955266237259, -0.045751750469207764, -0.060325004160404205, -0.03897414728999138, -0.043981779366731644, 0.057444337755441666, 0.01938360184431076, -0.05654324218630791, 0.07593149691820145, 0.011087300255894661, 0.030333077535033226, -0.02949480712413788, -0.07276198267936707, -0.07660606503486633, -0.018409600481390953, 0.014307307079434395, 0.00856005772948265, 0.02262185327708721, -0.007452830206602812, -0.009963668882846832, 0.019819343462586403, -0.07989168912172318, 0.07722068578004837, -0.004454129375517368, 0.027908332645893097, -0.023769628256559372, -0.04262454807758331, -0.02082711085677147, -0.034124162048101425, 0.02957272157073021, 0.02091033384203911, 0.02064778096973896, -0.041334234178066254, -0.058316003531217575, -0.03940968960523605, -0.005209445022046566, -0.0024619942996650934, 0.1109275370836258, 0.018445363268256187, 0.019612353295087814, 0.0020085577853024006, 0.022564325481653214, -0.01893633045256138, 0.02485164813697338, 0.03773997724056244, -0.06444452702999115, 0.051664743572473526, 0.023377005010843277, -0.02306186780333519, 0.06704936176538467, 0.006155336741358042, -0.05019093304872513, -0.027751026675105095, 0.0020722837653011084, -0.05878908932209015, 0.0623399056494236, -0.05550035461783409, 0.023170994594693184, 0.02770434133708477, -0.007890346460044384, 0.05306155979633331, 0.04893394187092781, -0.01575801707804203, 0.012670415453612804, 0.012931950390338898, 0.06449423730373383, -0.01896815374493599, 0.023372210562229156, -0.027383068576455116, 0.019133323803544044, -0.013803509995341301, -0.014492274262011051, -0.023105479776859283, -0.02902965247631073, 0.018004821613430977, -0.009457635693252087, -0.012043488211929798, -0.006059396080672741, 0.04550894722342491, -0.034682534635066986, 0.05244845524430275, -0.014580309391021729, -0.02249661087989807, -0.0048647779040038586, 0.06836706399917603, 0.053990688174963, -0.06583648920059204, -0.031752388924360275, -0.05218444764614105, -0.0096812779083848, -0.02255822904407978, 0.10067849606275558, 0.05116637051105499, -0.06265518814325333, 0.028525594621896744, -0.05910772457718849, -0.004873511381447315, -0.0055501568131148815, 0.03018123283982277, 0.009458879008889198, 0.04431184381246567, 0.043728139251470566, -0.02190651185810566, 0.01307440921664238, -0.02616947703063488, -0.028646249324083328, 0.019193535670638084, -0.042503245174884796, 0.03266880661249161, -0.03444366902112961, -0.023884959518909454, -6.184643121660687e-33, -0.008432004600763321, 0.014963134191930294, -0.05137752369046211, 0.005785554647445679, -0.03569316118955612, -0.006466899532824755, -0.0011781114153563976, 0.015557589940726757, -0.00020136938837822527, -0.011145842261612415, 0.036124005913734436, 0.007670518942177296, -0.0015119719319045544, -0.01855565793812275, 0.04146395996212959, 0.007107558194547892, -0.023035140708088875, 0.01625913381576538, 0.010237268172204494, -0.006900287698954344, 0.08749507367610931, 0.008619379252195358, 2.4416060114162974e-05, -0.11063909530639648, -0.05956362560391426, 0.02506440505385399, 0.023243824020028114, -0.012972665019333363, 0.003905660705640912, -0.005185739137232304, 0.018414748832583427, -0.02870773710310459, -0.003655694192275405, 0.038152970373630524, 7.621385884704068e-05, -0.04309999942779541, -0.04043152928352356, -0.04125763103365898, -0.04555707797408104, 0.01796516589820385, 0.018035665154457092, -0.010712552815675735, 0.03570307418704033, -0.021745504811406136, -0.006224640179425478, -0.051293063908815384, 0.029346294701099396, 0.00308810593560338, 0.001873658155091107, -0.02937871217727661, -0.04232263192534447, -0.021449128165841103, -0.08107730746269226, -0.005970139056444168, 0.011083371005952358, 0.002772890031337738, -0.02863362431526184, 0.03219063580036163, -0.012010776437819004, 0.06074574589729309, -0.011322636157274246, 0.08004375547170639, 0.0033194783609360456, 0.008507887832820415, 0.03877641260623932, -0.00019380226149223745, 0.021497273817658424, -0.038407713174819946, 0.025538727641105652, 0.015182802453637123, 0.006376955658197403, 0.0997530147433281, 0.037599045783281326, 0.03164432942867279, 0.06297405064105988, -0.07311802357435226, -0.04996534064412117, 0.0521758571267128, -0.06355464458465576, -0.023550963029265404, -0.08201810717582703, 0.007125368807464838, 0.005953894928097725, -0.010837252251803875, 0.012556588277220726, 0.018958015367388725, -0.04067057743668556, 0.007772467564791441, 0.0037719912361353636, -0.011480418033897877, 0.023062795400619507, 0.024103965610265732, -0.049921467900276184, 0.006997937802225351, 0.020578335970640182, -0.04529846832156181, -0.020720627158880234, 0.017432095482945442, 0.027714788913726807, -0.05744137242436409, 0.017693256959319115, -0.021953266113996506, 0.05106488987803459, 0.026711085811257362, 0.0464010052382946, -0.04485352709889412, 0.05603337287902832, -0.004812187049537897, -0.06629344820976257, -0.012747750617563725, 0.06498140841722488, -0.0737016573548317, 0.02324414625763893, -0.08007234334945679, -0.03057251125574112, -0.013507035560905933, 0.009883509948849678, 0.04948516935110092, 0.02743178978562355, -0.02179182693362236, -0.018651718273758888, 0.030758751556277275, -0.00964629277586937, 0.060753919184207916, 0.0013663838617503643, 0.016353704035282135, 0.0010582089889794588, -0.05007009953260422, 0.022547950968146324, -0.061270572245121, -0.0377003476023674, -0.04108776897192001, 3.0984315912974125e-07, -0.010160229168832302, 0.0403941385447979, 0.0386495478451252, -0.060050155967473984, 0.0024301940575242043, -0.040185119956731796, -0.0064160143956542015, 0.03744291141629219, 0.00021062782616354525, 0.006178233772516251, 0.018847182393074036, -0.016203956678509712, 0.016692975535988808, -0.0017802075017243624, 0.01845431514084339, 0.05745382979512215, -0.009961769916117191, -0.028803959488868713, -0.05086563527584076, 0.0181693397462368, 0.08463983982801437, -0.04016093909740448, 0.0006712591275572777, 0.010269835591316223, 0.0067271580919623375, 0.02305014058947563, 0.009492349810898304, -0.04915931075811386, 0.05281496420502663, -0.0021265484392642975, -0.0027232614811509848, -0.07764164358377457, 0.014691835269331932, 0.058200228959321976, -0.0007529815775342286, -0.0035744376946240664, 0.070445716381073, -0.03823462501168251, 0.03268180787563324, 0.04027165099978447, -0.0018248739652335644, 0.01863558031618595, -0.0037079742178320885, -0.03117513842880726, 0.046865589916706085, -0.015863269567489624, 0.004185899626463652, 0.008941179141402245, -0.10087287425994873, 0.05598841607570648, 0.035476814955472946, 0.029213890433311462, 0.019192984327673912, 0.005859729368239641, 0.01609954982995987, 0.040125153958797455, 0.04993128404021263, 0.0415366105735302, 0.004010096192359924, 0.060910556465387344, -0.007701636757701635, 0.006291783414781094, 0.03677850216627121, 0.005767268128693104, 0.02436615526676178, 0.019644124433398247, -0.05215355381369591, 3.1823010616109815e-34, -0.020870497450232506, 0.04373563826084137, 0.01970847137272358, -0.08481134474277496, -0.02074231579899788, -0.032185424119234085, -0.06270050257444382, 0.019136877730488777, -0.020808668807148933, -0.029562754556536674, 0.005175512749701738]

['Pol Blasco', 'Deniz Gündüz', 'Mischa Dohler']

1208.4290v2

A point-to-point wireless communication system in which the transmitter is equipped with an energy harvesting device and a rechargeable battery, is studied. Both the energy and the data arrivals at the transmitter are modeled as Markov processes. Delay-limited communication is considered assuming that the underlying channel is block fading with memory, and the instantaneous channel state information is available at both the transmitter and the receiver. The expected total transmitted data during the transmitter's activation time is maximized under three different sets of assumptions regarding the information available at the transmitter about the underlying stochastic processes. A learning theoretic approach is introduced, which does not assume any a priori information on the Markov processes governing the communication system. In addition, online and offline optimization problems are studied for the same setting. Full statistical knowledge and causal information on the realizations of the underlying stochastic processes are assumed in the online optimization problem, while the offline optimization problem assumes non-causal knowledge of the realizations in advance. Comparing the optimal solutions in all three frameworks, the performance loss due to the lack of the transmitter's information regarding the behaviors of the underlying Markov processes is quantified.

A Learning Theoretic Approach to Energy Harvesting Communication System Optimization

http://arxiv.org/pdf/1208.4290v2

Title Learning Theoretic Approach Energy Harvesting Communication System Optimization Summary pointtopoint wireless communication system transmitter equipped energy harvesting device rechargeable battery studied energy data arrival transmitter modeled Markov process Delaylimited communication considered assuming underlying channel block fading memory instantaneous channel state information available transmitter receiver expected total transmitted data transmitter activation time maximized three different set assumption regarding information available transmitter underlying stochastic process learning theoretic approach introduced assume priori information Markov process governing communication system addition online offline optimization problem studied setting Full statistical knowledge causal information realization underlying stochastic process assumed online optimization problem offline optimization problem assumes noncausal knowledge realization advance Comparing optimal solution three framework performance loss due lack transmitter information regarding behavior underlying Markov process quantified Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.005601472686976194, -0.029603902250528336, 0.010226809419691563, 0.009188649244606495, 0.02853233367204666, -0.01689690165221691, -0.0513179711997509, -0.005842909216880798, -0.047250617295503616, 0.02406293712556362, 0.06520339846611023, 0.08819260448217392, 0.014663899317383766, 0.0006909751682542264, 0.01507650502026081, 0.03268252685666084, 0.019756557419896126, 0.04153555631637573, 0.03860137239098549, -0.01181855984032154, 0.01119783241301775, -0.06233186647295952, 0.03535985201597214, 0.022339720278978348, -0.04696058854460716, -0.0004551529127638787, -0.02381790801882744, 0.025382157415151596, 0.003483002772554755, -0.07945439219474792, 0.027162684127688408, -0.05657287687063217, 0.02797640860080719, 0.07526487857103348, 2.0422241959749954e-06, 0.004145587794482708, -0.02415904961526394, -0.020408254116773605, 0.007629699539393187, -0.06910812854766846, -0.006702002603560686, 0.011807190254330635, 0.01628468930721283, 0.010970782488584518, 0.013835862278938293, -0.01587994024157524, 0.07559783011674881, 0.005414743907749653, -0.017828738316893578, 0.03918885439634323, -0.01325086411088705, 0.04671015217900276, 0.05262037739157677, -0.008173779584467411, 0.05386340990662575, 0.005440378095954657, 0.029434120282530785, 0.03198344632983208, -0.04210539534687996, -0.06362669914960861, -0.030048387125134468, 0.027212418615818024, 0.03287617862224579, 0.010063123889267445, 0.05523642897605896, -0.01933298073709011, -0.014339507557451725, 0.030361175537109375, -0.010050510987639427, -0.02171643264591694, -0.019034186378121376, -0.009525604546070099, -0.005067572928965092, 0.0207863450050354, -0.09144172817468643, -0.0015744174597784877, -0.04419627785682678, -0.04618075489997864, -0.027992887422442436, 0.026551395654678345, -0.05729205533862114, 0.03009745664894581, 0.02150086686015129, 0.00581779470667243, -0.00560328084975481, 0.06724344938993454, -0.07088635116815567, -0.01303852442651987, 0.02303025871515274, 0.029425274580717087, 0.06684373319149017, -0.016360225155949593, -0.010519747622311115, 0.03768184408545494, 0.027632126584649086, -0.022195009514689445, -0.005796654615551233, 0.039052121341228485, -0.009829695336520672, -0.01467571035027504, 0.04330175742506981, -0.03740282356739044, 0.060967642813920975, -0.002779753413051367, 0.021666839718818665, -0.06728877872228622, -0.0323241762816906, -0.0344347320497036, -0.056143272668123245, 0.0219429861754179, -0.04273676127195358, -0.02888142317533493, 0.00657100323587656, 0.08225318044424057, 0.019819309934973717, 0.015894100069999695, -0.04371465742588043, -0.013124171644449234, 0.017765970900654793, -0.05393696576356888, -0.051340050995349884, -0.002253785962238908, -0.03447962552309036, -0.019342735409736633, -0.021170541644096375, 0.016640817746520042, 0.013451529666781425, 0.06048382818698883, -0.027202146127820015, -0.056964196264743805, 0.007739882450550795, -0.00501055084168911, -0.03925536572933197, 0.04033226519823074, -0.04210314527153969, 0.08180389553308487, 0.04173891246318817, -0.011487554758787155, -0.06227923929691315, 0.010527743957936764, 0.04307350516319275, -0.008022661320865154, -0.036312002688646317, -0.04936794936656952, -0.016421310603618622, -0.031480997800827026, -0.005932613275945187, 0.0027415803633630276, 0.017585020512342453, 0.0010523675009608269, 0.02676563709974289, 0.023703010752797127, -0.0064101372845470905, -0.018472513183951378, 0.10699114203453064, -0.028976866975426674, -0.06175769120454788, 0.04432354494929314, 0.06377019733190536, 0.03747391700744629, -0.008858722634613514, -0.047008685767650604, 0.034327369183301926, 0.008781549520790577, 0.06836197525262833, -0.00708654522895813, 0.05972667410969734, -0.054975174367427826, -0.028837956488132477, 0.014197401702404022, -0.020173341035842896, -0.03997805714607239, 0.02549947053194046, 0.07607849687337875, 0.012837538495659828, 0.03642047941684723, 0.018889514729380608, -0.03501182422041893, -0.04087720438838005, 0.043258924037218094, -0.03303360939025879, -0.04414914548397064, 0.029614483937621117, 0.024403823539614677, -0.10552208125591278, -0.05912131071090698, 0.012476048432290554, -0.026056772097945213, -0.021922267973423004, -0.05210413783788681, 0.012924513779580593, -0.04942593723535538, -0.006251555867493153, 0.0327666699886322, 0.02412921003997326, -0.027933258563280106, 0.024010121822357178, 0.016722239553928375, 0.027269406244158745, 0.055825911462306976, -0.0027563776820898056, -0.04720074310898781, 0.019121142104268074, -0.05856514722108841, 0.03739861026406288, -0.01505594328045845, 0.02356409840285778, -0.020353209227323532, -0.020618094131350517, -0.06725212931632996, 0.007983256131410599, -0.05228641629219055, 0.012999847531318665, -0.009742275811731815, -0.02693372406065464, 0.0005680062458850443, 0.004434059839695692, 0.03136120364069939, -0.05377964675426483, 0.03979555889964104, 0.005071547813713551, 0.01584482006728649, -0.038311515003442764, 0.018270574510097504, 0.027217557653784752, 0.010341886430978775, -0.001111478777602315, 0.026444977149367332, 0.08421137928962708, -0.0400739461183548, 0.05190890654921532, 0.005995546001940966, 0.02029813639819622, -0.06445350497961044, -0.018457962200045586, 0.040606290102005005, -0.01123020425438881, -0.0017652480164542794, 0.00033272558357566595, -0.018471267074346542, 0.047359298914670944, 0.01286127045750618, 0.03501414880156517, -0.0677359476685524, -0.03741603344678879, -0.05139288678765297, 0.04397214204072952, 0.00191626010928303, 0.017232494428753853, 0.0035178260877728462, -0.010761343874037266, -0.02155526727437973, 0.04446784406900406, 0.06500881165266037, 0.04662887752056122, -0.0915091335773468, 0.001677828491665423, 0.0566006675362587, -0.0102682551369071, 0.04859494790434837, -0.0059893205761909485, -0.09374764561653137, -0.035843782126903534, 0.008070039562880993, -0.010957399383187294, 0.012158514000475407, 0.008936157450079918, 0.014735537581145763, -0.014639592729508877, -0.024009209126234055, 0.0584101676940918, -0.03755374625325203, 0.03473541885614395, 0.02920142561197281, 0.021980367600917816, -0.03363299369812012, 0.05019208416342735, -0.03508569300174713, -0.02077055536210537, -0.010302572511136532, -0.003607298480346799, -0.006961727514863014, 0.005781462416052818, 0.0018016918329522014, 0.02239699847996235, 0.02351241745054722, 0.04504534602165222, -0.03146420046687126, -0.044523220509290695, 0.006196978967636824, 0.03423483669757843, -0.0066906725987792015, -0.033148143440485, 0.025151357054710388, 0.015065867453813553, -0.005476661026477814, 0.010767410509288311, 0.007386527955532074, 0.05203266441822052, 0.030254701152443886, -0.0197659432888031, 0.0041175950318574905, -0.05307295545935631, 0.022891098633408546, -0.03297469764947891, -0.016995418816804886, -0.03665601834654808, 0.004843639675527811, 0.012790405191481113, -0.009641842916607857, 0.007384272292256355, 0.03375224024057388, 0.0414036326110363, 0.01936080865561962, -0.009357444941997528, -0.0802009180188179, -0.06408976763486862, 0.04277098923921585, 0.04882103204727173, 0.0010912619763985276, -0.0070905606262385845, -0.02831016667187214, 0.06333886086940765, 0.036306578665971756, 0.01985378935933113, -0.04466165602207184, -0.04251546785235405, 0.028541525825858116, -0.012455486692488194, 0.04592877998948097, 0.033710747957229614, -0.0271987933665514, -0.008543923497200012, 0.02888709492981434, -0.005524481646716595, 0.021440960466861725, 0.0024613626301288605, -0.07977806776762009, 0.06392888724803925, -0.002478938549757004, -0.013949169777333736, -0.01602013036608696, -0.012239807285368443, 0.03096948377788067, 0.012069339863955975, -0.04142976924777031, -0.05554705485701561, 0.0172653216868639, 0.044704753905534744, -0.030463306233286858, 0.05403025448322296, 0.024126330390572548, -0.005288878455758095, -0.041123367846012115, 0.014888609759509563, 0.020774349570274353, -0.04577379673719406, -0.06210947036743164, -0.033775217831134796, -0.0015118229202926159, -0.022860564291477203, -0.008978556841611862, 0.016142139211297035, 0.06997143477201462, -0.026725493371486664, 0.009397193789482117, 0.014280199073255062, -0.008130759000778198, 0.0015461884904652834, 0.021915044635534286, 0.036164168268442154, -0.042077742516994476, 0.0421011745929718, 0.004043425898998976, -0.0018930168589577079, -0.02317817322909832, -0.01831304468214512, -0.024046937003731728, -0.026009634137153625, -0.02883974090218544, 0.01723182201385498, -0.01666336879134178, -0.01141320075839758, 0.013304688967764378, 0.0452667698264122, -0.045616939663887024, -0.023454707115888596, -0.028250815346837044, -0.0395081453025341, -0.017994092777371407, -0.003113399026915431, -0.009147725999355316, -0.07458869367837906, -0.02470242977142334, -0.05143144726753235, -0.03692611679434776, -0.07839936017990112, 0.006510223262012005, 0.007990680634975433, 0.019978880882263184, 0.03004533424973488, -0.06543619930744171, -0.016179602593183517, -0.009243798442184925, -0.03897853568196297, -0.006214899010956287, 0.12049210071563721, 0.03812234476208687, 0.019206514582037926, 0.008685583248734474, -0.020720606669783592, -0.02362252213060856, -0.026228703558444977, -0.065888412296772, -0.08480416983366013, 0.040721748024225235, -0.002683263039216399, 0.006152021232992411, 0.06948141753673553, 0.019127896055579185, 0.012267687357962132, 0.006815046537667513, 0.02000560238957405, -0.01599806919693947, 0.010015539824962616, 0.01666845753788948, -0.04049200192093849, 0.11934830993413925, 3.394713348825462e-05, -0.021547334268689156, -0.002879308769479394, -0.07829698920249939, 0.019821181893348694, 0.00013710408529732376, -0.0005575956893153489, 0.07588741928339005, 0.002382391830906272, 0.016517994925379753, -0.011867400258779526, -0.03837713971734047, 0.004853900521993637, -0.043759267777204514, 0.003895686473697424, 0.044213131070137024, 0.11887195706367493, 0.08488485217094421, 0.05664431303739548, -0.07650011032819748, -0.06719068437814713, 0.05205665901303291, -0.0003480847517494112, 0.01182571891695261, 0.0031249041203409433, 0.023364638909697533, -0.009513155557215214, 0.026276201009750366, -0.05699610710144043, -0.038875408470630646, -0.039281170815229416, 0.007728596683591604, 0.033088598400354385, 0.010947320610284805, 0.043034616857767105, -0.0018557659350335598, 0.006805630400776863, 0.0016762993764132261, 0.025638628751039505, -0.007979625836014748, -0.027587149292230606, 0.05274725332856178, 0.07774584740400314, 0.015273073688149452, 0.024494003504514694, 0.018857168033719063, 0.05218490958213806, -0.02417943999171257, -0.03953222557902336, -0.03145776316523552, 0.004710436332970858, 0.006237164605408907, 0.03692501038312912, 0.03299427032470703, 0.021082792431116104, -0.06680475920438766, -0.011020786128938198, 0.041845183819532394, 0.033161409199237823, 0.025139356032013893, -0.07070284336805344, -0.005083704367280006, 0.036402735859155655, 0.002626247936859727, 0.05293915048241615, -0.04395928233861923, 0.06437837332487106, -0.06674245744943619, 0.03900166600942612, 0.039128873497247696, 0.01906760223209858, 0.04744777828454971, -0.004636775702238083, 0.02363591268658638, 0.01860467903316021, -0.010464856401085854, 0.01847173646092415, 0.0005286563537083566, -0.030941881239414215, -0.014037796296179295, -0.0031487152446061373, 0.006720908917486668, -0.003221433609724045, -0.03739185258746147, 0.06864070147275925, -0.048983074724674225, 0.00032550730975344777, 0.07907605916261673, 0.010643756948411465, 0.06278005987405777, -0.051993127912282944, -0.019241387024521828, -0.011419964954257011, 0.0009503986802883446, 0.03613627329468727, -0.03888164460659027, 0.0133623406291008, 0.020622797310352325, 0.06833736598491669, -0.04444750025868416, 0.01660797744989395, -0.008291296660900116, 0.033593811094760895, -0.013574966229498386, -0.05242058262228966, -0.016755100339651108, -0.009900740347802639, 0.0897965282201767, 0.028964437544345856, -0.016987191513180733, -0.00012323172995820642, 0.05446772277355194, 0.01670820266008377, 0.04448499158024788, 0.03311312198638916, -0.003733825171366334, 0.06314989924430847, 0.011374784633517265, 0.04533177986741066, 0.002788230311125517, -0.03620510175824165, 0.007023137994110584, -0.012650519609451294, -0.017679093405604362, 0.01750904880464077, 0.00932277087122202, 0.004710998386144638, -5.983348530290001e-33, 0.013501061126589775, -0.028887175023555756, -0.022575462237000465, 0.04510590806603432, -0.029678186401724815, -0.02692144736647606, 0.02249966375529766, -0.03495360165834427, 0.034753818064928055, -0.03646025061607361, 0.015496727079153061, -0.02964974008500576, 0.038654617965221405, 0.028838565573096275, -0.023879269137978554, 0.0353921502828598, 0.009739055298268795, -0.007363616023212671, -0.015057804062962532, -0.043799664825201035, 0.059378087520599365, 0.024505741894245148, -0.011600435711443424, -0.003812846029177308, 0.0032787281088531017, -0.05356719344854355, -0.0043691243045032024, -0.011214956641197205, -0.016151955351233482, -0.018753234297037125, -0.02351660653948784, -0.00046884582843631506, 0.00502672279253602, -0.01837579905986786, 0.0039756279438734055, 0.02797754481434822, -0.013670031912624836, -0.007990832440555096, -0.06541366875171661, 0.03211713209748268, -0.04271015152335167, -0.021230701357126236, 0.012007598765194416, -0.03244943544268608, -0.08244361728429794, 0.045930102467536926, 0.032257597893476486, -0.008612211793661118, -0.03576914221048355, -0.020543113350868225, 0.008391592651605606, -0.01442008651793003, -0.015739159658551216, -0.022731121629476547, -0.013852081261575222, -0.009103113785386086, -0.030343759804964066, -0.005119417794048786, -0.06766459345817566, 0.03442852944135666, -0.029841279610991478, 0.053812578320503235, -0.004892711527645588, 0.009081507101655006, 0.024755636230111122, 0.029785582795739174, 0.010079815052449703, -0.02893703617155552, -0.007561356760561466, -0.00298923347145319, -0.04077424108982086, -0.030209720134735107, -0.0008376340265385807, -0.027361875399947166, 0.041773222386837006, -0.040790949016809464, -0.06329872459173203, 0.011536418460309505, -0.00031191218295134604, 0.06818567216396332, -0.006451239809393883, -0.007685768883675337, 0.002033804776147008, -0.01189886312931776, 0.027467969805002213, 0.01828671805560589, 0.03785019740462303, -0.017818568274378777, -0.021919813007116318, 0.02494960092008114, 0.006877499632537365, -0.01776803657412529, -0.02542523667216301, 0.012765701860189438, 0.01789259724318981, -0.01744440756738186, 0.05770070478320122, -0.007501575164496899, 0.020143501460552216, -0.033891234546899796, -0.06786821037530899, -0.032347772270441055, -0.07418229430913925, 0.004738113842904568, -0.0029671303927898407, -0.003336531575769186, 0.007775382604449987, 0.01898188702762127, 0.0031051472760736942, 0.009786570444703102, -0.01233252789825201, 0.011510211043059826, -0.011003512889146805, -0.0047990139573812485, 0.02725519798696041, -0.05101308971643448, -0.00580954272300005, 0.05258747935295105, -0.029027059674263, -0.009060725569725037, -0.0047072465531528, -0.005315094254910946, -0.0029717290308326483, -0.016296084970235825, 0.007649359293282032, 0.01898295432329178, -0.05303087458014488, 0.04009084403514862, -0.06808705627918243, 0.013024172745645046, -0.00948834978044033, -0.014844072982668877, 2.867845694254356e-07, -0.016595685854554176, -0.03222403675317764, -0.01825660467147827, -0.02663983404636383, -0.01696624793112278, -0.02069893665611744, -0.034099187701940536, 0.013722737319767475, -0.029448876157402992, 0.007170273456722498, -0.010030372999608517, -0.07262056320905685, 0.045754339545965195, -0.01759006641805172, -0.08078761398792267, -0.06458550691604614, 0.015692561864852905, 0.0866260826587677, 0.01483017485588789, -0.025085341185331345, 0.013834278099238873, -0.020332472398877144, 0.002673546550795436, -0.03086254559457302, 0.06728783994913101, 0.01712675392627716, 0.0572100393474102, 0.005599496886134148, 0.02219894714653492, 0.013610594905912876, 0.06529169529676437, 0.008941611275076866, 0.01225380040705204, -0.06056453660130501, -0.003636519657447934, -0.004001532215625048, -0.036354415118694305, 0.0010500893695279956, 0.007099573500454426, -0.05336479842662811, -5.8502675528870896e-05, 0.05239269509911537, 0.028149297460913658, 0.022531991824507713, -0.024244729429483414, -0.06846946477890015, -0.06122836098074913, 0.018040670081973076, 0.05871598795056343, 0.017752064391970634, 0.004276602994650602, 0.021694378927350044, -0.010898061096668243, -0.11394445598125458, -0.06332564353942871, -0.03716195747256279, 0.014348131604492664, 0.04261912405490875, 0.01312428992241621, -0.008329126983880997, 0.03389891982078552, -0.030273020267486572, -0.030333252623677254, -0.015928035601973534, 0.040123965591192245, 0.012921247631311417, 0.016825860366225243, 2.1187009160175136e-34, 0.013168694451451302, -0.05151568353176117, 0.03035680018365383, -0.003166728653013706, -0.086161307990551, 0.0241270549595356, 0.0419248603284359, 0.002322389045730233, -0.004167381674051285, 0.011172663420438766, 0.020682860165834427]

['Paul M. B. Vitanyi', 'Nick Chater']

1208.5003v3

We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a real-life algorothm it has round-off errors, and (ii) it has no round-off errors. Assuming (i) we (a) consider a probability mass function of the elements of the language if the data are drawn independent identically distributed (i.i.d.), provided the probability mass function is computable and has a finite expectation. We give an effective procedure to almost surely identify in the limit the target probability mass function using the Strong Law of Large Numbers. Second (b) we treat the case of possibly incomputable probabilistic mass functions in the above setting. In this case we can only pointswize converge to the target probability mass function almost surely. Third (c) we consider the case where the data are dependent assuming they are typical for at least one computable measure and the language is finite. There is an effective procedure to identify by infinite recurrence a nonempty subset of the computable measures according to which the data is typical. Here we use the theory of Kolmogorov complexity. Assuming (ii) we obtain the weaker result for (a) that the target distribution is identified by infinite recurrence almost surely; (b) stays the same as under assumption (i). We consider the associated predictions.

Identification of Probabilities of Languages

http://arxiv.org/pdf/1208.5003v3

Title Identification Probabilities Languages Summary consider problem inferring probability distribution associated language given data consisting infinite sequence element languge two assumption algorithm concerned like reallife algorothm roundoff error ii roundoff error Assuming consider probability mass function element language data drawn independent identically distributed iid provided probability mass function computable finite expectation give effective procedure almost surely identify limit target probability mass function using Strong Law Large Numbers Second b treat case possibly incomputable probabilistic mass function setting case pointswize converge target probability mass function almost surely Third c consider case data dependent assuming typical least one computable measure language finite effective procedure identify infinite recurrence nonempty subset computable measure according data typical use theory Kolmogorov complexity Assuming ii obtain weaker result target distribution identified infinite recurrence almost surely b stay assumption consider associated prediction Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.008780895732343197, 0.056301359087228775, -0.02066374383866787, 0.0206903088837862, -0.060069501399993896, -0.009569229558110237, -0.03387949988245964, 0.032493289560079575, -0.038731999695301056, 0.025766562670469284, 0.06974092125892639, -0.011240189895033836, 0.04230860620737076, 0.05317742004990578, 0.002938132965937257, -0.015527029521763325, -0.03793206438422203, -0.045076142996549606, 0.004822122864425182, -0.0071670887991786, 0.006950417533516884, -0.07031378149986267, -0.017766157165169716, 0.015456623397767544, 0.04744185134768486, 0.006510317325592041, 0.02972220815718174, -0.07178672403097153, -0.02586178667843342, -0.040709737688302994, 0.002887903479859233, 0.05269871652126312, -0.04039229825139046, 0.03301648050546646, 1.821564069359738e-06, -0.0443832166492939, -0.01943463459610939, -0.04023001343011856, 0.02380860410630703, -0.049274519085884094, -0.0711623877286911, -0.04094063118100166, 0.023289067670702934, 0.006336407735943794, 0.04909883812069893, -0.007256512530148029, 0.0846564844250679, -0.01725449413061142, -0.04303734377026558, 0.009985385462641716, 0.036507610231637955, -0.045901328325271606, 0.028895769268274307, -0.017009804025292397, 0.03762248903512955, 0.008018742315471172, 0.03264770656824112, -0.010893815197050571, 0.01677262969315052, -0.046038173139095306, 0.0072846789844334126, 0.020603906363248825, 0.021917929872870445, -0.0005520684062503278, -0.04330006241798401, 0.006150820292532444, 0.015423622913658619, -0.0028526997193694115, -0.0015811834018677473, 0.012526496313512325, 0.002469934755936265, -0.06158364936709404, -0.020451363176107407, 0.0032329827081412077, -0.01819196529686451, 0.033877648413181305, -0.01800512708723545, 0.04164819046854973, -0.0547703318297863, 0.002931321505457163, -0.023525942116975784, 0.06063583120703697, 0.004689956083893776, -0.02052694745361805, -0.026708874851465225, 0.08590525388717651, -0.0018979469314217567, 0.010621211491525173, -0.015432140789926052, -0.01162972766906023, -0.041329726576805115, -0.05565943196415901, -0.01361288782209158, 0.004331649746745825, 0.003845489351078868, 0.018834782764315605, -0.01686837337911129, 0.02016325853765011, 0.011313973926007748, -0.019412430003285408, 0.04783220589160919, -0.014278200455009937, 0.004111663904041052, 0.028118662536144257, 0.015482562594115734, -0.00741218077018857, 0.02504826709628105, -0.04460927098989487, -0.005582968704402447, 0.07335507869720459, -0.025215400382876396, 0.029107440263032913, 0.02533295378088951, 0.02926032990217209, 0.04154559597373009, 0.014599108137190342, -0.06624633818864822, 0.024174990132451057, 0.006797492038458586, 0.030849037691950798, 0.005916647147387266, -0.05711675435304642, -0.05388534814119339, -0.0200349073857069, -0.07557591795921326, 0.01535124983638525, -0.02341558411717415, -0.01523992046713829, -0.0047719138674438, -0.041956931352615356, 0.015774443745613098, 0.050096336752176285, 0.0009455160470679402, 0.024945037439465523, -0.036380525678396225, 0.040591295808553696, 0.013734339736402035, 0.0414511114358902, -0.047750405967235565, -0.03779284656047821, -0.024067562073469162, -0.025633355602622032, -0.01798115111887455, -0.0816253200173378, -0.04557638242840767, -0.0032764237839728594, -0.040630798786878586, 0.02680545672774315, 0.0035491040907800198, -0.017595339566469193, 0.022074932232499123, 0.057621069252491, 0.02895258367061615, -0.013198821805417538, -0.013426431454718113, 0.01284863892942667, -0.0051224385388195515, 0.03594537824392319, -0.03764880448579788, 0.004280589520931244, 0.04451186582446098, -0.04830145463347435, 0.06277716904878616, 0.018970981240272522, -0.03362451493740082, 0.001568181673064828, 0.0065187616273760796, 0.012124850414693356, 0.03436468914151192, -0.016456272453069687, -0.004587880801409483, 0.04122999310493469, 0.007826241664588451, -0.0012880910653620958, -0.009082643315196037, 0.01158376969397068, 0.021697307005524635, 0.004700020886957645, 0.04123827815055847, -0.007685372140258551, 0.057609692215919495, 0.07856182008981705, -0.016606925055384636, -0.0042665014043450356, -0.026507068425416946, 0.020931590348482132, 0.0018048682250082493, -0.04545620083808899, -0.025084329769015312, -0.032396577298641205, -0.009834219701588154, -0.04015740007162094, -0.07475783675909042, -0.031725507229566574, 0.06940166652202606, 0.010281095281243324, 0.007058111019432545, -0.03438328579068184, -0.025782853364944458, 0.05049673467874527, -0.023978400975465775, -0.03225262835621834, 0.05766750127077103, -0.010615428909659386, -0.04021153226494789, -0.04911315068602562, 0.06139238923788071, 0.003334761131554842, -0.013620847836136818, -0.032881006598472595, -0.01480952836573124, 0.012337633408606052, -0.0012752909678965807, 0.02214973419904709, -0.007963787764310837, 0.09868485480546951, 0.00466065714135766, 0.014628213830292225, -0.05045030638575554, 0.023388762027025223, 0.006897235754877329, -0.01874459721148014, -0.012509210035204887, -0.017431173473596573, 0.016547804698348045, -0.03520844131708145, 0.03830152377486229, -0.023106427863240242, 0.047940295189619064, -0.025025054812431335, -0.04197655990719795, 0.055780649185180664, -0.001748819719068706, -0.006973785348236561, -0.025241097435355186, 0.029157457873225212, 0.0030044345185160637, -0.01766277849674225, 0.03451407700777054, -0.0197262205183506, 0.024127986282110214, -0.07229383289813995, 0.013627183623611927, -0.0019683914724737406, 0.048016130924224854, -0.06746431440114975, 0.03666946664452553, 0.01029582042247057, 0.044435497373342514, -0.0267900712788105, 0.01771029457449913, -0.014600617811083794, 0.06518856436014175, -0.01839512586593628, 0.06075141206383705, -0.01919146440923214, -0.027828972786664963, 0.028629368171095848, -0.052120406180620193, -0.028953926637768745, -0.025598572567105293, -0.012509690597653389, -0.02860066294670105, 0.07587163150310516, 0.006216369103640318, 0.007921237498521805, 0.017081597819924355, 0.000948507571592927, 0.010656949132680893, -0.01453233603388071, 0.07827123254537582, -0.022027304396033287, 0.008399569429457188, -0.019990144297480583, -0.026721887290477753, -0.02577671967446804, 0.03140118718147278, 0.011460850015282631, 0.0463893786072731, 0.03322750702500343, -0.015800030902028084, -0.025083988904953003, -0.004473741166293621, -0.03112577274441719, -0.0006456497358158231, 0.0376712903380394, 0.022378139197826385, -0.03472894802689552, -0.05206897109746933, 0.047210656106472015, -0.03130337968468666, 0.015436031855642796, -0.021443525329232216, -0.002756045199930668, 0.005006756167858839, -0.04832514747977257, -0.0008706034859642386, -0.02267569676041603, 0.004255856387317181, 0.017989348620176315, 0.012726696208119392, 0.019584190100431442, 0.03447228670120239, -0.057752788066864014, -0.03722168505191803, -0.04999902844429016, 0.025949543341994286, -0.019839581102132797, 0.008983791805803776, 0.034718092530965805, 0.017587151378393173, -0.03986773267388344, 0.01793207786977291, 0.02626657858490944, 0.032658904790878296, -0.005568456836044788, 0.01171721052378416, 0.0013141939416527748, 0.020882297307252884, 0.04911341518163681, -0.00024083176685962826, -0.08502799272537231, 0.06490225344896317, -0.010310311801731586, 0.051932305097579956, -0.014733214862644672, -0.05914011597633362, 0.0358785018324852, 0.012314185500144958, 0.05074441432952881, 0.025067968294024467, -0.020376989617943764, -0.006407548673450947, -0.004174939356744289, -0.007455900777131319, 0.042105533182621, -0.011698588728904724, 0.008684755302965641, -0.04628344252705574, -0.0013782711466774344, 0.0051278467290103436, -0.013172457925975323, 0.014290827326476574, -0.02966533973813057, 0.03777457773685455, -0.01927049085497856, -0.03323180973529816, -0.0050171297043561935, -0.03395630791783333, 0.07120487093925476, 0.043232228606939316, -0.00845360103994608, -0.004048622213304043, -0.015299157239496708, -0.0006687119603157043, -0.00011168952187290415, 0.04946452006697655, -0.0595867857336998, 0.01476861722767353, -0.0004957775236107409, 0.005620753858238459, 0.015762297436594963, -0.00993555411696434, 0.07942268997430801, -0.045569028705358505, -0.00974761787801981, 0.03886286914348602, -0.0709136500954628, -0.08121023327112198, 0.09309190511703491, -0.006821147166192532, -0.0257173553109169, 0.02751440927386284, 0.04216407239437103, -0.01165005099028349, -0.027965392917394638, 0.0173766128718853, 0.044055115431547165, -0.03645540028810501, 8.110503404168412e-05, 0.01963796839118004, -0.09888199716806412, 0.0269466582685709, -0.043077412992715836, -0.006615683436393738, -0.09264405071735382, -0.07962030917406082, 0.009233228862285614, -0.07897987961769104, 0.0207090862095356, -0.018794797360897064, -0.058100949972867966, -0.06700719147920609, -0.06944986432790756, 0.005390028934925795, -0.0015233125304803252, -0.06423892080783844, 0.041834767907857895, 0.0012098170118406415, 0.028277719393372536, 0.04874010384082794, -0.05066883936524391, -0.061161428689956665, -0.019843460991978645, -0.02961811237037182, -0.019773051142692566, 0.02647903561592102, 0.014761175028979778, -0.06075344607234001, -0.002937984885647893, -0.027957148849964142, -0.03304290771484375, -0.03259963542222977, 0.005413600709289312, -0.012158479541540146, 0.07277704775333405, -0.0035325472708791494, -0.02547547034919262, 0.05192724987864494, -0.01942007802426815, 0.056492310017347336, 0.047454074025154114, 0.08091969788074493, -0.05197429656982422, -0.08563878387212753, -0.005157510284334421, -0.00023532180057372898, 0.051927439868450165, 0.026887321844697, -0.012667828239500523, 0.03420354053378105, -0.026445724070072174, -0.023212095722556114, 0.035021793097257614, 0.025215405970811844, 0.043427370488643646, -0.014479626901447773, -0.0345909558236599, -0.09662531316280365, -0.04248664900660515, -0.0022425814531743526, -0.015382938086986542, 0.07031518965959549, 0.016116779297590256, 0.03187999129295349, 0.01577037014067173, -0.02906365878880024, -0.01030413806438446, -0.061368927359580994, 0.0002389587025390938, 0.018912415951490402, -0.03469662740826607, 0.029585035517811775, 0.013775568455457687, 0.002887509996071458, -0.018248042091727257, -0.005291368346661329, -0.10792363435029984, -0.02787674590945244, 0.010083087719976902, 0.05192384123802185, 0.026504291221499443, -0.04330422729253769, 0.017331501469016075, -0.04638088494539261, 0.0007613119669258595, -0.003819467965513468, 0.05017216131091118, -0.003377524670213461, -0.04188311845064163, 0.04159654304385185, 0.01240607537329197, 0.017900768667459488, 0.007636479567736387, 0.0050783101469278336, 0.010883857496082783, 0.010732793249189854, -0.040699467062950134, -0.08828700333833694, -0.0030411204788833857, 0.07579480856657028, 0.04710099846124649, -0.0023972250055521727, -0.09430588781833649, 0.005896155722439289, 0.027629032731056213, 0.02412339299917221, -0.010327618569135666, -0.008090073242783546, 0.031204067170619965, 0.0477963462471962, 0.027770331129431725, 0.0023820772767066956, -0.06509944051504135, 0.03150242567062378, -0.037564992904663086, 0.027534179389476776, 0.10206279903650284, 0.06464507430791855, 0.031626902520656586, 0.011551471427083015, -0.014419336803257465, 0.02909310907125473, 0.034016724675893784, 0.027547672390937805, 0.07732415199279785, 0.0285946074873209, 0.0008700599428266287, 0.006267430726438761, -0.0296719279140234, 0.026073727756738663, -0.03622568026185036, 0.00034073105780407786, -0.008866558782756329, 0.024667687714099884, 0.04589380323886871, 0.020609037950634956, -0.020001353695988655, -0.037977468222379684, -0.024591291323304176, 0.025276754051446915, -0.07495515793561935, 0.058639343827962875, 0.010849125683307648, 0.0378098338842392, 0.004564136732369661, 0.01611456647515297, -0.042508628219366074, 0.0139051778241992, 0.043698981404304504, 0.0106024956330657, -0.01826845109462738, -0.02800295688211918, -0.07090357691049576, 0.019881175830960274, -0.012628357857465744, -0.06006290018558502, 0.024416346102952957, 0.011056102812290192, -0.019340768456459045, -0.03708631172776222, -0.05139726772904396, 0.0054392339661717415, 0.049155838787555695, 0.05233084410429001, 0.037736181169748306, -0.0198011826723814, 0.03158324584364891, 0.003486018627882004, 0.043412502855062485, -0.07640235871076584, 0.038316335529088974, -0.010566005483269691, -0.0033000714611262083, -0.022209949791431427, -5.315639453690125e-33, 0.02510516531765461, -0.041945911943912506, -0.016595911234617233, -0.0176294706761837, 0.044183649122714996, -0.02883138880133629, -0.028316574171185493, 0.009975345805287361, 0.03474670276045799, -0.03402108699083328, 0.03240479901432991, -0.015082012861967087, 0.022043555974960327, 0.02588256634771824, 0.004997522570192814, -0.024588005617260933, -0.037277042865753174, 0.008022875525057316, 0.020207729190587997, -0.04749040678143501, 0.0764237642288208, -0.02522166445851326, 0.02653326280415058, -0.02101423405110836, 0.03185262903571129, 0.0036167800426483154, 0.03237856552004814, 0.028229333460330963, 0.04688984528183937, 0.04077092185616493, 0.01806788705289364, 0.040871016681194305, 0.008176513016223907, -0.04646003991365433, 0.008192954584956169, -0.03398929536342621, 0.03751567006111145, -0.05833039805293083, 0.0036165958736091852, 0.020075369626283646, 0.04633217677474022, -0.023778870701789856, 0.04552127793431282, -0.02626308985054493, -0.04196801036596298, -0.014370743185281754, 0.04486694931983948, -0.037817295640707016, 0.008134550414979458, -0.01750670187175274, 0.03912760689854622, 0.03685242682695389, -0.006378237158060074, 0.09134833514690399, 0.011421731673181057, -0.05127214640378952, -0.004019040614366531, -0.020160619169473648, -0.013713154941797256, 0.02529893070459366, -0.0017831983277574182, 0.08746672421693802, 0.048962268978357315, 0.022469960153102875, 0.07129993289709091, -0.01695568487048149, 0.044926851987838745, -0.014386080205440521, 0.010276063345372677, -0.002847160678356886, -0.023967856541275978, -0.027381952852010727, -0.005362551659345627, 0.015828439965844154, 0.07899387925863266, -0.01029185764491558, -0.04805292561650276, 0.06049787998199463, 0.056009672582149506, -0.02509758062660694, -0.03790919855237007, -0.01799025572836399, -0.0712764784693718, -0.0327199324965477, -0.035360004752874374, -0.008670837618410587, 0.0008275359286926687, -0.006968520116060972, 0.0007561978418380022, -0.06222889572381973, 0.05428657308220863, 0.06285564601421356, 0.02499942108988762, -0.026798667386174202, -0.04254079982638359, -0.062076687812805176, 0.009187674149870872, -0.0031894135754555464, -0.021558627486228943, 0.04228276014328003, -0.009483239613473415, -0.012177363969385624, -0.04534138739109039, -0.010191120207309723, -0.004522797651588917, 0.03379319980740547, -0.011220610700547695, -0.008413529023528099, -0.056435924023389816, 0.012159478850662708, -0.024229371920228004, -0.021746709942817688, 0.03670676425099373, 0.025447847321629524, 0.03954688832163811, -0.021429968997836113, 0.020485784858465195, -0.0017174598760902882, 0.03251016512513161, -0.023572174832224846, 0.04573909938335419, 0.05226518586277962, -0.0022583447862416506, 0.016420012339949608, -0.03214966133236885, -0.036131128668785095, -0.02904554083943367, 0.06366918981075287, 0.0022598151117563248, -0.022575872018933296, -0.0017914115451276302, 0.042544543743133545, 2.6105558958988695e-07, 0.018625251948833466, -0.062184739857912064, 0.012693419121205807, 0.03448517248034477, 0.01870846189558506, -0.030960332602262497, 0.002024830551818013, 0.020913327112793922, 0.00227174861356616, -0.014561491087079048, 0.025931794196367264, -0.04661354050040245, 0.027941526845097542, -0.03798174485564232, -0.06345611065626144, 0.00032073797774501145, -0.03029848262667656, 0.04623379185795784, -0.00900615006685257, 0.015982797369360924, 0.0008661397732794285, 0.06551381945610046, 0.02066296711564064, 0.022221103310585022, 0.032564565539360046, -0.04515950754284859, -0.01572466269135475, -0.007282571401447058, 0.02121211588382721, 0.0663432851433754, 0.0010183899430558085, -0.00932217575609684, 0.015206839889287949, 0.04519709572196007, -0.02310042642056942, -0.02633497305214405, 0.032093800604343414, 0.01292461808770895, 0.04124683886766434, 0.0966777503490448, 0.027041887864470482, -0.00797935388982296, 0.01428185123950243, 0.004528719000518322, 0.029184460639953613, 0.003850248409435153, -0.07188764214515686, 0.04086858034133911, -0.011920723132789135, -0.05563896894454956, 0.00604413403198123, 0.006415411829948425, -0.01616969145834446, 0.0014268698869273067, -0.017259301617741585, 0.0072702812030911446, 0.010819995775818825, 0.0598892904818058, -0.025946512818336487, 0.02602837048470974, -0.010784406214952469, -0.07100136578083038, -0.032951511442661285, -0.027173997834324837, 0.023361749947071075, -0.08782172203063965, -0.021371355280280113, 2.843464126220236e-34, -0.005108279176056385, 0.006363709922879934, -0.020215269178152084, -0.06104762479662895, 0.0045957122929394245, -0.0460691936314106, 0.006275549530982971, 0.06189258024096489, 0.05105295404791832, -0.056846264749765396, -0.028418444097042084]

['B. Mishra', 'G. Meyer', 'S. Bonnabel', 'R. Sepulchre']

1209.0430v2

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss relative usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with the state-of-the-art and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix.

Fixed-rank matrix factorizations and Riemannian low-rank optimization

http://arxiv.org/pdf/1209.0430v2

Title Fixedrank matrix factorization Riemannian lowrank optimization Summary Motivated problem learning linear regression model whose parameter large fixedrank nonsymmetric matrix consider optimization smooth cost function defined set fixedrank matrix adopt geometric framework optimization Riemannian quotient manifold study underlying geometry several wellknown fixedrank matrix factorization exploit Riemannian quotient geometry search space design class gradient descent trustregion algorithm proposed algorithm generalize previous result fixedrank symmetric positive semidefinite matrix apply broad range application scale highdimensional problem confer geometric basis recent contribution learning fixedrank nonsymmetric matrix make connection existing algorithm context lowrank matrix completion discus relative usefulness proposed framework Numerical experiment suggest proposed algorithm compete stateoftheart manifold optimization offer effective versatile framework design machine learning algorithm learn fixedrank matrix Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0036589698866009712, 0.02617887407541275, -0.012896829284727573, 0.037416890263557434, 0.036850154399871826, 0.010776466690003872, 0.008870267309248447, 0.013994279317557812, 0.05591784790158272, -0.007664703764021397, -0.0007811099058017135, 0.00489497696980834, 0.011627539992332458, 0.021171046420931816, 0.030184851959347725, -0.08336320519447327, -0.04222290962934494, -0.024180904030799866, -0.01073601096868515, -0.055500827729701996, -0.010899079032242298, -0.004240150097757578, 0.01924615167081356, 0.021175824105739594, -0.07139209657907486, -0.008095837198197842, 0.008957065641880035, -0.0051063052378594875, -0.007541226223111153, -0.01868612691760063, 0.002550812903791666, 0.040374938398599625, 0.024391846731305122, 0.01528173591941595, 2.2096078282629605e-06, 0.009601989760994911, -0.008885092101991177, -0.020811213180422783, 0.06388562172651291, 0.010659239254891872, -0.00882255844771862, 0.008614514954388142, -0.0027272426523268223, -0.049997035413980484, -0.04473932832479477, -0.03131949529051781, -0.02088172920048237, -0.014705227687954903, 0.02574199251830578, -0.011556325480341911, -0.010854728519916534, -0.03214274346828461, -0.004833685699850321, -0.04845031723380089, -0.03402266651391983, -0.04839911311864853, 0.02112739533185959, -0.004614001139998436, -0.0009468873613514006, 0.022238248959183693, -0.02519616298377514, 0.039620839059352875, -0.012776123359799385, 0.04249268025159836, 0.11589036881923676, 0.05586246773600578, -0.012134196236729622, 0.03324402868747711, 0.012630373239517212, 0.08313184976577759, -0.06872695684432983, 0.005203975830227137, 0.0564761646091938, -0.011528647504746914, -0.0005386515404097736, 0.023972440510988235, -0.020142992958426476, -0.027492443099617958, 0.0037003906909376383, -0.004088007379323244, -0.05450797080993652, -0.003091821214184165, -0.017202364280819893, -0.005919455084949732, -0.0210649985820055, 0.10178914666175842, 0.015586606226861477, 0.008348220959305763, -0.025555359199643135, -0.0294091384857893, -0.017463503405451775, 0.0024449157062917948, 0.011005984619259834, -0.012294990010559559, -0.023361090570688248, -0.029737072065472603, 0.02775321714580059, -0.0542665533721447, 0.02273000217974186, -0.024771636351943016, 0.03228909894824028, -0.03782501071691513, 0.06428293883800507, 0.037530653178691864, -0.03617260232567787, 0.009725110605359077, -0.044387467205524445, 0.05711241811513901, -0.047312431037425995, 0.021945776417851448, 0.03548349440097809, -0.0005666543147526681, 0.029477840289473534, 0.07673865556716919, 0.05068867653608322, 0.009914838708937168, -0.029072102159261703, 0.01613716408610344, -0.019438929855823517, 0.01430421695113182, 0.011738967150449753, 0.05239289999008179, 0.026817211881279945, -0.028596557676792145, -0.03929854556918144, -0.007460853084921837, 0.014571991749107838, 0.032405998557806015, -0.07975195348262787, 0.07314390689134598, 0.0006545436335727572, -0.006315190345048904, 0.010647586546838284, 0.02314082346856594, 0.02473408170044422, 0.014514211565256119, 0.0158978383988142, -0.00431100046262145, -0.021309595555067062, -0.0029247081838548183, -0.027517300099134445, -0.037374090403318405, 0.005470849107950926, -0.042880360037088394, 0.009296317584812641, 0.0034750779159367085, -0.004311645869165659, 0.012428863905370235, 0.007695917505770922, -0.035191211849451065, -0.09399570524692535, 0.06357389688491821, 0.06014523282647133, 0.0025822364259511232, 0.0776820108294487, -0.04679020494222641, 0.006095285061746836, 0.036608852446079254, -0.021253341808915138, 0.0665089562535286, 0.02538483403623104, -0.012997530400753021, -0.017975060269236565, 0.00430161552503705, 0.018106939271092415, -0.014664785005152225, 0.002250166842713952, -0.045696016401052475, 0.0015743818366900086, -0.004933455493301153, 0.015228110365569592, 0.01610555127263069, 0.027998734265565872, -0.016313761472702026, 0.02639801800251007, 0.0808463841676712, 0.019638242200016975, 0.02820040099322796, 0.007044123485684395, -0.033761683851480484, -0.03585830330848694, -0.0010383931221440434, -0.008841393515467644, 0.051307640969753265, 0.021999450400471687, -0.03267871215939522, 0.02715732529759407, 0.028043314814567566, -0.03417721763253212, -0.0321255624294281, 0.03193299099802971, -0.07232316583395004, -0.016308223828673363, -0.008022891357541084, 0.0724242776632309, -0.04740140214562416, -0.06630542129278183, -0.024740029126405716, -0.009636211208999157, -0.0016953865997493267, -0.03856470435857773, -0.0007271484937518835, 0.04950045421719551, -0.06677774339914322, -0.004654154647141695, -0.0693131536245346, -0.0394592322409153, -0.020864946767687798, 0.0190899521112442, -0.08216576278209686, -0.02794729173183441, -0.0016036010347306728, 0.0023422264494001865, 0.014195626601576805, -0.0133277028799057, 0.0666096955537796, 0.02376626431941986, 0.005308645311743021, -0.03483178839087486, -0.013318559154868126, -0.017469491809606552, -0.007181765977293253, 0.010474566370248795, -0.010181908495724201, 0.009551554918289185, 0.00993476901203394, 0.0726918950676918, 0.05872955545783043, 0.034961506724357605, 0.01933762989938259, 0.0505559965968132, -0.04408195987343788, 0.05800851434469223, -0.058105774223804474, -0.032470591366291046, -0.033864427357912064, -0.00427411450073123, 0.008341566659510136, 0.024938568472862244, -0.053596410900354385, -0.021143311634659767, 0.07877500355243683, 0.005300820339471102, -0.04721532389521599, 0.029062766581773758, 0.009293447248637676, -0.05746172368526459, -0.04057511314749718, 0.0027469012420624495, -0.0022876146249473095, 0.0160727109760046, -0.03519217669963837, 0.011597811244428158, -0.03718726709485054, 0.03183778002858162, 0.008277312852442265, -0.06440483033657074, 0.009249702095985413, 0.0031477422453463078, -0.016560889780521393, 0.051354020833969116, 0.005810422357171774, -0.02032410353422165, 7.034811278572306e-05, -0.002292788354679942, 0.06433277577161789, 0.00490938313305378, 0.04429676756262779, -0.019645508378744125, 0.013348385691642761, -0.037470076233148575, -0.005164811387658119, -0.021575413644313812, 0.022716764360666275, -0.011063440702855587, 0.05367541313171387, 0.027362534776329994, 0.016071181744337082, -0.054749708622694016, 0.027791345492005348, 0.005715175997465849, -0.010781069286167622, -0.012616556137800217, -0.043308570981025696, 0.00813974067568779, 0.048460155725479126, 0.023865779861807823, 0.023644287139177322, 0.004057693760842085, 0.04814476519823074, -0.027804259210824966, 0.017127148807048798, -0.017270753160119057, -0.035416990518569946, -0.036629606038331985, -0.01833367347717285, 0.039560381323099136, 0.08117349445819855, 0.0122928936034441, -0.03588307648897171, 0.011858201585710049, 0.0819510743021965, 0.009389645420014858, -0.0012113424018025398, -0.07369416952133179, 0.027206774801015854, 0.06449709832668304, -0.019666150212287903, 0.03979372978210449, -0.009448753669857979, 0.048155978322029114, -0.020983314141631126, 0.0013476716121658683, 0.011076129972934723, -0.023121992126107216, -0.02290121465921402, -0.0718829333782196, 0.03536062315106392, -0.008610441349446774, 0.0019574149046093225, 0.024212541058659554, -0.04077603295445442, 0.022548392415046692, 0.028816472738981247, -0.0009750762255862355, -0.013008810579776764, -0.030331367626786232, -0.023424001410603523, -0.06437869369983673, -0.004160289186984301, 0.0054128654301166534, -0.0856841653585434, 0.002944673178717494, 0.030272742733359337, 0.020097512751817703, 0.009433790110051632, -0.028719842433929443, -0.007595802191644907, -0.007366988342255354, -0.025737440213561058, 0.039982378482818604, -0.04321723431348801, -0.03717445582151413, -0.006589618977159262, 0.025749938562512398, -0.025424303486943245, 0.0018993924604728818, -0.0070846243761479855, 0.038292787969112396, -0.003657665802165866, -0.005083355586975813, 0.010492253117263317, -0.03292325511574745, 0.004040656145662069, 0.027721736580133438, 0.05657348781824112, 0.007021898403763771, -0.00842279102653265, -0.04693404212594032, -0.030972514301538467, 0.03789447247982025, 0.020916642621159554, -0.012742729857563972, 0.028012586757540703, -0.03714625537395477, 0.02340552769601345, 0.019472472369670868, 0.04465943202376366, -0.04769359156489372, -0.020064562559127808, -0.037548862397670746, 0.02100479044020176, 0.02308017760515213, 0.04473166912794113, 0.022817498072981834, -0.08207801729440689, -0.018154285848140717, -0.02160835824906826, 0.0828850194811821, 0.015029491856694221, -0.0015390210319310427, 0.07067946344614029, 0.0637182965874672, -0.008624332025647163, 0.0041137998923659325, 0.01449551060795784, -0.032619982957839966, 0.04158708080649376, -0.050127871334552765, 0.06190914660692215, 0.010690046474337578, -0.016776379197835922, -0.030162490904331207, -0.04637382924556732, -0.01465483009815216, -0.01692487858235836, -0.07787113636732101, -0.03119966760277748, -0.00016690931806806475, 0.0008127418695949018, 0.0034354913514107466, -0.10432276129722595, 0.010224553756415844, -0.014308039098978043, -0.048600997775793076, -0.0330987423658371, -0.0817803144454956, 0.05548541620373726, -0.056862976402044296, -0.06657981872558594, -0.017989300191402435, 0.04810686409473419, -0.027789179235696793, -0.056314654648303986, 0.05198704078793526, 0.022970151156187057, 0.014069604687392712, -0.028301741927862167, 0.07440569996833801, -0.023775756359100342, 0.05129873380064964, 0.0013605778804048896, 0.11871358007192612, 0.007466311566531658, 0.06348902732133865, -0.007129794452339411, -0.03218141198158264, -0.0006484555779024959, -0.019086986780166626, -0.02036992274224758, -0.0354221872985363, -0.0282890722155571, 0.025949392467737198, 0.07394659519195557, 0.012076574377715588, -0.024996282532811165, 0.011810991913080215, -0.011344513855874538, 0.0026367041282355785, -0.04297575354576111, 0.07493594288825989, -0.009566772729158401, 0.04745854437351227, -0.009261486120522022, -0.021855877712368965, -0.007693351712077856, -0.01778136007487774, -0.029440129175782204, -0.0235145203769207, 0.05401243641972542, 0.056083254516124725, -0.0017313509015366435, 0.016947396099567413, 0.04665710777044296, -0.03488274663686752, -0.035011522471904755, -0.03888801112771034, -0.019453518092632294, -0.013163173571228981, -0.05436233803629875, 0.06407500058412552, -0.0015402865828946233, 0.007901175878942013, -0.045300163328647614, -0.010741500183939934, 0.013694527558982372, -0.012259198352694511, 0.0006691502640023828, 0.0590960830450058, 0.06114396080374718, -0.021539703011512756, -0.021713392809033394, 0.011538319289684296, 0.00742980046197772, 0.02305614948272705, 0.007757555227726698, -0.07994738966226578, -0.01459714025259018, -0.025319868698716164, -0.009825707413256168, 0.0042824218980968, 0.07126317918300629, 0.017818864434957504, -0.015064960345625877, -0.04741396754980087, 0.027050631120800972, -0.015043645165860653, 0.03927670791745186, 0.0020254317205399275, -0.00750322500243783, 0.017311498522758484, 0.024224918335676193, -0.0644625872373581, -0.0919632762670517, 0.024968145415186882, 0.007058579009026289, -0.03828561678528786, -0.02036174200475216, -0.02114967256784439, -0.02742873504757881, -0.003612987929955125, 0.04295119643211365, 0.0064816842786967754, -0.03844861686229706, -0.000904042855836451, 0.0036708852276206017, 0.021426785737276077, -0.046559881418943405, -0.01972043327987194, 0.025136148557066917, -0.06525903940200806, 0.003913316410034895, -0.02856476418673992, -0.050174858421087265, -0.031152945011854172, -0.0003947107179556042, 0.07924602180719376, 0.012514247559010983, 0.008877507410943508, 0.020324639976024628, -0.024028850719332695, -0.017549023032188416, 0.023670531809329987, -0.03287285193800926, 0.0076827360317111015, 0.07500715553760529, -0.03848595172166824, 0.015912102535367012, 0.06291010975837708, 0.05375773459672928, 0.028618009760975838, -0.022059112787246704, -0.05243045091629028, -0.017479361966252327, -0.05317150056362152, 0.055640775710344315, 0.015593078918755054, 0.058861155062913895, -0.011700467206537724, 0.028208132833242416, -0.03551577031612396, -0.0563843660056591, 0.016220606863498688, -0.02360786497592926, -0.011295203119516373, 0.014998151920735836, 0.002056548837572336, 0.014208242297172546, -0.055036645382642746, 0.00956914946436882, -0.036850567907094955, -0.002663367660716176, -0.012930306605994701, -0.0670526921749115, -0.012495644390583038, -5.70490477530691e-33, 0.004655952099710703, -0.033748168498277664, -0.08418643474578857, 0.04723230004310608, -0.04653968662023544, 0.013138744980096817, 0.036814525723457336, 0.001169038936495781, 0.027045423164963722, -0.016762293875217438, -0.02573101595044136, -0.04482722282409668, -0.03125637024641037, 0.010796262882649899, 0.020200716331601143, 0.005272593814879656, 0.004112842492759228, 0.025784451514482498, 0.030448133125901222, 0.042996615171432495, 0.03886977210640907, 0.053864527493715286, -0.018379559740424156, -0.06711825728416443, -0.08246690034866333, -0.0004924312816001475, -0.014317584224045277, -0.010427731089293957, -0.02403075620532036, 0.01853957399725914, -0.02073495462536812, 0.01924310065805912, 0.012130863964557648, -0.024057911708950996, 0.003153898287564516, -0.03432038426399231, -0.031688056886196136, 0.016829492524266243, -0.01144855935126543, 0.018671685829758644, -0.030668143182992935, 0.00021980004385113716, 0.04868261143565178, 0.01826934702694416, -0.04351675882935524, -0.047296732664108276, 0.07481462508440018, 0.006717262323945761, -0.03990118205547333, -0.010322307236492634, -0.0033204550854861736, 0.015079576522111893, -0.027671022340655327, -0.00780941266566515, 0.04661167040467262, 0.045579053461551666, -0.012853160500526428, 0.0641009509563446, 0.006314788945019245, 0.060662806034088135, -0.06163273751735687, 0.01654226705431938, -0.01348234061151743, 0.019105542451143265, 0.0017982450081035495, 0.05206688493490219, 0.03175675496459007, -0.023057270795106888, -0.025662625208497047, -0.028592966496944427, 0.02366219088435173, 0.029379088431596756, 0.0031316063832491636, -0.021610043942928314, -0.005558569449931383, -0.04606635868549347, -0.04333319142460823, 0.02514132298529148, -0.08658205717802048, -0.008778425864875317, -0.036607980728149414, 0.03420831263065338, 0.003569906111806631, -0.001017941627651453, 0.016340680420398712, -0.007853816263377666, -0.0013731198851019144, 9.418676199857146e-05, -0.0038749424275010824, 0.009775489568710327, -0.047047894448041916, -0.018435698002576828, -0.025716310366988182, -0.02971740998327732, 0.022202016785740852, -0.03193174675107002, 0.009875216521322727, 0.05779571086168289, 0.05583806335926056, -0.03854413703083992, -0.013503077439963818, 0.019525595009326935, -0.031135516241192818, -0.006519934628158808, -0.00688580609858036, -0.001212684903293848, -0.014623529277741909, 0.010243494994938374, 0.008897579275071621, -0.02162080444395542, 0.01734292320907116, -0.05085308104753494, 0.013856498524546623, 0.04133683815598488, 0.01666119135916233, -0.03769565746188164, 0.000856880156788975, 0.09966158121824265, 0.0029818895272910595, 0.057687900960445404, -0.031860899180173874, -0.013342983089387417, -0.016480745747685432, 0.009902726858854294, -0.045113638043403625, -0.0288680512458086, 0.02172277309000492, -0.004755254834890366, 0.04193725436925888, -0.07263068854808807, -0.01721816696226597, -0.0851956158876419, 2.745925939962035e-07, -0.02259025350213051, 0.06643359363079071, -0.06167563050985336, -0.0738798975944519, 0.00361465266905725, -0.004516587592661381, 0.004145985469222069, 0.04203972965478897, -0.01608181558549404, 0.010011767037212849, 0.03365720063447952, -0.0447799414396286, 0.018566936254501343, -0.030638547614216805, -0.07186649739742279, 0.06117100641131401, -0.014465364627540112, 0.033152949064970016, -0.07220518589019775, -0.026605045422911644, 0.00718202767893672, 0.041848648339509964, 0.04209689423441887, -0.03883630037307739, 0.011230600997805595, 0.05239909514784813, 0.023371504619717598, -0.017718328163027763, 0.01152720209211111, -0.046502187848091125, 0.05522366985678673, -0.0070301853120327, 0.008434019051492214, 0.005796759855002165, -0.0012022368609905243, 0.04311443120241165, 0.05842025578022003, 0.00570707255974412, 0.011414775624871254, 0.030234012752771378, 0.016167722642421722, 0.0685180202126503, 0.021197963505983353, -0.0840483009815216, 0.062273699790239334, 0.017440199851989746, -0.01783234439790249, -0.02194475755095482, 0.006148528307676315, 0.05640152096748352, 0.09067431837320328, -0.008593445643782616, 0.024241065606474876, 0.021478867158293724, 0.01161715853959322, -0.03647719323635101, 0.09001441299915314, -0.008513147011399269, 0.0887974202632904, 0.04041050001978874, -0.07681015878915787, -0.010046499781310558, 0.04213938117027283, 0.046023160219192505, 0.04269598424434662, 0.008731142617762089, -0.01026442926377058, 2.8377620602637862e-34, -0.02012268453836441, -0.002762814983725548, 0.027704035863280296, 0.02568999119102955, -0.04431041330099106, -0.016289588063955307, 0.016174262389540672, -0.021966280415654182, 0.018550360575318336, -0.016568681225180626, -0.005869056563824415]

['Jan Oksanen', 'Jarmo Lundén', 'Visa Koivunen']

1209.1739v1

Finding an optimal sensing policy for a particular access policy and sensing scheme is a laborious combinatorial problem that requires the system model parameters to be known. In practise the parameters or the model itself may not be completely known making reinforcement learning methods appealing. In this paper a non-parametric reinforcement learning-based method is developed for sensing and accessing multi-band radio spectrum in multi-user cognitive radio networks. A suboptimal sensing policy search algorithm is proposed for a particular multi-user multi-band access policy and the randomized Chair-Varshney rule. The randomized Chair-Varshney rule is used to reduce the probability of false alarms under a constraint on the probability of detection that protects the primary user. The simulation results show that the proposed method achieves a sum profit (e.g. data rate) close to the optimal sensing policy while achieving the desired probability of detection.

Design of Spectrum Sensing Policy for Multi-user Multi-band Cognitive Radio Network

http://arxiv.org/pdf/1209.1739v1

Title Design Spectrum Sensing Policy Multiuser Multiband Cognitive Radio Network Summary Finding optimal sensing policy particular access policy sensing scheme laborious combinatorial problem requires system model parameter known practise parameter model may completely known making reinforcement learning method appealing paper nonparametric reinforcement learningbased method developed sensing accessing multiband radio spectrum multiuser cognitive radio network suboptimal sensing policy search algorithm proposed particular multiuser multiband access policy randomized ChairVarshney rule randomized ChairVarshney rule used reduce probability false alarm constraint probability detection protects primary user simulation result show proposed method achieves sum profit eg data rate close optimal sensing policy achieving desired probability detection Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0032045890111476183, 0.007365778088569641, -0.033517736941576004, -0.07002975791692734, -0.0451040156185627, -0.07000546902418137, -0.007544105406850576, -0.03902051970362663, 0.002726729027926922, 0.004128263331949711, -0.010601049289107323, 0.03023534268140793, -0.04259691759943962, -0.005154888611286879, -0.044455066323280334, 0.02547995187342167, 0.06110898405313492, -0.05964987352490425, 0.09083636105060577, 0.025435473769903183, -0.010527757927775383, -0.018360689282417297, -0.00542067876085639, -0.01293388195335865, -0.046459633857011795, 0.006667973939329386, -0.0353340208530426, -0.012649212032556534, 0.0011749834520742297, -0.05448915436863899, 0.040032919496297836, -0.029393287375569344, 0.05282309278845787, 0.0699889212846756, 2.0539785055007087e-06, -0.012244786135852337, -0.04850933700799942, -0.033128298819065094, 0.044664110988378525, -0.04224441573023796, 0.02419671230018139, -0.0010848966194316745, -0.00745343416929245, 0.007870202884078026, 0.015519922599196434, 0.022172074764966965, 0.011437027715146542, 0.02281101420521736, 0.022113511338829994, 0.020157938823103905, -0.0101109454408288, 0.010416876524686813, -0.01829829066991806, -0.0012012661900371313, 0.024028923362493515, -0.024731062352657318, 0.021409355103969574, 0.021884696558117867, 0.0411047637462616, -0.04788002744317055, 0.042779095470905304, -0.015013403259217739, 0.0203812588006258, 0.005001460202038288, 0.02341984026134014, -0.007372569292783737, -0.06043790280818939, -0.019450893625617027, -0.03905143588781357, -0.03533395752310753, -0.004215990658849478, -0.010237875394523144, 0.018510887399315834, 0.03632224723696709, -0.023204466328024864, -0.006900391075760126, -0.022776123136281967, -0.009786275215446949, -0.025987831875681877, 0.015405249781906605, -0.023834839463233948, 0.08888491243124008, -0.020352518185973167, 0.04944737255573273, -0.03383433446288109, 0.08034685999155045, -0.04952709749341011, -0.01261165551841259, 0.018653172999620438, -0.014460408128798008, -0.011075645685195923, -0.0044384910725057125, -0.001943401526659727, 0.012430214323103428, -0.08610411733388901, -0.023115677759051323, -0.04062919691205025, -0.02934938855469227, 0.030182218179106712, -0.027009615674614906, 0.0715387687087059, -0.03783213347196579, 0.06339779496192932, -0.018875768408179283, 0.011039524339139462, -0.059416044503450394, -0.035641614347696304, -0.02138652093708515, 0.005360803101211786, -0.015363342128694057, 0.011602930724620819, -0.03744913265109062, -0.007270319387316704, 0.08414565026760101, 0.10279026627540588, -0.05767087638378143, -0.05514858290553093, 0.012987571768462658, -0.008116770535707474, -0.023978888988494873, -0.01377149298787117, 0.0032672060187906027, -0.03166904300451279, 0.05717991292476654, 0.011250706389546394, -0.0556129552423954, 0.0038316429127007723, 0.0860525518655777, -0.03002803772687912, -0.019150137901306152, -0.007268666755408049, 0.030017409473657608, -0.029494604095816612, 0.006593506783246994, -0.03215481713414192, 0.039678025990724564, 0.0038198779802769423, 0.024403231218457222, -0.03776784613728523, -0.06125428155064583, 0.07278698682785034, -0.0071064201183617115, -0.02971639484167099, -0.04805745556950569, -0.03319849446415901, -0.033282894641160965, -0.01655813679099083, 0.06647411733865738, -0.015745962038636208, -0.018110241740942, 0.028499752283096313, 0.011479765176773071, 0.037699367851018906, -0.00489204004406929, 0.08954336494207382, 0.012672416865825653, -0.014486887492239475, 0.05319416522979736, 0.03135565295815468, -0.02343873307108879, 0.01506703533232212, 0.021371474489569664, -0.038922205567359924, -0.029139794409275055, 0.028849907219409943, -0.02751787379384041, 0.036593105643987656, -0.0239032581448555, 0.0159151591360569, 0.04559611901640892, 0.011279936879873276, -0.03506588935852051, -0.01716294139623642, 0.0270383283495903, -0.03749654442071915, 0.03731248155236244, 0.06217014417052269, -0.0646233856678009, -0.03475894406437874, 0.08746369183063507, -0.05572303384542465, -0.027270786464214325, 0.04482448473572731, 0.032160546630620956, -0.06212117150425911, -0.05288265272974968, 0.0034564968664199114, -0.015821147710084915, 0.0035233444068580866, 0.03856431692838669, 0.04486967995762825, -0.025773070752620697, -0.0012736038770526648, 0.013388695195317268, 0.008285826072096825, -0.05426160246133804, 0.06899239122867584, -0.016905074939131737, 0.013949628919363022, 0.03339201956987381, -0.01812685653567314, -0.058602992445230484, 0.004236949607729912, -0.07245554774999619, -0.015310601331293583, -0.01905348338186741, 0.052321601659059525, -0.006163600366562605, 0.005666688550263643, -0.04251505061984062, 0.042745400220155716, -0.002262603025883436, 0.0014315571170300245, 0.021127993240952492, -0.0053670452907681465, 0.026087919250130653, 0.030033988878130913, 0.05744974687695503, -0.013681127689778805, 0.050647836178541183, -0.031761907041072845, 0.03438641503453255, -0.002560703782364726, 0.02510353922843933, 0.0421876423060894, -0.0016127354465425014, -0.00810573436319828, 0.010780840180814266, 0.07001113891601562, -0.05175133794546127, 0.03387923911213875, 0.03244689851999283, -0.026187364012002945, 0.018477555364370346, -0.014796660281717777, -0.02104783058166504, -0.04514966905117035, -0.007502208463847637, -0.013945603743195534, -0.002144280821084976, 0.06133431941270828, 0.03132328391075134, 0.03384001925587654, -0.061055988073349, 0.03066239506006241, -0.03448709845542908, -0.022970808669924736, 0.002225385280326009, -0.049551717936992645, 0.0033470604103058577, -0.009822558611631393, -0.00500769866630435, 0.018205180764198303, 0.07220026850700378, -0.024548575282096863, 0.002447119215503335, -0.041994206607341766, 0.06789025664329529, -0.05954335629940033, 0.04821493476629257, -0.02735654078423977, -0.024361781775951385, -0.007762901484966278, -0.03925950080156326, 0.03465920686721802, 0.03780439868569374, -0.009728978388011456, 0.07455015182495117, -0.016108065843582153, -0.030731510370969772, 0.006679986137896776, -0.00997410248965025, -0.00830383226275444, 0.012024309486150742, -0.03910982608795166, -0.0041596717201173306, 0.014935215003788471, 0.01856808178126812, -0.02350578084588051, -0.04149477928876877, 0.013664064928889275, -0.017139816656708717, -0.007057067006826401, -0.02252914197742939, -0.013485858216881752, -0.011970707215368748, 0.03184352070093155, -0.07345755398273468, 0.002121797064319253, -0.05015243962407112, 0.0021670893765985966, 0.012794725596904755, -0.024248749017715454, 0.018642965704202652, 0.033090099692344666, -0.02317935973405838, -0.0823737308382988, 0.0046338667161762714, -0.0006358065293170512, 0.004613976459950209, -0.009765599854290485, 0.020713090896606445, -0.08220113813877106, 0.016398487612605095, -0.0017279490130022168, -0.008002838119864464, -0.011721272021532059, 0.028435053303837776, 0.059167440980672836, 0.002666868269443512, 0.020343875512480736, 0.008927186019718647, 0.013796189799904823, -0.011704633012413979, 0.003777323756366968, -0.07635601609945297, -0.09039611369371414, 0.0031737617682665586, 0.00013866758672520518, 0.01600692793726921, 0.055590540170669556, 0.0340447835624218, 0.03543384373188019, 0.09020838886499405, 0.02436242252588272, -0.03872990980744362, -0.0777529776096344, 0.014767512679100037, -0.025108957663178444, 0.011821211315691471, 0.04146631807088852, 0.003402506234124303, -0.003459786996245384, -0.027687177062034607, -0.046939313411712646, 0.05843786895275116, -0.05956174060702324, -0.07530827820301056, 0.00874768290668726, 0.026667116209864616, -0.0360136404633522, -0.017506873235106468, -0.04530509188771248, 0.089867502450943, 0.032866980880498886, 0.019343560561537743, -0.013929695822298527, 0.030453087761998177, 0.014085419476032257, -0.0008968199836090207, 0.016003761440515518, -0.020374193787574768, -0.013839978724718094, 0.008121727965772152, 0.01679113134741783, 0.04539822041988373, 0.03380207717418671, -0.030106695368885994, -0.031373683363199234, 0.025826748460531235, 0.015048330649733543, 0.023700308054685593, -0.021972307935357094, 0.04322756081819534, -0.002092411508783698, 0.06637565046548843, 0.004266918636858463, -0.02958788350224495, 0.030524449422955513, 0.02403479814529419, 0.056942809373140335, -0.029889076948165894, 0.06266679614782333, 0.012104932218790054, 0.009519449435174465, -0.06285122036933899, -0.04525614529848099, -0.052654314786195755, -0.016944298520684242, 0.027569541707634926, 0.031622882932424545, 0.011287606321275234, 0.014987536706030369, -0.02424211986362934, 0.03322050720453262, -0.0289341751486063, -0.04561910778284073, -0.007570216432213783, -0.026696184650063515, -0.009130068123340607, -0.014499145559966564, -0.0337013378739357, 0.012609214521944523, -0.008950527757406235, -0.012552675791084766, -0.027709586545825005, 0.037641990929841995, 0.015509916469454765, 0.03578079864382744, -0.010123951360583305, 0.03260175511240959, -0.00933828204870224, -0.0019704103469848633, -0.03619735687971115, -0.03240804374217987, 0.0406968779861927, -0.041307784616947174, 0.02552241086959839, -0.0125225018709898, -0.0417422316968441, -0.057630933821201324, -0.029454758390784264, -0.01873558759689331, -0.008961583487689495, -0.048274993896484375, 0.016492271795868874, 0.028710560873150826, -0.00767146609723568, 0.0634758397936821, 0.0625172033905983, 0.00019214360509067774, 0.006367718335241079, -0.014178956858813763, -0.01761380396783352, -0.01393286231905222, -0.017062753438949585, 0.04884190857410431, 0.08763796836137772, -0.0026981623377650976, -0.026887115091085434, -0.0036966674961149693, -0.05612356588244438, 0.009501860477030277, -0.007367528509348631, -0.0824662297964096, -0.00017004013352561742, -0.010492232628166676, 0.04855902120471001, -0.035908717662096024, 0.02103373035788536, 0.04405811429023743, -0.025228256359696388, 0.03358270600438118, -0.017930401489138603, 0.09921371191740036, 0.03020731545984745, 0.012440591119229794, -0.019514599815011024, -0.07522530108690262, 0.03840005770325661, 0.038254089653491974, -0.003736981889232993, 0.024576334282755852, -0.043296877294778824, -0.009709624573588371, -0.029255231842398643, -0.0589815191924572, -0.0360301211476326, -0.020974546670913696, 0.02685566432774067, 0.010620594024658203, 0.014171116054058075, -0.006905579939484596, -0.02416977472603321, 0.015348863787949085, -0.0031803494784981012, 0.03099437803030014, -0.08263419568538666, -0.0025328765623271465, 0.03256266191601753, 0.021548660472035408, -0.007424018811434507, 0.05053422600030899, 0.0009209585841745138, 0.060183484107255936, -0.016004612669348717, -0.017866067588329315, -0.031583022326231, 0.021754475310444832, 0.007539601996541023, -0.041361868381500244, -0.024748696014285088, 0.024962125346064568, 0.034879282116889954, 0.01177254319190979, -0.0014549228362739086, -0.008333713747560978, 0.014567566104233265, -0.006071905605494976, 0.012797419913113117, 0.0029304770287126303, -0.0003001222212333232, 0.0547616146504879, -0.03623418137431145, 0.06396740674972534, -0.041394539177417755, 0.048142291605472565, 0.010669463314116001, 0.04138275980949402, 0.008022703230381012, 0.017455119639635086, 0.01456691324710846, -0.0009699561051093042, 0.003892274806275964, 0.0490567609667778, 0.03235141187906265, -0.016004255041480064, -0.027002699673175812, -0.0037118829786777496, -0.022550925612449646, -0.005250074435025454, -0.03730390593409538, 0.01664801687002182, -0.0015421540010720491, 0.07813067734241486, 0.026150306686758995, -0.010247846134006977, 0.07518163323402405, -0.03970837965607643, -0.03090568818151951, 0.01419724803417921, 0.037705447524785995, -0.011210473254323006, -0.043063875287771225, 0.028216904029250145, 0.06861468404531479, 0.021378379315137863, 0.0031429454684257507, 0.01584736257791519, 0.01568278856575489, 0.05798249691724777, 0.01150186825543642, -0.07879871875047684, -0.04936040937900543, -0.029907532036304474, 0.03553991764783859, 0.053720906376838684, 0.059611570090055466, -0.04080361872911453, 0.05313274264335632, 0.026386365294456482, 0.02658604085445404, -0.010374775156378746, 0.023039592429995537, 0.011616431176662445, 0.0003126584051642567, 0.029069745913147926, -0.041977737098932266, -0.027323978021740913, 0.03744231536984444, 0.012036312371492386, -0.035092178732156754, -0.03456418961286545, -0.013232597149908543, -0.022559234872460365, -5.710156296319209e-33, -0.018797365948557854, 0.030792471021413803, -0.06071753799915314, -0.04293562471866608, -0.028035759925842285, -0.047738052904605865, 0.031026653945446014, -0.02653554268181324, 0.023642631247639656, -0.04962830990552902, 0.010564730502665043, 0.0055397734977304935, 0.02276807278394699, 0.008275479078292847, 0.011702761985361576, 0.02482783794403076, 0.019556110724806786, -0.016929512843489647, 0.002950018271803856, -0.026187393814325333, 0.006029795855283737, 0.00892724096775055, 0.0090402290225029, 0.02568134292960167, -0.07431858777999878, 0.06155329570174217, -0.02622651681303978, -0.034298598766326904, -0.09467875957489014, 0.044965773820877075, -0.00410404521971941, 0.024624429643154144, -0.01730514131486416, -0.0024147965013980865, 0.009421784430742264, 0.07758228480815887, -0.04044492915272713, -0.053591419011354446, -0.05903991311788559, 0.05723491311073303, -0.021599534898996353, 0.013824420049786568, 0.005197926424443722, 0.010166683234274387, -0.057938724756240845, 0.07072805613279343, 0.06705369800329208, -0.005776022095233202, -0.006504304241389036, -0.027783401310443878, 0.06670765578746796, -0.013633276335895061, 0.006080140359699726, 0.020963609218597412, -0.014509214088320732, -0.045671988278627396, -0.07669369131326675, 0.008276814594864845, -0.05539209023118019, 0.013300093822181225, -0.04949450492858887, 0.04027961567044258, -0.06567464023828506, 0.07507837563753128, 0.025149520486593246, 0.05544525012373924, -0.07470018416643143, -0.010495252907276154, 0.02651747688651085, -0.015329164452850819, -0.008833767846226692, -0.03635048493742943, -0.05991195887327194, 0.02244262769818306, 0.023545462638139725, -0.027205966413021088, -0.037458352744579315, 0.016362203285098076, 0.05614501237869263, 0.03400959074497223, -0.0052187079563736916, -0.006765708792954683, -0.00721083814278245, 0.007989290170371532, 0.03533492237329483, -0.026888161897659302, -0.006256943102926016, -0.010350284166634083, -0.008328749798238277, 0.02044835314154625, -0.00890304520726204, -0.04696481674909592, -0.040277693420648575, -0.04504246637225151, -0.06339419633150101, -0.02994762547314167, 0.027285141870379448, 0.00018424894369672984, 0.005632224027067423, -0.005790613126009703, -0.09734784811735153, -0.03130737692117691, 0.025875741615891457, 0.023045135661959648, 0.011544824577867985, -0.014051726087927818, 0.023771699517965317, 0.07438788563013077, -0.02759533002972603, 0.00490936916321516, 0.010646875947713852, 0.04782700538635254, 0.054690320044755936, 0.024055002257227898, 0.03465336188673973, -0.07691233605146408, -0.01587103120982647, -0.006121571641415358, -0.006070928182452917, -0.07828903943300247, 0.029031269252300262, -0.04916590824723244, -0.025882545858621597, 0.0014723542844876647, -0.01302291825413704, 0.05792718380689621, -0.0937580019235611, 0.0029137234669178724, -0.01500867772847414, -0.015929294750094414, 0.00297722895629704, -0.03397668898105621, 2.7906349941986264e-07, -0.016026347875595093, -0.03453068062663078, 0.011907052248716354, 0.0371854342520237, 0.02167900837957859, -0.009364544413983822, -0.03080986812710762, 0.023945532739162445, -0.0013509022537618876, 0.02963651716709137, -0.04196661338210106, -0.0476837232708931, 0.004791839048266411, 0.010953864082694054, -0.043032556772232056, -0.017109990119934082, -0.011000658385455608, 0.07486821711063385, -0.04861532896757126, 0.011246628127992153, 0.047737035900354385, -0.006923323031514883, -0.004231853410601616, -0.04013315215706825, 0.07623031735420227, 0.021105932071805, -0.009856157004833221, -0.005668302532285452, 0.001297726877965033, -0.011074206791818142, 0.04593204706907272, 0.05260935053229332, -0.01873195543885231, 0.019666217267513275, -0.008121317252516747, 0.05956698954105377, -0.055722687393426895, 0.013218950480222702, 0.046854641288518906, -0.015634868294000626, 0.016698764637112617, -0.008967949077486992, 0.04656989499926567, 0.013636385090649128, 0.036749497056007385, -0.030565226450562477, -0.02565905824303627, 0.0013416159199550748, 0.07494574785232544, -0.02742093615233898, -0.006016555242240429, -0.023248564451932907, -0.009378079324960709, -0.06280066817998886, 0.003008549101650715, 0.03838712349534035, 0.032798901200294495, 0.023790935054421425, 0.03623414412140846, 0.035087477415800095, 0.005389396101236343, -0.008058976382017136, 0.004121291451156139, 0.036279790103435516, 0.043523892760276794, 0.03173086792230606, 0.010549576953053474, 2.133253168738709e-34, 0.0216085072606802, 0.04179556667804718, -0.01818024553358555, -0.06068417429924011, -0.07294656336307526, -0.0032594564836472273, -0.020841354504227638, -0.012091899290680885, 0.07201207429170609, 0.0017399871721863747, -0.018250511959195137]

['Eitan Menahem', 'Alon Schclar', 'Lior Rokach', 'Yuval Elovici']

1209.1797v3

XML transactions are used in many information systems to store data and interact with other systems. Abnormal transactions, the result of either an on-going cyber attack or the actions of a benign user, can potentially harm the interacting systems and therefore they are regarded as a threat. In this paper we address the problem of anomaly detection and localization in XML transactions using machine learning techniques. We present a new XML anomaly detection framework, XML-AD. Within this framework, an automatic method for extracting features from XML transactions was developed as well as a practical method for transforming XML features into vectors of fixed dimensionality. With these two methods in place, the XML-AD framework makes it possible to utilize general learning algorithms for anomaly detection. Central to the functioning of the framework is a novel multi-univariate anomaly detection algorithm, ADIFA. The framework was evaluated on four XML transactions datasets, captured from real information systems, in which it achieved over 89% true positive detection rate with less than a 0.2% false positive rate.

Securing Your Transactions: Detecting Anomalous Patterns In XML Documents

http://arxiv.org/pdf/1209.1797v3

Title Securing Transactions Detecting Anomalous Patterns XML Documents Summary XML transaction used many information system store data interact system Abnormal transaction result either ongoing cyber attack action benign user potentially harm interacting system therefore regarded threat paper address problem anomaly detection localization XML transaction using machine learning technique present new XML anomaly detection framework XMLAD Within framework automatic method extracting feature XML transaction developed well practical method transforming XML feature vector fixed dimensionality two method place XMLAD framework make possible utilize general learning algorithm anomaly detection Central functioning framework novel multiunivariate anomaly detection algorithm ADIFA framework evaluated four XML transaction datasets captured real information system achieved 89 true positive detection rate le 02 false positive rate Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.046378567814826965, -0.02422209642827511, -0.019328588619828224, 0.02666659466922283, -0.01743960939347744, -0.017676232382655144, 0.025655873119831085, 0.023858509957790375, 0.017462242394685745, -0.013036949560046196, 0.05389374867081642, 0.02011130005121231, 0.0063597215339541435, 0.06840687990188599, -0.03226562589406967, 0.020661501213908195, 0.03887755051255226, -0.0018569219391793013, 0.0345107764005661, 0.031055089086294174, 0.01091579720377922, -0.0493122898042202, 0.040553174912929535, -0.0027904717717319727, -0.014805883169174194, -0.014744655229151249, 0.005397307686507702, 0.009076124988496304, 0.023346377536654472, -0.06101639196276665, 0.04923494905233383, -0.03261687234044075, -0.010713077150285244, 0.049208879470825195, 2.0690670226031216e-06, -0.03553088754415512, -0.02907632663846016, 0.0129201989620924, -0.00664150808006525, 0.02266838401556015, -0.09288785606622696, -0.030916692689061165, -0.009758801199495792, -0.003100343979895115, -0.01787911169230938, -0.009098106063902378, -0.0037107898388057947, 0.06883260607719421, 0.054145697504282, 0.03734035789966583, -0.021248627454042435, -0.01440603006631136, 0.004205130506306887, 0.056084051728248596, 0.03061383031308651, 0.030988598242402077, 0.037501491606235504, 0.02501605451107025, 0.02849213220179081, 0.029092557728290558, 0.0047104028053581715, -0.04639829322695732, -0.020902201533317566, -0.03943197429180145, -0.009354179725050926, 0.02005111053586006, -0.006007269490510225, 0.0031276103109121323, -0.0034299450926482677, 0.0005290841800160706, 0.00945226475596428, 0.030035236850380898, 0.042893361300230026, 0.003906498663127422, -0.017847489565610886, -0.016210507601499557, 0.004709477536380291, 0.04380292072892189, -0.0009968611411750317, -0.05207338184118271, 0.02646319381892681, 0.030281586572527885, -0.021485710516572, 0.01736481860280037, -0.051572978496551514, 0.008059547282755375, 0.0009798527462407947, -0.05164340138435364, -0.0719899982213974, -0.03156132996082306, 0.01564324088394642, -0.022887784987688065, 0.031787242740392685, 0.01776469685137272, -0.013623212464153767, -0.02714666537940502, -0.02534891664981842, -0.06431599706411362, 0.06242874264717102, -0.029799696058034897, 0.013142826966941357, -0.0097489720210433, -0.0068897646851837635, 0.016660014167428017, 0.032494813203811646, 0.06064553186297417, 0.002745073288679123, -0.0030056319665163755, 0.020671837031841278, 0.02380259521305561, -0.03420127183198929, 0.0026988345198333263, -0.007529802620410919, 0.049227554351091385, -0.006082192994654179, 0.04784533381462097, -0.0065739331766963005, 0.05927009508013725, -0.0174037367105484, 0.04646090418100357, -0.029775850474834442, -0.00786932185292244, 0.05538775771856308, 0.03382629528641701, 0.02601008489727974, -0.044577132910490036, -0.028152717277407646, -0.0008579208515584469, -0.03438932076096535, 0.004904763773083687, 0.010266507975757122, 0.03898032754659653, -0.010404001921415329, -0.00919312983751297, 0.013984435237944126, 0.032558295875787735, 0.06575457751750946, 0.020184237509965897, -0.10218028724193573, -0.06292103230953217, 0.016480764374136925, 0.014107445254921913, -0.008287510834634304, -0.011510259471833706, -0.06178165599703789, -0.029892809689044952, -0.027977684512734413, 0.07957517355680466, -0.027733419090509415, -0.01247538160532713, -0.016990553587675095, 0.007749732583761215, -0.012624011375010014, 0.025258773937821388, 0.04687541723251343, -0.011431034654378891, 0.022399453446269035, -0.059172339737415314, 0.004272023215889931, 0.021428534761071205, 0.04992883279919624, -0.02620801143348217, 0.026965593919157982, -0.0037383190356194973, -0.04677753895521164, -0.0377916619181633, 0.04389605671167374, 0.02914181537926197, 0.020133597776293755, -0.03565116226673126, -0.02647777646780014, -0.024086708202958107, 0.02176395058631897, -0.04566127806901932, 0.04084843024611473, 0.04701712355017662, -0.07123497128486633, -0.01652836985886097, -0.010416906327009201, 0.0716889500617981, -0.05327783524990082, -0.0026962049305438995, 0.03550201654434204, -0.008970464579761028, -0.06737996637821198, -0.032998476177453995, -0.0703224167227745, -0.006390866357833147, -0.007242490537464619, -0.02449491061270237, -0.049153633415699005, -0.00436707166954875, 0.0147521598264575, -0.04602303355932236, 0.008448679000139236, -0.003182827029377222, 0.0334659144282341, -0.049195561558008194, -0.003802422434091568, 0.05561411380767822, -0.028357764706015587, -0.06532441824674606, 0.030277220532298088, 0.009995661675930023, 0.020269259810447693, -0.03372357040643692, -0.03183993324637413, -0.01569804921746254, -0.05727699026465416, -0.029549257829785347, -0.03948598355054855, 0.000736517715267837, -0.018643397837877274, -0.02363913133740425, -0.013126734644174576, 0.053707655519247055, 0.020186251029372215, -0.02943466790020466, -0.02960706502199173, 0.036750342696905136, -0.0017292061820626259, -0.0015189622063189745, -0.048281457275152206, 0.0006041614688001573, -0.00345230451785028, -0.051928434520959854, 0.070942223072052, 0.03051946684718132, 0.009143555536866188, -0.02169656939804554, 0.031439684331417084, 0.020219547674059868, 0.019778797402977943, 0.012877128086984158, -0.01612042635679245, 0.04970541223883629, 0.0420323945581913, 0.040673915296792984, 0.020780470222234726, -0.012838654220104218, -0.00044924297253601253, 0.01086377166211605, -0.00849223230034113, -0.016661610454320908, 0.07444149255752563, -0.04785678908228874, -0.03527127578854561, -0.05458669736981392, 0.00041439099004492164, 0.009030438959598541, 0.03639362379908562, -0.030194459483027458, 0.030882371589541435, 0.03232353925704956, 0.021219560876488686, 0.005164137575775385, -0.029382728040218353, 0.07545981556177139, 0.032794322818517685, 0.01063541229814291, -0.026856718584895134, -0.06711506098508835, 0.03686166927218437, -0.006161884870380163, 0.014603623189032078, 0.015587718226015568, 0.02513313665986061, 0.07039415836334229, -0.0066819870844483376, -0.004384106490761042, 0.014932290650904179, 0.03467051312327385, 0.03418266773223877, -0.027721615508198738, -0.02877127006649971, -0.011333386413753033, -0.03774544969201088, 0.024507731199264526, -0.0255450289696455, 0.0808107778429985, 0.012808764353394508, -0.02146284468472004, 0.042378999292850494, -0.018708456307649612, -0.035577766597270966, 0.03440939635038376, 0.048346828669309616, -0.060490045696496964, -0.04764050617814064, -0.00517108803614974, -0.0071497717872262, -0.0483086034655571, -0.008685652166604996, -0.01827092655003071, -0.03002653829753399, -0.037265706807374954, -0.07118459045886993, 0.02699902281165123, 0.01713348738849163, 0.02201642096042633, -0.00030281979707069695, 0.006158158183097839, 0.02868049219250679, -0.010136101394891739, -0.0006305244751274586, 0.08684612065553665, 0.003954901359975338, 0.022026825696229935, 0.07707756757736206, 0.0065451390109956264, 0.022249288856983185, -0.02249973826110363, 0.045233726501464844, -0.046581070870161057, 0.02767280861735344, 0.007610986940562725, -0.03920159116387367, -0.03842733055353165, -0.023160869255661964, 0.026940105482935905, -0.015335852280259132, 0.009555951692163944, 0.03959943726658821, 0.014559103175997734, 0.012513108551502228, -0.051598045974969864, -0.06252717971801758, 0.01365408394485712, -0.005761032924056053, 0.0020501723047345877, 0.060182105749845505, 0.014910534024238586, -0.07588693499565125, 0.023511888459324837, -0.042587149888277054, 0.04492450878024101, -0.01942690648138523, -0.09002712368965149, -0.003246903419494629, -0.05239102616906166, 0.002317295176908374, 0.04429128021001816, -0.03955398127436638, -0.012130552902817726, 0.08809860795736313, -0.01556272804737091, 0.003713044337928295, -0.02846781350672245, -0.008378366939723492, 0.006481262855231762, -0.027987463399767876, 0.06743794679641724, -0.0028697799425572157, -0.021258046850562096, 0.003346491139382124, 0.08422014862298965, -0.042085688561201096, -0.06765139102935791, -0.01126786507666111, -0.02995355986058712, -0.04523000866174698, 0.036262884736061096, -0.07988175749778748, -0.030906008556485176, -0.0332074798643589, 0.031789038330316544, -0.022291699424386024, -0.06555462628602982, 0.0229991115629673, 0.017105767503380775, -0.024603577330708504, -0.028235243633389473, -0.04371282458305359, 0.03466857969760895, 0.051156651228666306, 0.02882557548582554, 0.0028638241346925497, -0.04003247246146202, -0.01197065133601427, -0.008945864625275135, 0.01378373708575964, 0.00417892262339592, 0.05409664660692215, -0.037891510874032974, 0.04570392891764641, -0.0366954579949379, -0.03355526179075241, 0.023378372192382812, -0.019560568034648895, 0.026652034372091293, -0.00929204747080803, -0.051156457513570786, -0.07012398540973663, -0.018912961706519127, -0.026536794379353523, 0.0019130586879327893, 0.017678581178188324, -0.004637264646589756, 0.015674054622650146, 0.01459919661283493, 0.02512596733868122, -0.13536298274993896, -0.029070235788822174, 0.03936303034424782, -0.05643294006586075, -0.014410842210054398, 0.031442198902368546, 0.028681421652436256, -0.028797021135687828, -0.020238028839230537, -0.046625636518001556, 0.016047770157456398, 0.014334965497255325, -0.004230189137160778, 0.02925141155719757, 0.046263836324214935, -0.02556169033050537, -0.009936660528182983, 0.042436208575963974, -0.04318966343998909, 0.003618566319346428, 0.005802376661449671, 0.084450863301754, -0.08013926446437836, 0.024477217346429825, -0.04082398861646652, -0.02754548005759716, 0.037845999002456665, 0.008883337490260601, -0.020906465128064156, -0.02844206430017948, -0.02320891246199608, 0.002755397465080023, 0.00956771057099104, 0.04068953916430473, 0.07216745615005493, 0.06904444098472595, 0.007893194444477558, -0.046453092247247696, -0.07644076645374298, -0.054406411945819855, -0.02744864858686924, 0.03379989042878151, 0.04027574881911278, -0.008419597521424294, -0.0372212789952755, 0.003580360673367977, -0.04250191152095795, -0.08369860798120499, 0.032543133944272995, 0.03418204188346863, 0.0524282269179821, 0.10598266124725342, -0.0024140076711773872, 0.01637907885015011, -0.04220699891448021, -0.013870952650904655, 0.0003818870463874191, -0.026476088911294937, -0.005602790508419275, -0.0024591379333287477, 0.019769391044974327, -0.01075018011033535, -0.060532037168741226, 0.029040846973657608, -0.016936728730797768, 0.007507721893489361, 0.008082304149866104, -0.07254496216773987, 0.051939647644758224, -0.05801811441779137, -0.02819444239139557, -0.03928001970052719, 0.031053483486175537, 0.026785654947161674, 0.03649580478668213, -0.066933274269104, -0.08481685072183609, -0.07020144909620285, 0.02851160056889057, 0.06607208400964737, -0.014626403339207172, 0.05967161804437637, 0.0032595270313322544, 0.0044302125461399555, 0.0009843517327681184, -0.008476506918668747, -0.0019444029312580824, 0.020042790099978447, -0.0041069146245718, 0.028143364936113358, 0.02149045839905739, 0.03469810634851456, 0.017207590863108635, -0.019518692046403885, -0.07621243596076965, 0.03256496414542198, 0.015296204946935177, 0.01906081847846508, 0.030738569796085358, -0.034578658640384674, 0.0031077025923877954, 0.041974715888500214, -0.012928495183587074, 0.05957707762718201, 0.05369727313518524, -0.026807207614183426, 0.011843579821288586, 0.004965251311659813, 0.029662026092410088, -0.003841300727799535, -0.023488376289606094, -0.017420750111341476, 0.026632141321897507, 0.011315735056996346, -0.07456715404987335, 0.006505982950329781, 0.0013523048255592585, -0.04643099009990692, -0.04020187258720398, 0.05009300634264946, -0.008914308622479439, 0.05788932368159294, -0.018032435327768326, 0.011627065017819405, -0.014505349099636078, -0.006010856945067644, -0.034528665244579315, 0.029557591304183006, 0.04918496683239937, -0.02441772259771824, 0.009130307473242283, -0.02737550437450409, -0.07921520620584488, -0.04667307063937187, 0.022045275196433067, 0.04290234297513962, 0.009066852740943432, -0.020961899310350418, -0.02694178745150566, 0.005072448868304491, 0.0005262543563731015, -0.01593637466430664, -0.0010859251488000154, 0.016876479610800743, 0.053121913224458694, 0.00032195670064538717, 0.03966795280575752, 0.010544941760599613, 0.0668482780456543, -0.027255354449152946, -0.04418317973613739, -0.013535615988075733, -0.006593811791390181, -0.0429973378777504, -4.891491704554673e-33, 0.045175112783908844, -0.05049661919474602, -0.03730836510658264, -0.004145878832787275, 0.03799816593527794, -0.022594116628170013, -0.013637975789606571, -0.013239586725831032, 0.033354926854372025, -0.0026703174225986004, -0.00024842945276759565, 0.0024476791732013226, 0.012162066996097565, 0.0054414160549640656, 0.007138868793845177, 0.06323596090078354, -0.0023533524945378304, 0.023232465609908104, 0.044908054172992706, -0.017282232642173767, 0.07128386199474335, 0.002219714457169175, 0.048052165657281876, -0.05074772611260414, 0.002235187916085124, -0.04813552647829056, 0.0008117168908938766, -0.0014741267077624798, -0.00347445928491652, 0.007604241371154785, -0.007292259484529495, -0.022418372333049774, 0.0076850163750350475, -0.05013876408338547, -0.03455653786659241, -0.0032994444482028484, -0.006019111257046461, -0.041037727147340775, -0.043496277183294296, 0.01978246122598648, 0.0580674484372139, -0.041987400501966476, 0.04646400362253189, -0.02080189250409603, -0.026987923309206963, 0.041896283626556396, 0.056530773639678955, -0.03057194873690605, -0.046275485306978226, -0.012064125388860703, -0.029677346348762512, -0.013867239467799664, -0.07251514494419098, 0.0763569325208664, 0.01336131151765585, -0.038558561354875565, 0.025079458951950073, -0.04082047939300537, -0.011886985041201115, 0.03538664057850838, 0.0123659772798419, -0.023962685838341713, -0.05520575866103172, -0.0095756771042943, 0.01816599816083908, 0.008364611305296421, 0.004199289716780186, -0.02893696166574955, 0.057233087718486786, 0.06816116720438004, -0.022885752841830254, 0.06492484360933304, 0.02022022195160389, 0.051611706614494324, 0.023815248161554337, -0.0426800511777401, -0.060525137931108475, 0.09410672634840012, -0.041576582938432693, 0.008593343198299408, 0.044642139226198196, -0.050868626683950424, -0.02849493734538555, 0.019838156178593636, 0.07226550579071045, -0.04172598570585251, -0.004891932941973209, -0.01997961290180683, -0.014945476315915585, -0.02093532122671604, -0.019120801240205765, 0.032329220324754715, -0.01695309951901436, -0.09124290943145752, -0.014695978723466396, 0.0036682721693068743, -0.014436355791985989, -0.015947390347719193, -0.008854812942445278, -0.03441067039966583, 0.018108034506440163, -0.027746915817260742, 0.010081480257213116, -0.036764390766620636, 0.002833479316905141, 0.007048401515930891, 0.046945713460445404, 0.03388166427612305, -0.05367284640669823, 0.021854771301150322, 0.02624957449734211, 0.02322031557559967, -0.03878346085548401, 0.08506784588098526, -0.006568274926394224, -0.04941805079579353, -0.02019066922366619, -0.002808009972795844, 0.004955087788403034, 0.025957198813557625, -0.02081761322915554, -0.010371189564466476, -0.03722035884857178, 0.004199966788291931, -0.028911340981721878, -0.007393643260002136, -0.015231113880872726, -0.002317965729162097, 0.06051822379231453, 0.024108588695526123, 0.02651914395391941, -0.022137517109513283, 2.751201009232318e-07, -0.037824470549821854, 0.03469976410269737, 0.034233421087265015, -0.020266784355044365, 0.03531688079237938, 0.05107402428984642, -0.00953292939811945, 0.048721782863140106, -0.035323455929756165, -0.018370363861322403, 0.04084860533475876, -0.07851376384496689, 0.015030857175588608, -0.011591208167374134, -0.040810856968164444, -0.013506320305168629, -0.017570719122886658, 0.0009130841353908181, -0.07173354178667068, 0.024872854351997375, 0.06302008777856827, 0.0593501515686512, 0.02742481604218483, -0.07219923287630081, 0.04727637767791748, -0.03317733108997345, -0.038995977491140366, 0.015977710485458374, -0.023894425481557846, -0.017011307179927826, 0.030475253239274025, 0.05577259883284569, 0.02455727569758892, 0.03961658477783203, -0.055814001709222794, -0.00752103328704834, -0.03857851028442383, 0.035435475409030914, 0.0017027613939717412, 0.03808041661977768, 0.010789894498884678, -0.051211338490247726, 0.027261290699243546, -0.015331218019127846, 0.013811038807034492, 0.03368246182799339, -0.049079760909080505, 0.030052293092012405, -0.028574014082551003, -0.019527850672602654, -0.00804839562624693, 0.017681952565908432, 0.018488194793462753, 0.028734976425766945, -0.004602062050253153, -0.025384195148944855, 0.07114598900079727, -0.02039201185107231, 0.01180767361074686, -0.007328090723603964, -0.012135203927755356, -0.0026298982556909323, 0.06969226896762848, 0.032762814313173294, 0.07382776588201523, 0.05773274973034859, 0.02302929200232029, 2.9409392401972894e-34, -0.02758409082889557, -0.009123130701482296, -0.01374613307416439, 0.02597283013164997, -0.06989636272192001, 0.02236340008676052, 0.03153356537222862, 0.02960394322872162, 0.04776556417346001, -0.004881512373685837, 0.007175661623477936]

['Barzan Mozafari', 'Purnamrita Sarkar', 'Michael J. Franklin', 'Michael I. Jordan', 'Samuel Madden']

1209.3686v4

Crowd-sourcing has become a popular means of acquiring labeled data for a wide variety of tasks where humans are more accurate than computers, e.g., labeling images, matching objects, or analyzing sentiment. However, relying solely on the crowd is often impractical even for data sets with thousands of items, due to time and cost constraints of acquiring human input (which cost pennies and minutes per label). In this paper, we propose algorithms for integrating machine learning into crowd-sourced databases, with the goal of allowing crowd-sourcing applications to scale, i.e., to handle larger datasets at lower costs. The key observation is that, in many of the above tasks, humans and machine learning algorithms can be complementary, as humans are often more accurate but slow and expensive, while algorithms are usually less accurate, but faster and cheaper. Based on this observation, we present two new active learning algorithms to combine humans and algorithms together in a crowd-sourced database. Our algorithms are based on the theory of non-parametric bootstrap, which makes our results applicable to a broad class of machine learning models. Our results, on three real-life datasets collected with Amazon's Mechanical Turk, and on 15 well-known UCI data sets, show that our methods on average ask humans to label one to two orders of magnitude fewer items to achieve the same accuracy as a baseline that labels random images, and two to eight times fewer questions than previous active learning schemes.

Active Learning for Crowd-Sourced Databases

http://arxiv.org/pdf/1209.3686v4

Title Active Learning CrowdSourced Databases Summary Crowdsourcing become popular mean acquiring labeled data wide variety task human accurate computer eg labeling image matching object analyzing sentiment However relying solely crowd often impractical even data set thousand item due time cost constraint acquiring human input cost penny minute per label paper propose algorithm integrating machine learning crowdsourced database goal allowing crowdsourcing application scale ie handle larger datasets lower cost key observation many task human machine learning algorithm complementary human often accurate slow expensive algorithm usually le accurate faster cheaper Based observation present two new active learning algorithm combine human algorithm together crowdsourced database algorithm based theory nonparametric bootstrap make result applicable broad class machine learning model result three reallife datasets collected Amazons Mechanical Turk 15 wellknown UCI data set show method average ask human label one two order magnitude fewer item achieve accuracy baseline label random image two eight time fewer question previous active learning scheme Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.031700119376182556, 0.03322158008813858, -0.007471201475709677, 0.012235318310558796, -0.009067857638001442, 0.02712348662316799, 0.01607501693069935, -0.010255335830152035, 0.013638300821185112, -0.0524890162050724, 0.016345113515853882, 0.003009339328855276, -0.010426532477140427, 0.06727747619152069, 0.026840701699256897, -0.059799764305353165, -0.02183697372674942, -0.008057832717895508, 0.026572372764348984, -0.014017803594470024, 0.010574930347502232, -0.006078144535422325, -0.007397947832942009, 0.015049634501338005, -0.03062729351222515, 0.06866546720266342, -0.030638324096798897, -0.02824682556092739, -0.0020493115298449993, -0.019072623923420906, 0.04564043879508972, 0.04609968140721321, -0.004587376024574041, 0.027220264077186584, 2.0347197278169915e-06, -0.05388094484806061, -0.03590281680226326, -0.015324462205171585, -0.007297303061932325, -0.025938795879483223, 0.012742032296955585, 0.026015494018793106, 0.027384305372834206, 0.004405900835990906, -0.05077917128801346, -0.03856790065765381, 0.045288000255823135, 0.026111962273716927, 0.057366665452718735, -0.00915965624153614, -0.005925990641117096, -0.011302681639790535, -0.008106430992484093, -0.0039080362766981125, 0.05293494090437889, -0.07904985547065735, 0.0369827002286911, -0.0255954097956419, 0.006566036958247423, 0.011264720000326633, 0.02089526876807213, 0.014289062470197678, -0.0322677306830883, 0.0037645206321030855, 0.07331418246030807, 0.007689348421990871, -0.053485531359910965, -0.03154454007744789, -0.01989009976387024, 0.03437943756580353, 0.06361906975507736, -0.02367847040295601, 0.022677632048726082, -0.014098785817623138, -0.013596612960100174, 0.04087788239121437, -0.03082408383488655, 0.005469133611768484, -0.03498505800962448, 0.019580600783228874, -0.08309081941843033, 0.018429351970553398, -0.0036554045509546995, 0.03494230657815933, 0.035862263292074203, 0.0048164427280426025, -0.023946529254317284, -0.032267529517412186, 0.04072852432727814, 0.04744488000869751, -0.023742318153381348, -0.017763448879122734, 0.03661401942372322, 0.012464042752981186, -0.03776472434401512, -0.01432030275464058, -0.005751296877861023, -0.043471068143844604, 0.056986767798662186, -0.049786560237407684, -0.004827064462006092, -0.08028262853622437, -0.020684676244854927, 0.08219321817159653, 0.036888282746076584, -0.024241136386990547, 0.022878697142004967, 0.025206785649061203, -0.009830879047513008, -0.009603421203792095, -0.07580799609422684, 0.015219928696751595, -0.006931766401976347, 0.03616020828485489, 0.007004390005022287, 0.016400447115302086, -0.06810282915830612, 0.014919178560376167, -0.0485474169254303, 0.003563293954357505, 0.026320908218622208, 0.034875884652137756, -0.007195642683655024, 0.004433418158441782, -0.011777560226619244, -0.029836859554052353, -0.012032320722937584, 0.044533804059028625, -0.03926387056708336, -0.00831023883074522, 0.08281571418046951, 0.008264655247330666, 0.03560300171375275, 0.008493130095303059, 0.013169128447771072, 0.024439198896288872, 0.015766847878694534, 0.008210300467908382, -0.05338490381836891, -0.018319126218557358, 0.03905884176492691, 0.03098696656525135, -0.029002945870161057, -0.05650012195110321, 0.010425647720694542, -0.05547560751438141, -0.02186461351811886, 0.0012674559839069843, -0.021137267351150513, 0.010731243528425694, -0.05685240402817726, 0.08831751346588135, -0.06091432645916939, 0.020422130823135376, 0.0891871526837349, -0.007722741924226284, 0.013368276879191399, 0.02993362583220005, -0.002530112164095044, 0.032363828271627426, 0.08760005235671997, -0.0002151804364984855, 0.011284726671874523, 0.0038953828625380993, 0.03234029933810234, -0.034751780331134796, 0.0027799082454293966, 0.026662345975637436, -0.006758463103324175, -0.020838234573602676, -0.08628886193037033, 0.04456835985183716, 0.004226861987262964, 0.012913604266941547, 0.04160593822598457, -0.002389194443821907, -0.04748060554265976, -0.05711321905255318, -0.039862122386693954, 0.03360903635621071, 0.026187030598521233, -0.05344315245747566, 0.006429669447243214, 0.013508633710443974, -0.03003472462296486, -0.039451662451028824, 0.020246626809239388, 0.00033296490437351167, -0.03695167973637581, -0.04641624167561531, -0.03660160303115845, -0.050758689641952515, -0.023740507662296295, 0.023500675335526466, 0.06870874762535095, 0.009284544736146927, 0.006895626895129681, -0.024529902264475822, 0.018467582762241364, 0.01071365736424923, -0.03507469221949577, -0.05377933382987976, 0.03269156813621521, -0.037236832082271576, -0.014212017878890038, -0.05324520170688629, 0.040710706263780594, -0.01625978574156761, 0.04768642783164978, -0.0332585908472538, 0.0022251508198678493, -0.039355941116809845, -0.036035213619470596, -0.0302840955555439, -0.0886349081993103, 0.07993406057357788, 0.029500016942620277, -0.020769299939274788, 0.031469713896512985, -0.013601437211036682, 0.0017793255392462015, 0.0025187761057168245, -0.022436190396547318, 0.034346383064985275, 0.03336075320839882, -0.0074166166596114635, 0.015964269638061523, 0.04011756181716919, 0.02627529948949814, 0.013320458121597767, 0.00036001577973365784, -0.024221504107117653, 0.0373944416642189, 0.01216842606663704, -0.0632084310054779, 0.01421508938074112, 0.06132260710000992, 0.05565235763788223, 0.019421424716711044, -0.012794561684131622, -0.04754622280597687, -0.0029445732943713665, -0.0517951101064682, -0.003809165209531784, -0.0509837344288826, -0.015135431662201881, -0.07311909645795822, -0.023435475304722786, 0.010961102321743965, -0.006426877807825804, 0.0033356426283717155, -0.06120152398943901, 0.07088031619787216, -0.0022404459305107594, -0.009340272285044193, -0.03590225800871849, -0.06241440773010254, 0.06893035769462585, -0.026493074372410774, -0.02443268895149231, -0.0032437879126518965, 0.00031625176779925823, 0.03422056883573532, 0.007152637932449579, 0.018625343218445778, -0.053670287132263184, 0.050072163343429565, -0.04721067473292351, -0.007631764747202396, 0.026477884501218796, -0.016629474237561226, 0.004766902420669794, 0.011217059567570686, 0.029307551681995392, 9.734625928103924e-05, -0.019443996250629425, 0.03318404406309128, -0.011425466276705265, 0.02575826458632946, 0.03161967918276787, 0.03126579895615578, 0.04693690314888954, -0.01676250994205475, -0.016642645001411438, -0.00390038569457829, 0.019879089668393135, 0.08733237534761429, -0.05725350230932236, -0.019336948171257973, -0.03755994513630867, -0.03485698252916336, 0.004476714413613081, 0.04493984580039978, -0.024266401305794716, -0.016352619975805283, -0.016511783003807068, -0.05021202936768532, 0.021797792986035347, 0.022924670949578285, -0.013855363242328167, -0.021440668031573296, 0.025299012660980225, -0.004307150840759277, 0.007891877554357052, -0.025986693799495697, -0.042451705783605576, 0.03283122554421425, -0.04568858444690704, 0.026992138475179672, -0.025394106283783913, -0.002387728076428175, -0.011987818405032158, -0.005763910710811615, 0.010739927180111408, -0.004246041178703308, -0.023779813200235367, -0.1401241570711136, -0.006407897919416428, -0.020410098135471344, 0.057312656193971634, -0.011377329006791115, -0.06088601425290108, 0.037926673889160156, 0.024151897057890892, 0.006716654170304537, 0.012744167819619179, -0.03007015772163868, -0.0059111095033586025, 0.021595986559987068, 0.03829435631632805, 0.046109624207019806, -0.043924666941165924, 0.023519249632954597, -0.00219968450255692, -0.047072287648916245, 0.03406694903969765, -0.04077381640672684, -0.01525083277374506, -0.028941970318555832, -0.006093183998018503, 0.0025905678048729897, -0.03237573057413101, -0.05576588585972786, -0.028144674375653267, -0.033150989562273026, -0.016302287578582764, 0.016430849209427834, -0.008269669488072395, 0.03276395797729492, 0.02003704011440277, -0.002334712538868189, -0.002044161781668663, 0.04971602186560631, -0.040828268975019455, 0.02276936173439026, 0.028722692281007767, 0.023613154888153076, -0.024476656690239906, -0.039705611765384674, -0.008618084713816643, -0.056543514132499695, 0.05602868273854256, 0.03235715255141258, -0.045654457062482834, -0.006292485166341066, 0.01506365742534399, 0.020575447008013725, -0.0006940651219338179, 0.009997883811593056, -0.0032482482492923737, -0.022060664370656013, 0.018215108662843704, 0.03147580847144127, 0.05238383263349533, 0.04563043639063835, -0.06580256670713425, -0.03312372416257858, -0.006621021777391434, -0.031202219426631927, 0.023151157423853874, 0.02184724621474743, -0.039341576397418976, -0.02098701149225235, -0.011152618564665318, 0.07193872332572937, -0.01498393900692463, -0.06614715605974197, 0.013370035216212273, -0.09893828630447388, 0.04307486489415169, -0.029858825728297234, -0.016494406387209892, -0.003202330321073532, -0.03702334687113762, 0.009809802286326885, -0.06768378615379333, -0.0368257611989975, -0.02186049148440361, 0.02349713444709778, 0.01650884933769703, 0.04156775400042534, -0.03253507986664772, -0.013325160369277, 0.015215415507555008, -0.08014142513275146, 0.05635625123977661, 0.029026346281170845, 0.04469228535890579, -0.018279733136296272, -0.0699167549610138, 0.03197789564728737, 0.0036618169397115707, -0.010500388219952583, -0.01142757385969162, 0.10657821595668793, 0.023241320624947548, -0.005000737961381674, 0.007644730154424906, 0.023131441324949265, -0.014040153473615646, 0.03911709785461426, 0.06160798668861389, 0.05396787449717522, 0.02221953310072422, 0.02600252814590931, -0.027948157861828804, -0.01173792127519846, 0.04878958687186241, -0.002739794785156846, -0.019247861579060555, -0.029294481500983238, -0.002849954180419445, -0.018547413870692253, -0.022124895825982094, 0.012017023749649525, -0.03312818333506584, 0.0461592935025692, -0.08269441872835159, -0.1101149469614029, -0.08294489979743958, 0.022590793669223785, 0.0473213717341423, 0.07686261832714081, 0.018269453197717667, 0.04591616243124008, 0.017694178968667984, 0.00946512259542942, -0.026720242574810982, -0.028896940872073174, 0.030369263142347336, 0.026255378499627113, -0.054210562258958817, -0.05528583005070686, -0.008338517509400845, -0.030937902629375458, -0.04253104701638222, -0.014383859932422638, -0.01875637285411358, -0.0468292199075222, 0.06970037519931793, 0.05313944071531296, 0.019333243370056152, -0.008268391713500023, -0.03345551714301109, -0.0721578374505043, -0.0010893972357735038, 0.05447505787014961, 0.02104976959526539, -0.017138062044978142, 0.011712081730365753, -0.012253628112375736, -0.016121558845043182, 0.008380899205803871, -0.05120335519313812, 0.044697392731904984, 0.02539210207760334, -0.07113942503929138, -0.045492347329854965, -0.012912406586110592, 0.012446635402739048, 0.06521575152873993, 0.11363185197114944, 0.008243901655077934, -0.07603464275598526, -0.011802653782069683, 0.011788147501647472, 0.03890419378876686, -0.04723583161830902, -0.04329115152359009, -0.025088801980018616, 0.025858847424387932, 0.03816673159599304, -0.03177344799041748, 0.0024925072211772203, 0.06357815116643906, -5.960487669653958e-06, -0.010974075645208359, 0.015330340713262558, 0.043277546763420105, 0.0668635293841362, -0.015826262533664703, 0.004563085734844208, 0.028860002756118774, 0.023347308859229088, 0.03644264116883278, 0.05076223611831665, 0.01785215362906456, -0.006726343184709549, -0.003377186134457588, 0.030480297282338142, 0.002244508359581232, 0.028842682018876076, -0.013738952577114105, -0.056523244827985764, -0.017358100041747093, 0.07367052137851715, 0.016045263037085533, -0.024018051102757454, -0.013296243734657764, 0.008551262319087982, -0.035153694450855255, -0.003332237945869565, 0.005019682925194502, 0.004345110151916742, -0.017196957021951675, 0.020191004499793053, -0.0035595721565186977, -0.01804574392735958, 0.04121217131614685, 0.05234580487012863, 0.012107005342841148, -0.012907510623335838, -0.04515780135989189, -0.07056286931037903, -0.021166956052184105, 0.06782759726047516, 0.047422103583812714, -0.04114352539181709, -0.006788586266338825, 0.03225889429450035, 0.016593176871538162, -0.029693564400076866, 0.012751426547765732, -0.0022292661014944315, 0.03340119868516922, 0.02434355765581131, 0.04750307649374008, 0.03446733579039574, 0.006685792934149504, 0.03817472979426384, -0.03990146145224571, 0.01478511095046997, -0.008749834261834621, -0.00725529482588172, 0.003258723998442292, -6.165974067317721e-33, -0.008741557598114014, -0.09050602465867996, -0.044856030493974686, -0.034113820642232895, 0.017725002020597458, 0.02272559516131878, 0.027686823159456253, -0.019218550994992256, 0.03899955376982689, -0.002180887619033456, 0.003717587096616626, 0.00017620129801798612, 0.007043106947094202, -0.0064575523138046265, 0.04686891287565231, -0.03433707356452942, 0.01600503921508789, -0.011954300105571747, 0.02986624650657177, -0.008615308441221714, 0.02164824865758419, 0.020279986783862114, -0.010739064775407314, -0.12708933651447296, 0.024386335164308548, 0.016252445057034492, -0.05139093101024628, 0.04332150146365166, 0.006367460824549198, 0.024432353675365448, 0.0196391548961401, 0.030317287892103195, 0.017080646008253098, 0.00038686039624735713, 0.007003793027251959, -0.010708380490541458, -0.04494066908955574, 0.03135151416063309, -0.04674345999956131, 0.04616723209619522, -0.018949851393699646, 0.07465615123510361, 0.025691287592053413, -0.01134854182600975, -0.0121375797316432, 0.008958523161709309, 0.07908369600772858, -0.031583208590745926, -0.02223336137831211, -0.01160173024982214, 0.018379952758550644, 0.0033205561339855194, -0.03187369927763939, 0.050301652401685715, 0.021013421937823296, 0.009613707661628723, -0.010682041756808758, 0.027562636882066727, -0.08356374502182007, 0.01568380929529667, -0.03025702014565468, -0.007905472069978714, -0.005390367936342955, 0.03117075189948082, 0.022684773430228233, 0.009805474430322647, 0.018660875037312508, -0.015895524993538857, -0.0015281849773600698, 0.0022352261003106833, -0.07018053531646729, 0.055288057774305344, 0.059211332350969315, 0.09463761001825333, 0.028749952092766762, -0.04547051712870598, -0.001330218045040965, 0.07922273129224777, 0.021829549223184586, -0.05095139518380165, -0.048642080277204514, 0.01767006143927574, -0.04955082759261131, 0.004868489224463701, 0.0344819575548172, 0.03429152071475983, -0.021282613277435303, 0.008621872402727604, -0.017808087170124054, 0.0068837497383356094, -0.05295204743742943, 0.00014962026034481823, -0.010871116071939468, -0.016496259719133377, -0.029700079932808876, -0.029801800847053528, 0.046142708510160446, 0.029568813741207123, -0.0071062664501369, -0.05461796745657921, -0.0643453374505043, -0.03252561390399933, -0.03566407784819603, 0.0421769805252552, 0.010590498335659504, 0.01773255132138729, 0.06684783101081848, 0.010638958774507046, -0.037024807184934616, 0.018241096287965775, 0.021746721118688583, -0.013895765878260136, 0.017375066876411438, 0.020957637578248978, 0.00804528035223484, -0.023035628721117973, -0.003529098816215992, 0.03383200988173485, 0.024517951533198357, -0.021466394886374474, -0.02318507991731167, -0.0663132518529892, -0.03573911264538765, -0.06309085339307785, -0.020555080845952034, 0.009242473170161247, -0.016440238803625107, -0.05583213269710541, 0.032229986041784286, -0.04104825109243393, 0.0028610462322831154, -0.04945860058069229, 2.647547603373823e-07, 0.029642052948474884, 0.029416441917419434, -0.028944438323378563, -0.030991852283477783, -0.028089074417948723, 0.06811334937810898, -0.011621620506048203, 0.01796957477927208, 0.027313126251101494, 0.021277116611599922, 0.0437796525657177, -0.015848372131586075, 0.03212631121277809, 0.03902469575405121, -0.08379735052585602, -0.058861054480075836, -0.02859576977789402, 0.06247834488749504, -0.02528569847345352, 0.04872185364365578, 0.026431666687130928, 0.045932650566101074, 0.05985383689403534, -0.019348982721567154, 0.024371428415179253, -0.06684823334217072, -0.003088780213147402, -0.033247679471969604, 0.01611480303108692, -0.012591119855642319, 0.028489943593740463, 0.008451242931187153, -0.021535111591219902, 0.02210443653166294, -0.06860880553722382, -0.04268549010157585, 0.07090555876493454, 0.003826611442491412, 0.002948450157418847, 0.034742143005132675, 0.009075506590306759, -0.017750706523656845, 0.04474876448512077, 0.005533698946237564, 0.049636341631412506, -0.013416660018265247, -0.03610043227672577, -0.012909144163131714, 0.0030821834225207567, -0.041502270847558975, 0.03792934864759445, 0.03354043886065483, -0.006032614503055811, -0.012392735108733177, 0.006639925297349691, -0.0027936086989939213, -0.013629603199660778, -0.053996630012989044, 0.02893366850912571, -0.03427756577730179, -0.015685919672250748, -0.04044855758547783, 0.037151627242565155, 0.0688977912068367, 0.006349510978907347, -0.0020204547327011824, 0.02057473734021187, 2.142552890257148e-34, 0.03440268710255623, 0.043869584798812866, 0.025759223848581314, -0.023165317252278328, 0.024801073595881462, 0.012359928339719772, 0.024890201166272163, -0.02962161786854267, -0.002145952545106411, 0.003096221946179867, 0.016586899757385254]

['Kasturi Varadarajan', 'Xin Xiao']

1209.4893v2

In this article, we study shape fitting problems, $\epsilon$-coresets, and total sensitivity. We focus on the $(j,k)$-projective clustering problems, including $k$-median/$k$-means, $k$-line clustering, $j$-subspace approximation, and the integer $(j,k)$-projective clustering problem. We derive upper bounds of total sensitivities for these problems, and obtain $\epsilon$-coresets using these upper bounds. Using a dimension-reduction type argument, we are able to greatly simplify earlier results on total sensitivity for the $k$-median/$k$-means clustering problems, and obtain positively-weighted $\epsilon$-coresets for several variants of the $(j,k)$-projective clustering problem. We also extend an earlier result on $\epsilon$-coresets for the integer $(j,k)$-projective clustering problem in fixed dimension to the case of high dimension.

On the Sensitivity of Shape Fitting Problems

http://arxiv.org/pdf/1209.4893v2

Title Sensitivity Shape Fitting Problems Summary article study shape fitting problem epsiloncoresets total sensitivity focus jkprojective clustering problem including kmediankmeans kline clustering jsubspace approximation integer jkprojective clustering problem derive upper bound total sensitivity problem obtain epsiloncoresets using upper bound Using dimensionreduction type argument able greatly simplify earlier result total sensitivity kmediankmeans clustering problem obtain positivelyweighted epsiloncoresets several variant jkprojective clustering problem also extend earlier result epsiloncoresets integer jkprojective clustering problem fixed dimension case high dimension Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.05666789412498474, -0.04563053697347641, -0.047936830669641495, 0.04983086138963699, 0.01749299094080925, -0.023324361070990562, 0.03445558249950409, 0.05444558709859848, 0.012083201669156551, 0.03790907934308052, 0.009918554686009884, 0.006541362497955561, 0.03812752664089203, 0.06130325794219971, -0.007377707865089178, -0.10952790081501007, -0.02698662504553795, -0.0024947260972112417, -0.04600975662469864, -0.010224045254290104, 0.007491816766560078, -0.018946008756756783, -0.013396545313298702, 0.029132606461644173, -0.06455736607313156, 0.03797993063926697, 0.02463739737868309, -0.011257965117692947, -0.004792400635778904, -0.02287055179476738, 0.06612248718738556, 0.032005395740270615, -0.028650201857089996, 0.0029562688432633877, 2.1614559955196455e-06, -0.05876545235514641, -0.0067510539665818214, 0.005924778524786234, 0.05965891480445862, 0.011349072679877281, 0.05537812411785126, -0.08966580033302307, -0.0001456018362659961, -0.07596844434738159, 0.02910519763827324, 0.03558759763836861, 0.019617097452282906, 0.04871002584695816, -0.002901390427723527, -0.014091049320995808, 0.0016499713528901339, -0.0047202748246490955, -0.005991595331579447, -0.006749663967639208, 0.007124620955437422, 0.002385028637945652, -0.005751083604991436, -0.004125155042856932, -0.01956116035580635, 0.004223573487251997, -0.039632637053728104, 0.030849285423755646, -0.023510240018367767, 0.025375694036483765, 0.038216207176446915, -0.025484301149845123, -0.06677471101284027, 0.0007349902880378067, 0.022211246192455292, 0.05598035827279091, -0.007853121496737003, 0.02424388937652111, 0.00557974586263299, -0.03799707069993019, -0.041986532509326935, 0.01573660969734192, -0.029260706156492233, -0.037424132227897644, 0.007684329990297556, -0.0684460997581482, -0.11528607457876205, 0.053486693650484085, -0.045967284590005875, -0.05134182050824165, 0.020537972450256348, 0.010248079895973206, 0.04106202349066734, 0.01855596713721752, -0.02758605219423771, -0.03542608022689819, -0.05368742719292641, 0.004189871717244387, -0.003941090777516365, -0.04030611738562584, -0.0034321430139243603, -0.06462899595499039, 0.0026248658541589975, -0.02865673415362835, 0.062012188136577606, -0.011097491718828678, 0.06919386237859726, 0.004116882104426622, 0.032944172620773315, 0.004494646564126015, -0.05786522850394249, 0.06225936859846115, -0.05996372923254967, 0.015247825533151627, -0.019354714080691338, 0.00277653313241899, 0.014221358112990856, 0.07239038497209549, -0.0017687386134639382, -0.02009335719048977, -0.022236432880163193, 0.03811393678188324, -0.03054850362241268, 0.021283823996782303, 0.030949948355555534, -0.03324037417769432, 0.015127051621675491, 0.06161762773990631, 0.023807169869542122, -0.056249186396598816, -0.02782999910414219, -0.0015961836325004697, -0.03515159711241722, 0.041497692465782166, -0.04979495331645012, 0.04382285103201866, 0.015575144439935684, 0.011506537906825542, 0.03693395480513573, -0.015423749573528767, 0.03615082427859306, 0.03507975861430168, 0.00695020379498601, 0.0022767207119613886, -0.057354170829057693, 0.003878833493217826, -0.0302503053098917, 0.012218876741826534, -0.01103529054671526, -0.012708669528365135, -0.012620508670806885, -0.037978872656822205, -0.00786822009831667, 0.009058408439159393, 0.0028664092533290386, -0.0752013772726059, -0.0214986652135849, 0.05850185081362724, 0.019578350707888603, -0.0031864766497164965, 0.04375685378909111, -0.009109294041991234, -0.05271255597472191, 0.033867064863443375, 0.021491002291440964, 0.03542104363441467, 0.022693198174238205, -0.051394272595644, -0.02025519125163555, -0.05324960872530937, -0.0254202950745821, 0.012980647385120392, -0.01388070359826088, 0.04205448552966118, 0.018148550763726234, 0.004065470304340124, 0.06229348108172417, -0.049385640770196915, 0.032293662428855896, -0.049841947853565216, 0.027660708874464035, 0.07410255074501038, 0.004619536455720663, -0.0037446925416588783, -0.09454719722270966, -0.0017404839163646102, -0.019455796107649803, -0.03170359134674072, 0.00040010103839449584, 0.03626643866300583, -0.08972208946943283, 0.007383619900792837, -0.013276907615363598, -0.009244254790246487, -0.014501810073852539, -0.025711551308631897, -0.024204900488257408, -0.02856048010289669, 0.009570819325745106, -0.061850909143686295, 0.029415717348456383, -0.028070645406842232, 0.011148255318403244, -0.049571868032217026, -0.009900664910674095, -0.021644417196512222, -0.03510966897010803, -0.020752890035510063, 0.038808487355709076, -0.09943721443414688, -0.04221178963780403, -0.06864387542009354, -0.028385967016220093, 0.03790471702814102, -0.023992789909243584, -0.004606540314853191, 0.035319939255714417, 0.0005493314820341766, 0.011899018660187721, 0.0009312176262028515, 0.023814596235752106, 0.04814237728714943, 0.05345115810632706, -0.020500753074884415, -0.008836719207465649, -0.008329203352332115, 0.008220226503908634, -0.031130485236644745, 0.023240260779857635, 0.02092045173048973, 0.002691815374419093, 0.021192874759435654, 0.04484664648771286, 0.05315018817782402, 0.025997808203101158, 0.015397726558148861, 0.0666419118642807, -0.0515325590968132, 0.051776934415102005, -0.020422369241714478, 0.0018809550674632192, -0.04024958610534668, 0.04993120953440666, 0.013400153256952763, -0.00548070203512907, -0.0007805621135048568, 0.0420171357691288, 2.4365017452510074e-05, 0.019379831850528717, -0.030953139066696167, 0.06462915241718292, 0.011419970542192459, -0.0034182227682322264, -0.0003456990234553814, 0.04000190645456314, -0.06923220306634903, 0.021279441192746162, -0.04440714791417122, 0.002199941547587514, 0.018722517415881157, 0.03700386360287666, -0.026914790272712708, -0.01981406845152378, -0.016834480687975883, -0.02078503929078579, -0.003804867621511221, -0.03779180347919464, -0.020237579941749573, 0.027524229139089584, 0.050724659115076065, 0.006871510297060013, -0.0008458576048724353, -0.02148710936307907, 0.05119679123163223, -0.020861243829131126, 0.03359251469373703, -0.005239991005510092, 0.03169067203998566, -0.0027409696485847235, -0.0008821305236779153, 0.018175233155488968, 0.03358360379934311, 0.016566824167966843, -0.013679908588528633, -0.015523883514106274, 0.06087964400649071, -0.033286724239587784, -0.018977122381329536, -0.036894284188747406, -0.016654180362820625, -0.031534045934677124, -0.012321749702095985, 0.030543189495801926, -0.039418403059244156, 0.012677494436502457, 0.04802781343460083, -0.015022430568933487, 0.015255928039550781, -0.001461610198020935, -0.06356623768806458, -0.02660750225186348, -0.005042255390435457, -0.03661670908331871, 0.12231132388114929, -0.000977654242888093, -0.0787808746099472, -0.03100210428237915, 0.06775444000959396, -0.019400808960199356, 0.013931644149124622, -0.03994939476251602, 0.028300320729613304, 0.053812410682439804, -0.044760894030332565, 0.05886613950133324, -0.002414208371192217, 0.019914884120225906, -0.04424259439110756, -0.021062010899186134, 0.034125689417123795, 0.02735082432627678, 0.03367755189538002, -0.011548119597136974, 0.03375382721424103, 0.019379496574401855, 0.04484430328011513, -0.013977437280118465, -0.002717335242778063, -0.00648131687194109, 0.002105908701196313, -0.003878513816744089, 0.043467890471220016, 0.011645673774182796, -0.00754543486982584, -0.050216589123010635, 0.04929646849632263, 0.030743828043341637, -0.00973507296293974, 0.030706334859132767, -0.011002189479768276, 0.011542215012013912, 0.0302487313747406, -0.010886486619710922, -0.007465860806405544, 0.03626362979412079, -0.030835436657071114, -0.03079822286963463, -0.02834816835820675, -0.010103404521942139, 0.05955423787236214, 0.06581553816795349, -0.028867680579423904, -0.004508241545408964, -0.04426652938127518, -0.042672257870435715, 0.04992089048027992, 0.02506033517420292, 0.03030099906027317, -0.03337715566158295, -0.0036624835338443518, -0.011660597287118435, 0.013720753602683544, -0.019899075850844383, -0.0009059114381670952, -0.024009499698877335, 0.023746810853481293, -0.003659985726699233, 0.015742529183626175, 0.003254542825743556, 0.03447559475898743, -0.011821144260466099, 0.041031815111637115, 0.02061488665640354, 0.007934645749628544, -0.03321615606546402, 0.00995318777859211, 0.09581515192985535, 0.021232852712273598, 0.03292322903871536, 0.03336993604898453, 0.012317290529608727, -0.06756742298603058, -0.02825055457651615, -0.048645980656147, 0.010155245661735535, 0.04037879407405853, -0.004616204649209976, 0.08204543590545654, 0.01948043517768383, 0.00018004002049565315, 0.006715977098792791, -0.005591180175542831, -0.05220509320497513, 0.056528717279434204, -0.015355924144387245, -0.02752518653869629, 0.04806632921099663, -0.09348222613334656, -0.10193237662315369, -0.016642268747091293, 0.04970613867044449, -0.05721469968557358, -0.024024266749620438, 0.02017209120094776, -0.00028331411886028945, -0.06549001485109329, 0.05182709917426109, -0.047007251530885696, 0.02448689006268978, 0.02423260547220707, -0.08208062499761581, -0.023693708702921867, -0.05033835768699646, 0.020464427769184113, 0.01060699112713337, -0.0186971016228199, -0.01242256909608841, 0.03296160697937012, -0.01671290397644043, -0.006872192025184631, 0.011830266565084457, 0.08966804295778275, 0.03300132974982262, 0.016418565064668655, 0.05506031587719917, -0.006844550836831331, 0.031372081488370895, 0.03665154054760933, 0.05188232660293579, 0.047821205109357834, 0.035561226308345795, -0.06117754802107811, -0.019004350528120995, -0.03802723437547684, -0.038484565913677216, 0.002139412797987461, -0.028550051152706146, 0.028233008459210396, -0.03673093765974045, 0.03097749687731266, 0.010801906697452068, -0.009172475896775723, 0.02367589622735977, -0.013168075121939182, -0.00241459789685905, -0.08363347500562668, 0.09987994283437729, -0.016600580886006355, 0.04463350027799606, 0.028821492567658424, -0.060379523783922195, -0.029603933915495872, -0.015206641517579556, 0.01958165317773819, 0.03182784467935562, 0.016198158264160156, 0.007385989185422659, -0.05216943100094795, 0.057809773832559586, 0.005721208173781633, -0.01205755677074194, -0.01827128417789936, -0.026048777624964714, 0.001715287333354354, -0.021227430552244186, 0.0030872062779963017, 0.07008429616689682, 0.006560905836522579, -0.004482585471123457, -0.06675988435745239, -0.03756055608391762, 0.01571003347635269, 0.0011067689629271626, 0.0035357442684471607, 0.01703748293220997, 0.030214307829737663, 0.018884066492319107, -0.010997874662280083, 0.009773612022399902, 0.0051535735838115215, 0.02285688929259777, -0.002956360811367631, -0.05021790787577629, -0.01753719337284565, -0.09595967084169388, -0.045627936720848083, 0.04450378194451332, 0.048901524394750595, 0.05813007056713104, -0.027732448652386665, -0.030960984528064728, 0.03422965481877327, 0.014235271140933037, 0.009813262149691582, 0.012146271765232086, -0.036634281277656555, 0.044400401413440704, 0.03595220670104027, -0.052955128252506256, -0.06885771453380585, 0.019289325922727585, 0.0027273553423583508, -0.03771142661571503, 0.04149114713072777, 0.06507545709609985, 0.05434324964880943, 0.003622722811996937, 0.03286964073777199, -0.0020891851745545864, -0.01767146773636341, -0.026140479370951653, 0.035888977348804474, 0.015429402701556683, -0.03601488843560219, -0.03647792711853981, 0.025586554780602455, -0.08837119489908218, 0.03715845197439194, 0.014812329784035683, 0.09914339333772659, -0.0957547202706337, -0.02652929536998272, -0.016608169302344322, -0.025847844779491425, -0.04481976851820946, -7.612403715029359e-05, -0.03683394566178322, -0.03244013339281082, 0.058727145195007324, 0.04211010783910751, 0.020343316718935966, 0.05874156206846237, -0.0036327755078673363, -0.0019034279976040125, -0.002289435127750039, 0.01740487478673458, -0.029759149998426437, -0.03513868898153305, 0.00791068747639656, -0.0486597865819931, -0.008261068724095821, 0.06338576972484589, 0.017062107101082802, 0.0549563504755497, -0.013207171112298965, -0.005639615003019571, -0.0013998515205457807, -0.03744450584053993, 0.055657289922237396, -0.012217337265610695, 0.003497001249343157, 0.0548723042011261, -0.036074794828891754, -0.0382099486887455, 0.0035460684448480606, -0.04496283456683159, 0.0348287969827652, -0.06581161171197891, -0.05246283486485481, 0.03269415721297264, 0.024211794137954712, -5.225867684801796e-33, -0.01729750633239746, 0.021984774619340897, -0.11758532375097275, 0.008162186481058598, -0.01146635040640831, -0.028670821338891983, 0.03692448139190674, 0.002732397522777319, -0.015285958535969257, -0.059921812266111374, -0.03295637294650078, -0.06678012758493423, -0.02206198312342167, -0.018277093768119812, -0.0010399258462712169, 0.05363797768950462, -0.024764645844697952, 0.01304370816797018, -0.0300929956138134, -0.009890844114124775, -0.003014000365510583, -0.016386287286877632, -0.013698595575988293, -0.018592651933431625, -0.04735226184129715, 0.048440273851156235, 0.011929244734346867, 0.0032140815164893866, -0.0333036407828331, 0.05085905268788338, 0.010230443440377712, 0.037718795239925385, -0.03594154119491577, 0.05121150240302086, -0.019291799515485764, -0.031980160623788834, -0.013249887153506279, -0.039581332355737686, -0.023008309304714203, 0.03972921520471573, 0.07408874481916428, -0.0059631625190377235, 0.009434153325855732, -0.046952299773693085, -0.006877195555716753, -0.034432701766490936, 0.03761981800198555, -0.05429881438612938, -0.012553376145660877, 0.043056778609752655, -0.003351580584421754, 0.00871109589934349, -0.010687156580388546, 0.05068967491388321, 0.008909923024475574, -0.0026277608703821898, 0.01470162719488144, 0.007976480759680271, 0.02043471857905388, 0.020350905135273933, 0.007353055290877819, 0.04683811962604523, -0.02213282696902752, 0.06190003827214241, 0.03505617752671242, 0.002501662354916334, 0.027873501181602478, -0.014485317282378674, 0.008470767177641392, -0.03175937756896019, 0.04038706421852112, 0.016188962385058403, 0.02636711858212948, 0.045974716544151306, -0.028649669140577316, -0.0453493632376194, -0.004372311756014824, 0.03677141293883324, -0.07320218533277512, -0.022112570703029633, -0.02747899480164051, 0.009419511072337627, -0.03467565029859543, 0.0008092084899544716, 0.015341508202254772, -0.03419875353574753, -0.05454423651099205, 0.022597946226596832, -0.033565640449523926, -0.028778793290257454, -0.04489973932504654, -0.0034694625064730644, -0.0550602488219738, -0.00430806539952755, 0.1035446897149086, -0.06326163560152054, 0.0077094207517802715, 0.02817775495350361, 0.03704134747385979, 0.020220788195729256, 0.00789661705493927, -0.04793012514710426, 0.007426162716001272, -0.026847951114177704, 0.018252603709697723, -0.03443446755409241, -0.006765888072550297, -0.01577482372522354, -0.026459913700819016, 0.0018062822055071592, 0.023475315421819687, -0.034132715314626694, 0.0299388375133276, 0.05517304316163063, -0.010214129462838173, -0.07369259744882584, -0.006261357106268406, 0.05329782888293266, 0.01786504127085209, -0.0010571047896519303, -0.01792643405497074, -0.009153524413704872, -0.03232618421316147, 0.003966385964304209, -0.0428737998008728, -0.04300582408905029, 0.012424291111528873, -0.022404853254556656, 0.042452916502952576, -0.015952622517943382, -0.027366461232304573, -0.047332871705293655, 2.787502069168113e-07, 0.009566993452608585, 0.03945155814290047, -0.027545325458049774, -0.034962233155965805, -0.021933823823928833, 0.018444722518324852, -0.042230624705553055, 0.030588671565055847, -0.032530199736356735, 0.04439922049641609, 0.025340940803289413, -0.0450226292014122, 0.018163900822401047, -0.013213095255196095, -0.016080796718597412, 0.03462091088294983, 0.05137550085783005, 0.07871519029140472, -0.019580891355872154, 0.04886585474014282, -0.03957067430019379, 0.0092598432675004, 0.007683964911848307, 0.00584830716252327, -0.0018131360411643982, -0.020566599443554878, 0.0027789000887423754, -0.06448187679052353, 0.034963954240083694, 0.01413627527654171, 0.01177966594696045, -0.025864506140351295, 0.012921039015054703, 0.04517228901386261, 0.012833936139941216, 0.050324637442827225, 0.01856362819671631, 0.01600820943713188, 0.0029648919589817524, 0.007638297043740749, 0.02324223704636097, 0.039674121886491776, 0.035263676196336746, -0.04957745224237442, 0.015299432910978794, 0.0017235612031072378, -0.0022361099254339933, 0.024200407788157463, 0.0014719230821356177, 0.008588987402617931, 0.06257753819227219, -0.021747643128037453, 0.0003038737049791962, 0.0027817459776997566, 0.021473156288266182, -0.02301316149532795, 0.053056322038173676, 0.009131274186074734, 0.020003413781523705, -0.010308457538485527, -0.024504967033863068, 0.011537497863173485, 0.058522116392850876, 0.03891121223568916, 0.05301666259765625, 0.02620466984808445, -0.00903684739023447, 3.1070864127251443e-34, -0.019713619723916054, 0.01994970627129078, 0.007789762690663338, -0.026414837688207626, -0.011498340405523777, 0.00867094099521637, 0.053523268550634384, -0.004068267531692982, 0.03979208692908287, -0.04739714786410332, -0.010500448755919933]

['Makiko Konoshima', 'Yui Noma']

1209.5833v2

We propose a learning method with feature selection for Locality-Sensitive Hashing. Locality-Sensitive Hashing converts feature vectors into bit arrays. These bit arrays can be used to perform similarity searches and personal authentication. The proposed method uses bit arrays longer than those used in the end for similarity and other searches and by learning selects the bits that will be used. We demonstrated this method can effectively perform optimization for cases such as fingerprint images with a large number of labels and extremely few data that share the same labels, as well as verifying that it is also effective for natural images, handwritten digits, and speech features.

Locality-Sensitive Hashing with Margin Based Feature Selection

http://arxiv.org/pdf/1209.5833v2

Title LocalitySensitive Hashing Margin Based Feature Selection Summary propose learning method feature selection LocalitySensitive Hashing LocalitySensitive Hashing convert feature vector bit array bit array used perform similarity search personal authentication proposed method us bit array longer used end similarity search learning selects bit used demonstrated method effectively perform optimization case fingerprint image large number label extremely data share label well verifying also effective natural image handwritten digit speech feature Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.025564763695001602, 0.008919981308281422, -0.014311829581856728, 0.03544965758919716, -0.037395864725112915, 0.013330638408660889, 0.12088780850172043, 0.03242192417383194, -0.009027518332004547, -0.029070522636175156, 0.03221758455038071, -0.004489467479288578, 0.0018885196186602116, 0.02542285807430744, -0.019689539447426796, -0.017777930945158005, -0.006664704065769911, 0.0029643699526786804, -0.023373575881123543, -0.023128507658839226, -0.004773888271301985, -0.01786879077553749, 0.011558016762137413, 0.0327744297683239, -0.030330730602145195, 0.02376321144402027, -0.017856871709227562, -0.012397345155477524, 0.006733942311257124, -0.010725286789238453, 0.013196023181080818, 0.020382672548294067, 0.011353687383234501, 0.0065382556058466434, 2.366449052715325e-06, -0.033136941492557526, -0.06522940844297409, -0.015172690153121948, 0.04772401973605156, -0.04490690678358078, 0.019021788612008095, -0.00644051656126976, -0.01078894454985857, -0.025770720094442368, -0.011272146366536617, -0.036307837814092636, 0.07400955259799957, 0.09020111709833145, -0.0006045923801138997, 0.01673104241490364, -0.02840488590300083, -0.062396977096796036, -0.05590450391173363, 0.010058892890810966, 0.048194680362939835, 0.013683951459825039, 0.010965701192617416, 0.004269391763955355, -0.0018375616054981947, -0.01266163494437933, -0.021928662434220314, -0.000847051152959466, -0.009223765693604946, -0.0023223417811095715, 0.08161762356758118, 0.05452042445540428, -0.008740431629121304, 0.03114503249526024, 0.023187430575489998, 0.030948922038078308, -0.0762973502278328, -0.04379252716898918, 0.03601755574345589, 0.008208902552723885, -0.07018644362688065, 0.04803890734910965, -0.0013263656292110682, -0.010929265059530735, 0.01828145422041416, 0.01531963050365448, -0.095113106071949, 0.04633811116218567, -0.026410961523652077, -0.01295192539691925, -0.019249996170401573, -0.019135938957333565, 0.008938501589000225, -0.03900282084941864, -0.01617918349802494, -0.026969825848937035, -0.02553851157426834, -0.014685770496726036, 0.04485617205500603, -0.023832373321056366, 0.029485655948519707, -0.04081123694777489, 0.017028184607625008, -0.03449443355202675, 0.060604359954595566, -0.023240920156240463, 0.0199423935264349, -0.02101266011595726, -0.02562590502202511, 0.008420751430094242, -0.04677118360996246, 0.0023287911899387836, 0.0017100210534408689, 0.03473259136080742, -0.01879330538213253, 0.025841642171144485, -0.047282591462135315, 0.02424313873052597, 0.00394014734774828, 0.04198648780584335, 0.07713563740253448, -0.0213153213262558, -0.037903741002082825, -0.026628704741597176, -0.014560490846633911, 0.021492760628461838, -0.03159954026341438, -0.0010890128323808312, 0.07685256004333496, 0.007546437904238701, 0.017252938821911812, -0.04584634676575661, -0.043075114488601685, 0.017945170402526855, -0.08495395630598068, 0.05190647020936012, -9.258990758098662e-05, 0.05078495666384697, 0.044069841504096985, -0.014427282847464085, 0.00319298030808568, 0.01635359413921833, 0.03318185731768608, -0.028315475210547447, -0.018246350809931755, 0.014010891318321228, -0.03199306130409241, 0.003226851113140583, 0.012745811603963375, -0.05613848939538002, -0.0018264540703967214, -0.06498679518699646, -0.005224254447966814, 0.025944169610738754, -0.017422478646039963, -0.0029625515453517437, -0.01773482747375965, 0.07520418614149094, -0.007491272408515215, 0.026643522083759308, 0.061686333268880844, 0.01916101761162281, 0.05204925313591957, -0.062380459159612656, -0.0072537376545369625, 0.06893619149923325, 0.050041232258081436, -0.04648694023489952, 0.0020357000175863504, -0.026991575956344604, -0.03481202572584152, -0.04234190657734871, 0.001779414713382721, 0.0065014660358428955, 0.04932183772325516, -0.03264300525188446, -0.008212078362703323, -0.015269952826201916, -0.015603152103722095, -0.04934195429086685, 0.01203262060880661, 0.13507871329784393, 0.04891013354063034, -0.004129902925342321, -0.037225037813186646, 0.06441330909729004, -0.06398028880357742, -0.019083820283412933, 0.030886678025126457, 0.03381931409239769, -0.0493728406727314, -0.049473464488983154, 0.06534329801797867, -0.010480816476047039, -0.02875705622136593, -0.012971064075827599, -0.02708599530160427, -0.03339241072535515, -0.0023001288063824177, 0.015974266454577446, 0.018650975078344345, -0.02482161484658718, 0.03445207327604294, 0.01988629251718521, 0.009411891922354698, -0.054965659976005554, -0.07326333969831467, -0.04270758852362633, 0.07935284078121185, -0.00940040685236454, 0.0011445758864283562, -0.0035326711367815733, 0.05927908048033714, -0.0028125455137342215, -0.027241062372922897, -0.06291239708662033, -0.019306058064103127, 0.0015290044248104095, 0.018543830141425133, -0.08837983012199402, -0.044474199414253235, 0.04840178042650223, -0.01945841871201992, -0.025045625865459442, 0.0029134086798876524, 0.052891358733177185, 0.04893729090690613, 0.009621040895581245, 0.034452199935913086, -0.017035480588674545, 0.05346465855836868, 0.001922262366861105, 0.06157581880688667, 0.0668785497546196, 0.028577925637364388, -0.02453947626054287, 5.619091461994685e-05, -0.03293249383568764, 0.057502686977386475, -0.032518420368433, -0.0035281034652143717, -0.018846791237592697, 0.03421479091048241, 0.032683711498975754, 0.021746862679719925, -0.036106545478105545, 0.05357006564736366, -0.001328723388724029, -0.009734554216265678, -0.01897336170077324, -0.00400304002687335, -0.05098981037735939, -0.06028319522738457, -0.04037007316946983, 0.02338811568915844, -0.05366659536957741, 0.025326434522867203, -0.05060720816254616, 0.06252873688936234, 0.01213918998837471, 0.028326526284217834, -0.0960896760225296, -0.004503441508859396, 0.04952072352170944, -0.05851335451006889, 0.0217599980533123, -0.006558912806212902, -0.025905271992087364, 0.006161946803331375, 0.023247214034199715, 0.04022102802991867, 0.002893509343266487, -0.03310829773545265, -0.05210241302847862, -0.00601283460855484, 0.0067636254243552685, -0.01756526157259941, -0.00046379517880268395, -0.02135995589196682, 0.003361761337146163, -0.03895456716418266, -0.029785780236124992, -0.027780583128333092, -0.04146938398480415, -0.024062879383563995, 0.030959542840719223, -0.02447867952287197, -0.01731908693909645, 0.0345078706741333, -0.03018222004175186, 0.01347217708826065, 0.021569373086094856, -0.010035833343863487, -0.06341563910245895, -0.010886859148740768, 0.01111254096031189, -0.020146416500210762, -0.048104654997587204, 0.024426527321338654, 0.04463654011487961, -0.01645956002175808, -0.022315993905067444, -0.05433249473571777, -0.0038578223902732134, 0.039831142872571945, -0.0466068834066391, 0.06920556724071503, 0.045764029026031494, 0.0036924362648278475, -0.01923440210521221, 0.010830003768205643, 0.056974999606609344, 0.0694323405623436, -0.01925494708120823, 0.001718754880130291, -0.06534705311059952, 0.01751917041838169, 0.010425861924886703, -0.009986395947635174, 0.014429647475481033, 0.0364251546561718, 0.014612549915909767, -0.08750632405281067, 0.014657212421298027, 0.019222339615225792, 0.02749059908092022, -0.004495132248848677, -0.029784070327878, 0.03547001630067825, -0.032095685601234436, 0.027951376512646675, -0.015245827846229076, -0.041442569345235825, 0.01544971950352192, 0.029686566442251205, 0.016582854092121124, 0.049850236624479294, -0.04088551551103592, -0.040689464658498764, 0.046595219522714615, -0.014898138120770454, 0.024269551038742065, -0.046524833887815475, -0.012399290688335896, 0.01850081793963909, 0.002681268844753504, -0.00277016987092793, -0.014274618588387966, -0.0002726072270888835, -0.03699188306927681, 0.03668668121099472, -0.05488799512386322, -0.07537930458784103, -0.044204410165548325, 0.0374259315431118, 0.0322655588388443, -0.012879627756774426, 0.0555427148938179, 0.006994394585490227, -0.0011553774820640683, 0.022798463702201843, 0.038548897951841354, 0.029432378709316254, 0.032723382115364075, -0.021437764167785645, 0.00838120561093092, -0.008320175111293793, 0.05792974680662155, 0.036649711430072784, 0.01878102868795395, -0.0417838990688324, 0.040574248880147934, 0.021080004051327705, -0.03832719475030899, -0.037541646510362625, 0.002823401242494583, 0.029113708063960075, 0.00311555084772408, 0.021693453192710876, 0.0479021854698658, 0.025260591879487038, -0.075432188808918, -0.017856016755104065, -0.0401962473988533, -0.05899099260568619, -0.029758650809526443, 0.0443800613284111, -0.06817879527807236, -0.006422990467399359, -0.0005917179514653981, 0.020617639645934105, -0.0498666912317276, -0.03782745450735092, 0.021258382126688957, -0.039083052426576614, 0.07974248379468918, 0.008454225026071072, -0.005775069817900658, -0.04746744781732559, -0.03961095213890076, -0.004358141683042049, -0.001058149035088718, 0.0003571061824914068, -0.012921583838760853, -0.03326423466205597, -0.044246286153793335, 0.007916363887488842, -0.02242198772728443, 0.010732610709965229, 0.05225661024451256, -0.053505789488554, -0.057839956134557724, 0.012631863355636597, 0.0398867130279541, 0.010661542415618896, -0.07028400897979736, -0.06389455497264862, 0.0028474319260567427, 0.03779466822743416, -0.04787278175354004, 0.05874008685350418, 0.025502637028694153, -0.0037763267755508423, 0.013483834452927113, 0.041642580181360245, 0.030880818143486977, -0.022572217509150505, 0.02097514271736145, -0.01042341347783804, -0.04871365800499916, 0.025835668668150902, 0.0016902447678148746, 0.02564273588359356, 0.0008176290430128574, 0.014825866557657719, 0.01593436859548092, -0.0022839712910354137, -0.05392744392156601, 0.05219022184610367, -0.0027321965899318457, 0.059511322528123856, -0.02388523891568184, 0.010670131072402, 0.0013287916081026196, -0.055622730404138565, -0.06360314041376114, 0.03125344589352608, 0.002216113731265068, 0.04957674443721771, -0.002316675614565611, -0.006849901285022497, -0.0005955346277914941, -0.006630865857005119, -0.05835527554154396, 0.0008516531088389456, -0.011962338350713253, 0.031109336763620377, -0.010461021214723587, 0.05727711692452431, -0.003976583946496248, 0.0009321631514467299, -0.02464188076555729, -0.052468910813331604, -0.002654465613886714, -0.026526115834712982, 0.017892304807901382, 0.02651813253760338, 0.0095879677683115, -0.03896386921405792, -0.05764021351933479, -0.07454775273799896, 0.04709705337882042, 0.0074424888007342815, 0.0033591841347515583, 0.014145377092063427, 0.013407964259386063, -0.08798763900995255, -0.014268603175878525, -0.007255659904330969, 0.0007835827418603003, 0.06353578716516495, 0.05149088054895401, -0.09546336531639099, -0.06570795178413391, -0.021502694115042686, -0.025586923584342003, 0.05098025128245354, 0.058792002499103546, 0.02378503791987896, 0.03377440199255943, -0.014472265727818012, 0.07824363559484482, 0.015328515321016312, 0.016074424609541893, 0.00830999668687582, -0.04352501034736633, 0.009282894432544708, 0.023637373000383377, -0.007068790029734373, 0.0005146601470187306, -0.0015668115811422467, -0.00914958119392395, -0.005092711187899113, 0.02209157682955265, -0.039661772549152374, 0.10287422686815262, -0.04096927493810654, -0.0008304767543449998, -0.04254665970802307, 0.0030170942191034555, 0.03776196017861366, 0.06056215986609459, -0.02954977937042713, 0.01227902714163065, -0.01667903922498226, 0.014709074050188065, -0.04874876141548157, 0.06463979184627533, -0.014633586630225182, -0.03989115357398987, -0.018443260341882706, -0.016071418300271034, 0.032809846103191376, -0.07930600643157959, -0.01036305446177721, -0.0029778392054140568, 0.023030538111925125, -0.04105681926012039, 0.030359316617250443, -0.01477295532822609, -0.014470410533249378, -0.02490411512553692, 0.01942201890051365, -0.014969896525144577, 0.057681530714035034, 0.025382574647665024, -0.010116846300661564, -0.03479130566120148, 0.0010469375411048532, -0.026004398241639137, -0.014060989953577518, 0.022672468796372414, 0.024829892441630363, 0.03738967701792717, -0.0417991541326046, -0.01413517165929079, 0.0173763670027256, 0.027564212679862976, 0.05147670954465866, -0.041860487312078476, 0.02117144502699375, 0.07672173529863358, 0.0245161522179842, 0.011081287637352943, -0.02026704140007496, 0.014621547423303127, -0.02671055495738983, -0.02844459004700184, 0.010494938120245934, -0.005088946782052517, -0.025160405784845352, -5.94152811470759e-33, 0.034087084233760834, -0.06422566622495651, -0.03597026690840721, -0.007830826565623283, -0.014180947095155716, -0.008641050197184086, 0.02433597855269909, -0.0017293242271989584, 0.009865287691354752, -0.03894403949379921, -0.009363837540149689, -0.008017638698220253, 0.035440005362033844, 0.0017023334512487054, 0.01634136401116848, -0.004361521918326616, 0.017666399478912354, 0.02972550131380558, 0.06146771088242531, 0.010548424907028675, 0.07234306633472443, -0.002619518432766199, -0.0007600208627991378, -0.08940890431404114, -0.06944302469491959, -0.0019520185887813568, -0.028790408745408058, -0.010408861562609673, -0.032954659312963486, 0.01263858750462532, -0.009409070014953613, -0.03024570271372795, -0.002043267246335745, -0.0160423144698143, -0.011454259045422077, -0.000607830414082855, -0.009370214305818081, -0.01839008741080761, -0.06315981596708298, 0.02282225713133812, 0.08817891776561737, -0.049172185361385345, 0.026007860898971558, -0.01696721278131008, -0.04577484726905823, 0.009105746634304523, 0.03745586425065994, -0.035976704210042953, -0.07969241589307785, 0.0017354770097881556, -0.009523075073957443, 0.011251626536250114, -0.010783851146697998, 0.034889377653598785, 0.06782223284244537, -0.009494694881141186, -0.003492270829156041, 0.00035948181175626814, -0.046139027923345566, 0.05347682908177376, 0.016540180891752243, 0.008132620714604855, -0.022090302780270576, -0.01894405297935009, 0.042914979159832, 0.07297076284885406, 0.04671766981482506, -0.06416913866996765, 0.03365872800350189, -0.05312500521540642, 0.0007182591944001615, 0.04719748720526695, 0.015735581517219543, 0.02991330251097679, 0.07859115302562714, -0.06052982434630394, -0.06488555669784546, 0.027584020048379898, -0.017222827300429344, 0.026005493476986885, -0.023116417229175568, 0.01738760620355606, -0.010802638716995716, -0.008058331906795502, 0.038547057658433914, 0.015714256092905998, -0.01793261058628559, -0.03512120246887207, -0.012837757356464863, -0.0026422543451189995, -0.030881723389029503, 0.08321740478277206, -0.013779292814433575, -0.010582515969872475, 0.05853067338466644, -0.03248731791973114, 0.013567935675382614, 0.014178725890815258, 0.001289005042053759, -0.07280921936035156, 0.0008879281813278794, -0.045392654836177826, 0.0037839014548808336, -0.05016818642616272, 0.014153280295431614, 0.006430465262383223, 0.05231349915266037, 0.0240853913128376, -0.06527626514434814, -0.0003518174053169787, 0.03544924408197403, -0.03944001719355583, -0.02819719910621643, 0.027404742315411568, -0.01134108193218708, -0.019353976473212242, 0.04000815749168396, 0.07440703362226486, 0.004940138664096594, 0.005840667989104986, 0.007772109471261501, -0.0025098761543631554, 0.009561492130160332, 0.0213761068880558, -0.0015765901189297438, 0.03543196991086006, -0.03014451637864113, -0.019759314134716988, 0.06519967317581177, 0.0008759098127484322, 0.02027406543493271, -0.017565904185175896, 2.95845381970139e-07, -0.0369294248521328, 0.022893045097589493, 0.001001971890218556, -0.08528650552034378, -0.03553444892168045, 0.03317343443632126, 0.00864786934107542, 0.02349412441253662, -0.037469759583473206, 0.01864122599363327, 0.05006204545497894, -0.019413001835346222, 0.06816492974758148, 0.0520978607237339, -0.07611367851495743, 0.06161758303642273, -0.019609786570072174, 0.011346198618412018, -0.044637005776166916, 0.044054578989744186, 0.04464070871472359, 0.047730766236782074, 0.01956062763929367, -0.02607615478336811, 0.06405898183584213, -0.043751850724220276, 0.001729335286654532, -0.01765541173517704, 0.009113499894738197, -0.0510045625269413, 0.02043784223496914, -0.032289840281009674, 0.0025237787049263716, 0.019492359831929207, -0.02026071585714817, 0.005120213609188795, 0.025827795267105103, 0.05350450798869133, 0.007157429587095976, 0.0032653340604156256, -0.018406681716442108, 0.028924928978085518, -0.0066862767562270164, -0.011337376199662685, 0.05650797486305237, 0.029717743396759033, -0.023681670427322388, -0.0445437952876091, 0.020547203719615936, 0.001447684713639319, 0.0384519025683403, 0.015275146812200546, 0.020887423306703568, 0.030339382588863373, 0.04661428555846214, -0.0585244782269001, 0.022164851427078247, -0.05376436561346054, -0.004213365726172924, 0.036986276507377625, 0.0011701489565894008, 0.03427262231707573, 0.006170939654111862, -0.025515539571642876, 0.08718826621770859, -0.03206465020775795, -0.015728725120425224, 3.039815304668233e-34, -0.04578907787799835, 0.014063285663723946, 0.014868651516735554, 0.0026341828051954508, -0.01704793982207775, 0.013652346096932888, 0.017690977081656456, -0.001654353691264987, 0.005376018583774567, -0.03554379567503929, -0.0037209137808531523]

['Pablo Sprechmann', 'Alex M. Bronstein', 'Guillermo Sapiro']

1209.6393v1

In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This approach connects robust principal component analysis (RPCA) with dictionary learning techniques and allows its approximation via trainable encoders. We propose an efficient feed-forward architecture derived from an optimization algorithm designed to exactly solve robust low dimensional projections. This architecture, in combination with different training objective functions, allows the regressors to be used as online approximants of the exact offline RPCA problem or as RPCA-based neural networks. Simple modifications of these encoders can handle challenging extensions, such as the inclusion of geometric data transformations. We present several examples with real data from image, audio, and video processing. When used to approximate RPCA, our basic implementation shows several orders of magnitude speedup compared to the exact solvers with almost no performance degradation. We show the strength of the inclusion of learning to the RPCA approach on a music source separation application, where the encoders outperform the exact RPCA algorithms, which are already reported to produce state-of-the-art results on a benchmark database. Our preliminary implementation on an iPad shows faster-than-real-time performance with minimal latency.

Learning Robust Low-Rank Representations

http://arxiv.org/pdf/1209.6393v1

Title Learning Robust LowRank Representations Summary paper present comprehensive framework learning robust lowrank representation combining extending recent idea learning fast sparse coding regressors structured nonconvex optimization technique approach connects robust principal component analysis RPCA dictionary learning technique allows approximation via trainable encoders propose efficient feedforward architecture derived optimization algorithm designed exactly solve robust low dimensional projection architecture combination different training objective function allows regressors used online approximants exact offline RPCA problem RPCAbased neural network Simple modification encoders handle challenging extension inclusion geometric data transformation present several example real data image audio video processing used approximate RPCA basic implementation show several order magnitude speedup compared exact solver almost performance degradation show strength inclusion learning RPCA approach music source separation application encoders outperform exact RPCA algorithm already reported produce stateoftheart result benchmark database preliminary implementation iPad show fasterthanrealtime performance minimal latency Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.005062490701675415, 0.046525292098522186, -0.0085265152156353, 0.0668376237154007, 0.05255812034010887, -0.017110170796513557, -0.004924585577100515, 0.017801199108362198, -0.041474632918834686, -0.0018485027831047773, -0.012961297295987606, 0.009733282960951328, -0.004616088233888149, 0.0393550768494606, 0.027790451422333717, -0.07995719462633133, -0.02644396759569645, -0.00013216325896792114, -0.002821143949404359, 0.002036598278209567, -0.00206513493321836, -0.055110275745391846, 0.015785660594701767, 0.011312663555145264, -0.0462869293987751, -0.024883165955543518, -0.013610788621008396, -0.025435511022806168, -0.012927084229886532, -0.03976672515273094, -0.027027694508433342, 0.024632666260004044, 0.061356283724308014, 0.0329686738550663, 2.4035787191678537e-06, 0.03775126487016678, -0.005428337957710028, -0.016497112810611725, 0.0525326132774353, -0.003989281132817268, -0.036264192312955856, 0.016224578022956848, -0.02179984748363495, -0.02950265444815159, 0.0013596918433904648, -0.024522781372070312, 0.030018433928489685, 0.04309258237481117, 0.07311396300792694, 0.015984948724508286, -0.027164822444319725, -0.028728563338518143, -0.017968349158763885, -0.029405029490590096, -0.01759476400911808, -0.028183327987790108, 0.010449177585542202, -0.04003436490893364, 0.010893193073570728, -0.0006640588981099427, -0.05130913853645325, 0.013869144022464752, -0.021308230236172676, -0.0294398982077837, 0.062196604907512665, 0.02023247256875038, -0.06563319265842438, -0.05434340983629227, -0.011102714575827122, 0.054071977734565735, -0.0444253608584404, 0.004533425904810429, -0.00392837543040514, 0.023846885189414024, 0.006673501338809729, -0.03979801386594772, -0.04298752173781395, 0.01451503112912178, 0.01900535076856613, 0.020763114094734192, -0.12139298766851425, 0.055653102695941925, 0.0019910905975848436, -0.03511517494916916, 0.038831137120723724, 0.006590116303414106, 0.020000308752059937, -0.03991075977683067, -0.007472378667443991, 0.015643296763300896, -0.026153720915317535, 0.0378948338329792, 0.023401791229844093, -0.049595776945352554, 0.0007958902860991657, -0.018903709948062897, -0.021283527836203575, -0.013099808245897293, -0.028115244582295418, -0.029704825952649117, 0.004646450746804476, -0.015490117482841015, -0.024705197662115097, 0.025420106947422028, -0.040917541831731796, 0.047437697649002075, -0.025599323213100433, 0.03212895616889, -0.004784442018717527, 0.0021310325246304274, 0.0034585262183099985, -0.01036478579044342, 0.04944377765059471, 0.09806089103221893, -0.010891135782003403, 0.0057439981028437614, -0.05393655598163605, -0.005804559215903282, -0.09014074504375458, 0.018323734402656555, -0.0038206875324249268, 0.08474314212799072, 0.018263952806591988, -0.00953998975455761, 0.02971862442791462, 0.05458996444940567, 0.016695190221071243, 0.045408811420202255, -0.07392171025276184, 0.023319358006119728, 0.010495574213564396, 0.036856479942798615, 0.0007800436578691006, 0.04010112211108208, 0.04804271087050438, 0.03380409628152847, -0.027214234694838524, 0.027326663956046104, 0.009214784018695354, 0.022078467532992363, -0.00411413935944438, -0.014461638405919075, -0.02406936138868332, -0.05759677663445473, 0.010454370640218258, -0.023147594183683395, 0.011769155040383339, -0.06419550627470016, 0.008101025596261024, -0.013910802081227303, -0.08284937590360641, 0.06508918106555939, -0.03947172686457634, 0.0027865006122738123, 0.034071214497089386, 0.026814278215169907, -0.019823964685201645, 0.016597101464867592, 0.0001997463114093989, -0.00841617677360773, 0.022558562457561493, -0.0017690393142402172, -0.030351433902978897, 0.025893712416291237, -0.0019044888904318213, -0.044686511158943176, -0.05402578040957451, -0.04550464451313019, 0.031880125403404236, -0.030948473140597343, 0.013154368847608566, 0.030809679999947548, 0.037559669464826584, -0.02399597130715847, 0.014042261056602001, 0.046295709908008575, 0.0019197919173166156, 0.015100814402103424, -0.046865519136190414, -0.013531693257391453, 0.001972197787836194, 0.00736283091828227, 0.05364500731229782, 0.053894493728876114, 0.001963141607120633, -0.040600184351205826, -7.283035665750504e-05, 0.019198182970285416, -0.022380301728844643, 0.013014965690672398, 0.0033076133113354445, 0.004942050203680992, -0.041648782789707184, -0.0034051486290991306, 0.025939635932445526, -0.03996257483959198, 0.0013958768686279655, -0.05393777787685394, -0.015412691980600357, -0.004909198731184006, -0.02858690917491913, -0.02388705313205719, 0.03005615435540676, -0.06220285966992378, -0.01823153719305992, -0.08413992822170258, 0.0608995258808136, -0.04893425852060318, -0.010029537603259087, -0.026856496930122375, -0.0665191188454628, -0.03250754252076149, 0.042642444372177124, -0.0016971738077700138, -0.05607758089900017, 0.043068286031484604, 0.020305288955569267, 0.02342434599995613, -0.05275113508105278, -0.02666385844349861, 0.008464248850941658, 0.0662190243601799, 0.041466664522886276, -0.01259615458548069, 0.013999040238559246, 0.03538874164223671, 0.06097857281565666, 0.02972484566271305, 0.059934161603450775, 0.056662388145923615, 0.01663133129477501, -0.013422586023807526, 0.04411598667502403, -0.04233870655298233, 0.03732459247112274, -0.03159617260098457, -0.025020122528076172, -0.008618230931460857, 0.0587918795645237, -0.05806149169802666, 0.007334000896662474, 0.09262212365865707, 0.006281750742346048, -0.026039596647024155, 0.03183002769947052, 0.004301475360989571, -0.0565512478351593, -0.022350331768393517, 0.03031727857887745, -0.037107404321432114, 0.027076350525021553, 0.003934906329959631, 0.03956069424748421, -0.002757342765107751, 0.0396200567483902, 0.03817014768719673, 0.0038203669246286154, 0.03487234562635422, -0.029455294832587242, -0.05159885063767433, 0.03174736723303795, -0.01794983632862568, -0.014303559437394142, -0.006880687549710274, 0.0002600026782602072, 0.029531976208090782, 0.01868138462305069, 0.0478900782763958, -0.01823417656123638, -0.005059405229985714, -0.06438352912664413, -0.016284652054309845, -0.025770381093025208, 0.03385378047823906, -0.04696246236562729, -0.003848397871479392, 0.04454638063907623, 0.0023337434977293015, -0.02178003638982773, 0.004995416849851608, 0.03555712103843689, -0.008263791911303997, -0.022456364706158638, -0.02666964754462242, 0.03132785111665726, -0.011165313422679901, -0.010898089967668056, -0.06072675809264183, 0.017572704702615738, 0.015030174516141415, 0.018835728988051414, 0.026545001193881035, 0.009044352918863297, -0.021639375016093254, -0.03886059299111366, -0.008640987798571587, 0.0010659336112439632, 0.02045077458024025, -0.013514374382793903, 0.016735825687646866, 0.06915192306041718, 0.07333627343177795, 0.015254984609782696, 0.0003659474023152143, 0.025327447801828384, 0.01749718189239502, 0.05066157504916191, 0.03916747123003006, -0.032402824610471725, -0.054119277745485306, 0.0531640388071537, 0.005784154403954744, -0.027477500960230827, -0.012374037876725197, 0.022346585988998413, -0.04066385328769684, -0.11377370357513428, -0.01569189317524433, -0.01286324579268694, -0.020975904539227486, 0.0018961005844175816, -0.011535881087183952, 0.014429571107029915, 0.008933357894420624, -0.005873704329133034, 0.01467254851013422, -0.07423020154237747, 0.00983678549528122, -0.045658327639102936, -0.009799293242394924, -0.00491299806162715, -0.08302924036979675, -0.011118903756141663, -0.038435615599155426, 0.003365304321050644, 0.007556485012173653, -0.05655822530388832, 0.0011363292578607798, 0.03515848517417908, -0.04209071025252342, -0.02931009978055954, -0.02867044135928154, -0.04619886726140976, -0.020847966894507408, 0.03803398460149765, 0.008531497791409492, -0.018125735223293304, 0.035666026175022125, 0.0008774008601903915, 0.028877098113298416, 0.0028287468012422323, 0.03657390922307968, -0.009698493406176567, 0.022549381479620934, -0.014986994676291943, 0.11411455273628235, 0.0167711041867733, 0.027152197435498238, -0.01573065109550953, -0.011863123625516891, 0.05886127054691315, 0.022345958277583122, 0.0011467505246400833, -0.06905259937047958, -0.05657560005784035, 0.07125760614871979, 0.0060066720470786095, 0.06819698959589005, -0.024295274168252945, 0.05719355493783951, -0.046267714351415634, 0.022346464917063713, 0.0025761001743376255, 0.037814076989889145, 0.015876831486821175, -0.09921973198652267, -0.021554118022322655, -0.014495129697024822, 0.038224976509809494, 0.07015826553106308, -0.005438126157969236, 0.0569743812084198, 0.020189525559544563, -0.03153015673160553, 0.06698668003082275, 0.036320991814136505, -0.033823102712631226, -0.02219923958182335, -0.061761099845170975, 0.07715188711881638, 0.005562909413129091, 0.02611291967332363, -0.10083853453397751, -0.03021889366209507, 0.016835330054163933, -0.0004793336847797036, 0.002842435147613287, -0.009780092164874077, 0.001105796778574586, -0.02601649798452854, 0.0075652115046978, -0.06695637851953506, -0.015308557078242302, -0.03244916722178459, -0.061709120869636536, 0.023981444537639618, -0.030366217717528343, 0.040033403784036636, -0.02678145095705986, 0.006280447356402874, -0.06039462238550186, 0.004317548591643572, -0.002293652156367898, -0.0029091958422213793, 0.02465660125017166, 0.0507124699652195, -0.02484070137143135, 0.03958576172590256, 0.03899715095758438, 0.004617633763700724, 0.030539631843566895, 0.000602395215537399, 0.09460555016994476, -0.026395726948976517, 0.007489731069654226, -0.01982327550649643, 0.018186287954449654, -0.00947938859462738, 0.02432817779481411, -0.0038450947031378746, 0.04617590457201004, 0.0035115410573780537, 0.04364527016878128, 0.05891919881105423, 0.051827169954776764, -0.00682523287832737, -0.002479019807651639, 0.009541074745357037, -0.005070963874459267, -0.017659742385149002, 0.04959610849618912, -0.0001512760791229084, 0.0340307354927063, -0.016339387744665146, 0.01240524835884571, 0.0002695075236260891, 0.003883760655298829, -0.027447344735264778, -0.04122164472937584, 0.029148519039154053, -0.03161114826798439, 0.003815643722191453, 0.007129634264856577, 0.046443577855825424, -0.034399062395095825, -0.008305746130645275, -0.04471820592880249, -0.021434752270579338, -0.007282034028321505, -0.0068723042495548725, 0.007322633173316717, -0.0005612415843643248, 0.03560278192162514, 0.0018491073278710246, -0.015506465919315815, -0.021758057177066803, 0.03619925305247307, 0.006528815254569054, 0.03094332478940487, 0.04259652644395828, -0.08695601671934128, -0.023265253752470016, 0.0303513016551733, -0.053245607763528824, 0.06145487725734711, -0.00506069278344512, -0.00584851810708642, 0.006112057249993086, 0.0008137503755278885, 0.02624673955142498, 0.03205743059515953, 0.061070773750543594, 0.03271148353815079, -0.0021861791610717773, -0.03639565035700798, 0.03487589955329895, -0.0855802372097969, 0.008910042233765125, -0.0020405505783855915, 0.015168817713856697, 0.008325834758579731, 0.02015933021903038, -0.043768495321273804, -0.024853892624378204, 0.03654327988624573, -0.004825442098081112, -0.05225594341754913, 0.03632183372974396, 0.015307714231312275, -0.08669804781675339, -0.05106789991259575, 0.01903274655342102, 0.0471385233104229, 0.006345800589770079, 0.05715753138065338, 0.006035474129021168, -0.0143795907497406, -0.01570218801498413, -0.011867918074131012, 0.029456960037350655, -0.031520236283540726, 0.04186602309346199, 0.005055634770542383, 0.004526528995484114, -0.03103811666369438, 0.017777232453227043, 0.08082003146409988, -0.021282218396663666, -0.033474840223789215, 0.014232587069272995, -0.016717083752155304, -0.013167697936296463, 0.006856515072286129, -0.014160395599901676, -0.01887929067015648, 0.056119486689567566, -0.01749458722770214, 0.0033597219735383987, 0.029531311243772507, 0.036046870052814484, 0.008337228558957577, -0.03854965791106224, -0.04898929223418236, -0.00195681001059711, -0.04191276431083679, 0.04256799444556236, 0.00876977201551199, 0.04546600580215454, -0.011563899926841259, 0.0230796430259943, 0.04448876529932022, -0.0426039919257164, 0.01894957758486271, -0.08544868975877762, 0.027040014043450356, -0.011171712540090084, 0.0051954686641693115, -0.02872340939939022, 0.006588751450181007, 0.05424440652132034, 0.0209879819303751, -0.03816070035099983, -0.0017503179842606187, -0.0018462985754013062, -0.017432423308491707, -6.032430194882632e-33, -0.012163946405053139, 0.010806551203131676, -0.06697788834571838, -0.024329787120223045, -0.0029658174607902765, 0.0070073469541966915, -0.011946558952331543, -0.014579921029508114, 0.01601317897439003, -0.010229966603219509, -0.02674562856554985, 0.018336808308959007, -0.0035018909256905317, 0.01872660219669342, 0.03094603307545185, 0.0038401512429118156, 0.05093484744429588, -0.03252590447664261, 0.01438867673277855, 0.0004982965183444321, 0.05500218644738197, 0.012655769474804401, -0.024497920647263527, -0.11444921046495438, -0.12723560631275177, 0.02817070111632347, -0.02165399305522442, -0.022775186225771904, 0.016717420890927315, 0.006302801892161369, -0.02411978878080845, 0.02937781997025013, -0.004493543412536383, -0.018274813890457153, 0.008790000341832638, 0.015604299493134022, -0.043672218918800354, -0.01991591602563858, -0.047621652483940125, -0.017329446971416473, 0.042215097695589066, -0.021252669394016266, 0.04613199830055237, 0.017560340464115143, -0.05425775423645973, -0.0158392284065485, 0.04972322657704353, -0.048504315316677094, -0.014755554497241974, -0.05050648748874664, 0.008219178766012192, -0.008464695885777473, -0.04169956594705582, 0.024419935420155525, 0.029439762234687805, -0.002756723901256919, -0.04244161769747734, 0.06313171237707138, -0.04758792370557785, 0.04382328689098358, -0.048321012407541275, 0.0558040514588356, 0.03413177654147148, 0.0106090372428298, -0.006907682400196791, 0.03614885360002518, -0.021076995879411697, -0.08853968977928162, 0.014948124997317791, -0.02022395096719265, -0.005145751405507326, 0.02467220462858677, 0.08549970388412476, 0.009908448904752731, 0.04365122690796852, -0.04328709840774536, -0.06034306064248085, 0.02787947468459606, -0.0009313924238085747, -0.004984098486602306, 0.018037257716059685, 0.019123129546642303, -0.0312427319586277, -0.0016638424713164568, 0.04522646963596344, -0.02185305953025818, -0.022599903866648674, -0.014364304952323437, 0.04360702261328697, -0.006575891748070717, 0.0042138718999922276, 0.03024635836482048, 0.016379011794924736, -0.05814531445503235, 0.06338119506835938, 0.039727192372083664, -0.010516146197915077, 0.019059156998991966, 0.04806170612573624, -0.02015620656311512, -0.009235032834112644, 0.008745001628994942, 0.07256999611854553, -0.005921387113630772, 0.004917575046420097, -0.03801418095827103, -0.012334741652011871, 0.03914420306682587, 0.008544438518583775, -0.02266397327184677, 0.0545215979218483, -0.006973435170948505, 0.00680746091529727, 0.07581640779972076, -0.009193142876029015, -0.025015775114297867, 0.015360960736870766, 0.04887644201517105, 0.01103891059756279, 0.06557990610599518, -0.014597862958908081, -0.01799895614385605, 0.024052632972598076, -0.019616134464740753, -0.006399712525308132, 0.04582260549068451, -0.036189038306474686, -0.007099661510437727, 0.04340878501534462, -0.06488189101219177, -0.0050560240633785725, -0.03146003186702728, 3.0246729920690996e-07, -0.07253663241863251, 0.016025284305214882, -0.035541336983442307, -0.07096558064222336, 0.007255153264850378, -0.02094792015850544, -0.033662497997283936, 0.026994986459612846, 0.007718394044786692, -0.05558541417121887, 0.0083846440538764, -0.07993452250957489, 0.011358148418366909, 0.010902083478868008, -0.04798746109008789, 0.010145536623895168, -0.06416963040828705, 0.009026851505041122, -0.015871785581111908, -0.023577479645609856, 0.0709632858633995, 0.12024911493062973, -0.022567404434084892, -0.045325521379709244, -0.017195817083120346, 0.056401610374450684, 0.004810761660337448, 0.03664343059062958, 0.03756523132324219, -0.0935707688331604, 0.04532691091299057, 0.01303812488913536, -0.006746908649802208, 0.0066098300740122795, -0.04765727370977402, 0.07587841153144836, 0.07315238565206528, 0.012952208518981934, -0.0488644577562809, -0.02440035715699196, 0.005883367266505957, 0.07140996307134628, 0.02206685207784176, -0.007650218438357115, 0.038732223212718964, 0.004712558351457119, -0.04454612731933594, -0.006887975614517927, -0.05545777827501297, 0.03722700849175453, -0.033095113933086395, -0.021321037784218788, 0.019949866458773613, -0.05529937520623207, -0.019463786855340004, -0.017808031290769577, 0.0029312381520867348, -0.02640611119568348, 0.042438942939043045, -0.01111582014709711, -0.03678642958402634, 0.010233784094452858, 0.025625281035900116, -0.0032852659933269024, 0.07562089711427689, 0.018678506836295128, -0.009816483594477177, 2.6987019969164712e-34, -0.014295883476734161, -0.013648874126374722, 0.021951861679553986, -0.016886863857507706, -0.05255439132452011, -0.021618936210870743, 0.020833460614085197, 0.011135091073811054, -0.019547076895833015, -0.021583518013358116, -0.005560913123190403]

['Houtao Deng', 'George Runger']

1209.6425v3

The regularized random forest (RRF) was recently proposed for feature selection by building only one ensemble. In RRF the features are evaluated on a part of the training data at each tree node. We derive an upper bound for the number of distinct Gini information gain values in a node, and show that many features can share the same information gain at a node with a small number of instances and a large number of features. Therefore, in a node with a small number of instances, RRF is likely to select a feature not strongly relevant. Here an enhanced RRF, referred to as the guided RRF (GRRF), is proposed. In GRRF, the importance scores from an ordinary random forest (RF) are used to guide the feature selection process in RRF. Experiments on 10 gene data sets show that the accuracy performance of GRRF is, in general, more robust than RRF when their parameters change. GRRF is computationally efficient, can select compact feature subsets, and has competitive accuracy performance, compared to RRF, varSelRF and LASSO logistic regression (with evaluations from an RF classifier). Also, RF applied to the features selected by RRF with the minimal regularization outperforms RF applied to all the features for most of the data sets considered here. Therefore, if accuracy is considered more important than the size of the feature subset, RRF with the minimal regularization may be considered. We use the accuracy performance of RF, a strong classifier, to evaluate feature selection methods, and illustrate that weak classifiers are less capable of capturing the information contained in a feature subset. Both RRF and GRRF were implemented in the "RRF" R package available at CRAN, the official R package archive.

Gene selection with guided regularized random forest

http://arxiv.org/pdf/1209.6425v3

Title Gene selection guided regularized random forest Summary regularized random forest RRF recently proposed feature selection building one ensemble RRF feature evaluated part training data tree node derive upper bound number distinct Gini information gain value node show many feature share information gain node small number instance large number feature Therefore node small number instance RRF likely select feature strongly relevant enhanced RRF referred guided RRF GRRF proposed GRRF importance score ordinary random forest RF used guide feature selection process RRF Experiments 10 gene data set show accuracy performance GRRF general robust RRF parameter change GRRF computationally efficient select compact feature subset competitive accuracy performance compared RRF varSelRF LASSO logistic regression evaluation RF classifier Also RF applied feature selected RRF minimal regularization outperforms RF applied feature data set considered Therefore accuracy considered important size feature subset RRF minimal regularization may considered use accuracy performance RF strong classifier evaluate feature selection method illustrate weak classifier le capable capturing information contained feature subset RRF GRRF implemented RRF R package available CRAN official R package archive Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.02368643321096897, 0.011692280881106853, -0.050486400723457336, -0.026351409032940865, -0.014464985579252243, -0.006727985572069883, 0.05204164981842041, 0.04182351753115654, 0.016101108863949776, -0.0019776555709540844, 0.06942356377840042, 0.029723137617111206, 0.027660762891173363, 0.026518844068050385, -0.00471819331869483, -0.03033679537475109, -0.00443792250007391, 0.012138950638473034, 0.019566211849451065, 0.005543842446058989, -0.0013362704776227474, 0.009409111924469471, 0.053289152681827545, 0.04772553965449333, -0.04541676491498947, 0.019946645945310593, 0.004652672912925482, -0.02467171847820282, 0.03668070584535599, -0.04625482112169266, 0.02574172429740429, 0.01037193275988102, 0.0061576333828270435, -0.014563915319740772, 2.207988472946454e-06, -0.06097971647977829, -0.024511685594916344, 0.0015412995126098394, 0.026088865473866463, -0.03428946062922478, -0.0032951110042631626, 0.037466127425432205, 0.04756291210651398, -0.023932553827762604, 0.0166489128023386, -0.04401993378996849, 0.050859421491622925, 0.05887040123343468, -0.04133758321404457, 0.009198039770126343, -0.007913422770798206, -0.026221666485071182, 0.0014082748675718904, -0.004505650606006384, 0.10523143410682678, -0.0006595500162802637, 0.018469233065843582, 0.0023458122741431, 0.011930974200367928, -0.029351871460676193, -0.02052742801606655, -0.014877311885356903, -0.0005534515366889536, 0.017769422382116318, 0.04004182294011116, 0.002317698672413826, -0.039774712175130844, -0.04129945859313011, 0.02425757236778736, 0.0024431785568594933, -0.03780055418610573, -0.03718435391783714, 0.01927054300904274, 0.04202879220247269, -0.033375464379787445, -0.0032979233656078577, 0.0015206729294732213, -0.006181161850690842, -0.06777739524841309, -0.00595159363001585, -0.033225417137145996, 0.03453126549720764, 0.014142142608761787, -0.014192179776728153, 0.025362851098179817, 0.015218136832118034, 0.0019849019590765238, 0.007712311577051878, 0.020411057397723198, -0.037964627146720886, -0.03581419214606285, 0.0021278110798448324, -0.00900976825505495, -0.028233595192432404, -0.02211270108819008, -0.06076863780617714, 0.010657185688614845, 0.0018648476107046008, 0.11133795976638794, 0.02135479636490345, -0.020028699189424515, -0.025977211073040962, 0.007262245751917362, 0.011983472853899002, -0.03724468871951103, -0.023773666471242905, -0.007608677260577679, 0.06309236586093903, 0.028807442635297775, 0.009273091331124306, -0.06505540758371353, 0.049845825880765915, 0.02085236646234989, 0.048792388290166855, 0.0008548879995942116, -0.0002594839606899768, -0.0808970108628273, -0.05004662275314331, -0.002988524967804551, -0.02855270355939865, 0.05520417168736458, 0.05997217819094658, 0.029125632718205452, 0.0752716213464737, 0.018901562318205833, -0.007916135713458061, -0.04192688316106796, -0.0025196566712111235, -0.010453803464770317, -0.009473264217376709, 0.016118763014674187, 0.010634839534759521, 0.04204608500003815, -0.011461302638053894, 0.002484380966052413, 0.02980821020901203, 0.0415840707719326, -0.04082360491156578, -0.008904234506189823, -0.005996822379529476, -0.03183826059103012, -0.03539669141173363, -0.04557659104466438, 0.00758710689842701, -0.0321706123650074, 0.025505028665065765, 0.012825430370867252, 0.05300426483154297, 0.02590167708694935, -0.05468739569187164, -0.006120862904936075, 0.03579634428024292, -0.03952061012387276, 0.019082587212324142, 0.021422067657113075, -0.020310675725340843, 0.023198923096060753, -0.024555521085858345, -0.0047168550081551075, 0.023719074204564095, 0.05954664200544357, -0.050874967128038406, -0.012264188379049301, -0.015446298755705357, -0.08194830268621445, -0.05404257774353027, 0.03482744097709656, -0.0024459578562527895, 0.026193803176283836, -0.027385035529732704, 0.007122502196580172, -0.03559351712465286, 0.020865043625235558, -0.045851051807403564, 0.026691043749451637, 0.049609068781137466, 0.05244441702961922, 0.038293369114398956, 0.033527713268995285, 0.03803020715713501, -0.00953385978937149, -0.054242588579654694, 0.052492059767246246, 0.049250610172748566, -0.09857700020074844, -0.012556799687445164, -0.023424308747053146, 0.02008683979511261, -0.0034964585211127996, -0.022475138306617737, -0.026895690709352493, 0.015465062111616135, -0.032446615397930145, -0.0308873001486063, 0.036599647253751755, 0.01062720362097025, 0.025187773630023003, -0.04716701805591583, 0.015432246960699558, -0.011860369704663754, -0.08302442729473114, -0.03612370043992996, 0.06871084868907928, -0.04865724965929985, -0.0019980156794190407, -0.06622704863548279, 0.011500110849738121, -0.03574036434292793, -0.05684442073106766, -0.06596442312002182, 0.0007199012325145304, -0.00521725881844759, 0.05650348216295242, -0.020888900384306908, -0.012356076389551163, 0.06576070189476013, 0.03775062412023544, 0.04100346937775612, -0.023916563019156456, 0.021102076396346092, 0.019188402220606804, -0.0028209115844219923, -0.029180776327848434, 0.017935074865818024, -0.007727423682808876, 0.006492207292467356, 0.06135766953229904, -0.0004896074533462524, 0.03654410317540169, -0.03836549073457718, -0.010202943347394466, -0.013840082101523876, 0.05143599957227707, -0.006842726841568947, -0.008765376172959805, 0.01620752550661564, 0.049480244517326355, -0.02269403263926506, -0.06666495651006699, 0.007678438909351826, -0.017922082915902138, 0.028591278940439224, -0.053645193576812744, 0.010099274106323719, -0.023937564343214035, -0.06208885833621025, 0.008307178504765034, -0.024311073124408722, 0.0065064337104558945, -0.028491435572504997, -0.035697028040885925, -0.004747568629682064, 0.04474423825740814, 0.04664848744869232, 0.021782999858260155, 0.0018916140543296933, -0.11556514352560043, 0.027488525956869125, -0.04097481071949005, 0.040784161537885666, -0.023873714730143547, -0.05449342727661133, -0.03590874373912811, 0.00826989021152258, 0.061596766114234924, -0.019153602421283722, 0.041136689484119415, -0.00701500941067934, -0.0030314677860587835, 0.01386389508843422, 0.017725160345435143, -0.0384758897125721, -0.003959266934543848, 0.017691385000944138, -0.015408922918140888, 0.021787507459521294, 0.044325631111860275, -0.011999924667179585, -0.03973918780684471, 0.004494934342801571, -0.03882795199751854, -0.020071012899279594, -0.058857306838035583, 0.0029966675210744143, 0.005298996344208717, 0.039911504834890366, 0.07468980550765991, -0.0770929753780365, 0.033882781863212585, 0.03655393794178963, -0.02684183046221733, -0.05465080216526985, 0.007838649675250053, -0.01543864980340004, -0.026131147518754005, -0.001354622421786189, -0.06279653310775757, -0.024843625724315643, -0.007609473541378975, -0.011848721653223038, 0.009406408295035362, 0.06551870703697205, 0.005113736726343632, 0.035332053899765015, -0.017440512776374817, 0.015255004167556763, 0.014265005476772785, 0.001280894153751433, 0.02587888017296791, 0.003789322217926383, 0.030963031575083733, -0.010119648650288582, -0.02100999839603901, -0.005755779333412647, 0.03588295355439186, 0.018712254241108894, -0.05654986947774887, 0.020643873140215874, -0.000534761231392622, 0.042443450540304184, -0.008002016693353653, -0.0797041580080986, 0.04446116089820862, 0.06109273061156273, -0.0005457013612613082, -0.02887018956243992, -0.03504618629813194, 0.02552107907831669, 0.007253047078847885, 0.007467672694474459, 0.012123951688408852, -0.005599064752459526, 0.005493875127285719, 0.04565834626555443, 0.016730958595871925, 0.016733679920434952, -0.05044526234269142, -0.010810892097651958, -0.0056354207918047905, -0.008393597789108753, 0.04418071731925011, 0.02992239221930504, -0.017289912328124046, 0.01899499073624611, 0.028754254803061485, -0.015648946166038513, 0.046412114053964615, -0.02498186193406582, -0.014228826388716698, 0.03179118409752846, -0.007850050926208496, 0.03157495707273483, -0.052228860557079315, -0.013939466327428818, 0.03997057303786278, 0.032838959246873856, 0.013548147864639759, -0.04003246873617172, -0.027842307463288307, 0.007885927334427834, 0.06024395301938057, 0.0096253277733922, -0.042942509055137634, -0.031852591782808304, -0.02341580204665661, 0.028757067397236824, -0.04270778223872185, 0.005459345877170563, 0.0029410445131361485, -0.02604515478014946, 0.07736043632030487, -0.015571651048958302, -0.005039161071181297, 0.04203251376748085, 0.05965042859315872, -0.0871652290225029, -0.012008278630673885, -0.06286433339118958, 0.010095153003931046, 0.009876225143671036, 0.045299503952264786, 0.02495935745537281, 0.001515130396001041, -0.016466183587908745, -0.026898615062236786, -0.03379224240779877, -0.06288494169712067, 0.04621042683720589, -0.02948351576924324, 0.019915997982025146, 0.006352737080305815, -0.09007109701633453, -0.030329206958413124, -0.06546097248792648, -0.017475156113505363, -0.03967611864209175, -0.05614801496267319, -0.009932866320014, -0.00693913409486413, -0.04353964328765869, -0.017416127026081085, -0.08401814103126526, -0.015676867216825485, 0.05674276500940323, -0.03818454220890999, -0.032740820199251175, 0.0522359199821949, 0.03964005038142204, 0.009584381245076656, -0.003300175303593278, 0.0034055609721690416, -0.012625975534319878, 0.013969690538942814, -0.08751746267080307, 0.13401134312152863, 0.07578621804714203, -0.012725235894322395, -0.02959544211626053, 0.003240829100832343, 0.033703986555337906, -0.006669154390692711, 0.024233553558588028, 0.04694750905036926, -0.02932113967835903, -0.05823497474193573, -0.011548451147973537, 0.017127467319369316, -0.0012285226257517934, 0.017391398549079895, 0.028840631246566772, -0.015626734122633934, -0.029815129935741425, 0.0007356134592555463, -0.004719768185168505, -0.05521012470126152, -0.021025201305747032, 0.04815205559134483, -0.046199820935726166, -0.04705432802438736, -0.062427520751953125, 0.035164594650268555, 0.08513876050710678, 0.022031515836715698, 0.00641209352761507, 0.009834934957325459, -0.0633162260055542, -0.01131299789994955, -0.007712210528552532, 0.010081805288791656, 0.10265921801328659, -0.01405044924467802, -0.026369178667664528, -0.029216855764389038, 0.03431635722517967, 0.010801119729876518, 0.00899713858962059, 0.003959656693041325, -0.007609378546476364, -0.02273363433778286, -0.03726192191243172, 0.08850385248661041, 0.013004270382225513, -0.06700555235147476, -0.006881720386445522, -0.020808830857276917, 0.021919619292020798, 0.004541550297290087, 0.004793841391801834, 0.0015007960610091686, -0.023970913141965866, -0.09267394989728928, -0.02878103218972683, 0.015975961461663246, -0.016650857403874397, 0.07497352361679077, 0.014415916986763477, -0.010906114242970943, 0.02049253322184086, -0.026682181283831596, 0.029901856556534767, 0.0357084646821022, 0.05326564237475395, 0.013775753788650036, -0.0520583875477314, -0.006739316042512655, 0.03525369241833687, 0.0029047492425888777, 0.025410130620002747, 0.00455276295542717, 0.0038271488156169653, -0.02535138465464115, 0.05835873633623123, -0.03126329928636551, -0.03593455255031586, 0.0019837399013340473, -0.010251663625240326, -0.04442388564348221, 0.017985153943300247, -0.0010685346787795424, 0.03586158901453018, 0.0043352567590773106, 0.0441979318857193, 0.003990062512457371, -0.025838539004325867, 0.026496171951293945, 0.031039923429489136, 0.02449726313352585, 0.01290940959006548, -0.02557358518242836, 0.03465774282813072, -0.023961614817380905, -0.025133993476629257, 0.021510502323508263, 0.04206845536828041, 0.018506640568375587, 0.023977722972631454, 0.02091692015528679, -0.063876211643219, 0.04772453382611275, 0.014903671108186245, 0.00020290762768127024, -0.08120182901620865, 0.054004620760679245, -0.01709219068288803, 0.020976554602384567, 0.0029721837490797043, 0.00738596823066473, -0.044341087341308594, -0.008459399454295635, 0.021807163953781128, 0.06920962035655975, -0.023578671738505363, -0.03761443495750427, -0.08044164627790451, -0.029487885534763336, 0.03793616592884064, 0.05790293961763382, 0.00091374950716272, -0.02253212034702301, -0.046022653579711914, -0.004177618771791458, -0.022632131353020668, 0.0628289207816124, -0.03657632693648338, 0.0249861478805542, 0.04559757933020592, -0.042135078459978104, -0.042502257972955704, 0.0006321104592643678, -0.07378639280796051, -0.024468760937452316, -0.04255160316824913, -0.03556521236896515, 0.008890547789633274, -0.037478379905223846, -5.885529767886324e-33, 0.017491329461336136, -0.07902909815311432, -0.0645119696855545, 0.010200094431638718, 0.010164089500904083, 0.034126538783311844, -0.04400404170155525, -0.026811527088284492, 0.044872310012578964, 0.023168113082647324, 0.017903488129377365, -0.05486186593770981, -0.012139641679823399, 0.003137933788821101, 0.07367139309644699, 0.024922309443354607, 0.013363205827772617, 0.035384804010391235, 0.06001238897442818, -0.007389145903289318, 0.05456025153398514, 0.04602235555648804, 0.007104467134922743, -0.014169002883136272, -0.039616405963897705, 0.05991474911570549, -0.019321970641613007, -0.017476707696914673, -0.07242199033498764, 0.036247894167900085, 0.04733239859342575, 0.017174730077385902, -0.00239223032258451, 0.010615969076752663, -0.008882813155651093, -0.0371246412396431, -0.021191926673054695, -0.027927415445446968, -0.031027060002088547, -0.02194955013692379, -0.01940550096333027, 0.010345647111535072, 0.05495739355683327, 0.0047917794436216354, -0.02220030315220356, -0.02293916419148445, 0.07687342166900635, -0.06289611756801605, -0.046482548117637634, -0.06699595600366592, -0.010536196641623974, 0.026298150420188904, -0.013986380770802498, 0.046467531472444534, -0.0018640892812982202, 0.02905336581170559, -0.052480366080999374, 0.02295093610882759, 0.04498572647571564, -0.005166830960661173, 0.013602359220385551, 0.01189539022743702, 0.012214625254273415, 0.015481531620025635, 0.0317082479596138, 0.01006012037396431, -0.0073913587257266045, -0.06362216919660568, 0.02402409352362156, 0.020245037972927094, -0.0859593078494072, 0.07520792633295059, 0.04414094239473343, 0.03787663206458092, 0.06002778559923172, -0.03976793214678764, -0.07565301656723022, 0.08252253383398056, -0.02118922956287861, 0.026635827496647835, -0.04857794567942619, -0.016827203333377838, 0.009732840582728386, 0.06127310171723366, 0.018650414422154427, 0.025145694613456726, -0.00911526009440422, -0.030063683167099953, 0.02834267169237137, -0.0014289489481598139, -0.02296043187379837, 0.04405524581670761, 0.0035050217993557453, 0.011819048784673214, 0.028968358412384987, -0.007720810826867819, 0.008337141014635563, 0.009009944275021553, -0.001122289919294417, -0.041201021522283554, 0.026926223188638687, 0.01970747672021389, 0.020517872646450996, -0.059166908264160156, 0.03883323445916176, -0.035645801573991776, 0.01913708820939064, -0.006317619234323502, -0.056980475783348083, -0.0008437154465354979, 0.03652085363864899, 0.006334970705211163, -0.006813534535467625, 0.05592663958668709, -0.021094636991620064, -0.03537263721227646, 0.015699680894613266, 0.06134214997291565, 0.028013208881020546, -0.020416205748915672, -0.013798058032989502, -0.0038627684116363525, 0.003547288477420807, -0.025264360010623932, -0.028613001108169556, -0.012972126714885235, -0.03017556108534336, -0.00031789386412128806, -0.03534592315554619, 0.004697657190263271, 0.012058733031153679, 0.008431917987763882, 2.839549040345446e-07, 0.01178056187927723, 0.020817168056964874, -0.021488463506102562, -0.080562062561512, -0.0395108126103878, -0.025147877633571625, -0.02311132289469242, 0.0072484263218939304, -0.05850023031234741, -0.01148192211985588, 0.04933421313762665, -0.0413907952606678, 0.04235396161675453, 0.013677041977643967, -0.04559234157204628, 0.005987279117107391, -0.009278482757508755, 0.043127335608005524, -0.0188420619815588, 0.015974555164575577, 0.02704775705933571, 0.10024803876876831, 0.02637520059943199, -0.018563974648714066, 0.02483651414513588, -0.010781409218907356, -0.01776754856109619, -0.04905394837260246, -0.02034553326666355, -0.019927045330405235, 0.0042572892270982265, -0.036415308713912964, -0.028284016996622086, 0.05527704581618309, -0.033000070601701736, -0.043282993137836456, -0.06526553630828857, 0.029643971472978592, -0.03839908167719841, 0.03855380043387413, 0.04417546093463898, 0.07116184383630753, 0.07103024423122406, -0.02171717770397663, 0.025801409035921097, 0.020534200593829155, -0.023111959919333458, 0.012205887585878372, 0.06444895267486572, -0.014613596722483635, 0.08035993576049805, 0.011404088698327541, 0.027849141508340836, 0.04392316937446594, -0.0059873973950743675, -0.01685490272939205, -0.027275940403342247, -0.017198266461491585, 0.04541146382689476, -0.006022056099027395, -0.06155970320105553, 0.00564629677683115, -0.015611257404088974, 0.03460409492254257, 0.05094138905405998, -0.01322068553417921, 0.012630373239517212, 3.2733940677825353e-34, -0.024968931451439857, 0.0038152961060404778, -0.018922876566648483, -0.012325268238782883, -0.009599057026207447, -0.0017892576288431883, 0.028883209452033043, 0.01275885570794344, -0.04536154121160507, -0.02945178933441639, 0.005051388405263424]

['F. Ozgur Catak', 'M. Erdal Balaban']

1301.0082v1

In conventional method, distributed support vector machines (SVM) algorithms are trained over pre-configured intranet/internet environments to find out an optimal classifier. These methods are very complicated and costly for large datasets. Hence, we propose a method that is referred as the Cloud SVM training mechanism (CloudSVM) in a cloud computing environment with MapReduce technique for distributed machine learning applications. Accordingly, (i) SVM algorithm is trained in distributed cloud storage servers that work concurrently; (ii) merge all support vectors in every trained cloud node; and (iii) iterate these two steps until the SVM converges to the optimal classifier function. Large scale data sets are not possible to train using SVM algorithm on a single computer. The results of this study are important for training of large scale data sets for machine learning applications. We provided that iterative training of splitted data set in cloud computing environment using SVM will converge to a global optimal classifier in finite iteration size.

CloudSVM : Training an SVM Classifier in Cloud Computing Systems

http://arxiv.org/pdf/1301.0082v1

Title CloudSVM Training SVM Classifier Cloud Computing Systems Summary conventional method distributed support vector machine SVM algorithm trained preconfigured intranetinternet environment find optimal classifier method complicated costly large datasets Hence propose method referred Cloud SVM training mechanism CloudSVM cloud computing environment MapReduce technique distributed machine learning application Accordingly SVM algorithm trained distributed cloud storage server work concurrently ii merge support vector every trained cloud node iii iterate two step SVM converges optimal classifier function Large scale data set possible train using SVM algorithm single computer result study important training large scale data set machine learning application provided iterative training splitted data set cloud computing environment using SVM converge global optimal classifier finite iteration size Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.006209544371813536, -0.00982762686908245, -0.018499057739973068, -0.005178053397685289, -0.003448692848905921, 0.02942487969994545, 0.05858026444911957, -0.006144756451249123, 0.031212763860821724, -0.015909504145383835, 0.04506094753742218, 0.018799154087901115, 0.00515797920525074, 0.03708494454622269, -0.009600420482456684, -0.04714949056506157, 0.024837614968419075, 0.0177049171179533, -0.06499388813972473, -0.033384259790182114, 0.014779170043766499, 0.03039442002773285, 0.0022969315759837627, -0.012592566199600697, -0.010527911596000195, -0.027151333168148994, -0.008335327729582787, -0.014124841429293156, 0.02317037060856819, -0.01067795418202877, 0.02489139325916767, -0.05013273283839226, 0.02363467402756214, 0.057867590337991714, 1.7506532685729326e-06, -0.018978971987962723, -0.04039084166288376, -0.011152815073728561, 0.011123871430754662, -0.0020080062095075846, 0.03996949642896652, -0.022960666567087173, -0.005066997371613979, 0.05057373270392418, -0.05105326324701309, 0.04486488923430443, 0.042153723537921906, 0.02515026554465294, 0.05755350738763809, 0.03128474950790405, -0.014341972768306732, -0.0771036297082901, -0.0195033997297287, 0.025332344695925713, -0.06791413575410843, 0.0027358904480934143, 0.028920987620949745, 0.010900291614234447, -0.026135435327887535, -0.026358775794506073, 0.015827950090169907, 0.007268915418535471, 0.002616604557260871, 0.0279234666377306, 0.03382556512951851, 0.06544637680053711, -0.05441514030098915, 0.007129887118935585, -0.05254720523953438, -0.01795821078121662, 0.018374431878328323, -0.006635784171521664, 0.018645260483026505, 0.013388908468186855, -0.04666374251246452, 0.011316138319671154, 0.003211335279047489, 0.006531549617648125, 0.023476270958781242, 0.020010631531476974, 0.00954090803861618, -0.005441579967737198, -0.024972349405288696, 0.00447535514831543, 0.02536940947175026, 0.025882011279463768, -0.04475760832428932, -0.028196319937705994, -0.012374271638691425, 0.009654578752815723, -0.050005197525024414, 0.0022079586051404476, 0.03806503489613533, 0.03562457859516144, -0.07387883216142654, -0.01142127811908722, -0.0492793545126915, -0.07906584441661835, 0.03128035366535187, -0.058877695351839066, 0.06348377466201782, -0.06799831241369247, 0.03588011860847473, 0.015212609432637691, -0.004735786002129316, 0.011549646966159344, 0.002158426446840167, -0.009181458503007889, -0.0021209698170423508, 0.04392527416348457, -0.07324177771806717, 0.00040255903149954975, 0.006211867555975914, 0.05146037042140961, 0.040956784039735794, -0.013582020066678524, -0.07270552217960358, 0.03672798350453377, 0.022043313831090927, 0.013270780444145203, 0.009936003014445305, 0.005886551924049854, 0.04011310264468193, 0.062204889953136444, -0.007518014870584011, -0.01759796030819416, -0.025062769651412964, 0.04527369141578674, -0.056375566869974136, -0.02076544426381588, 0.037372346967458725, 0.012701788917183876, -0.01304518710821867, 0.042327579110860825, 0.05406703054904938, 0.001207668916322291, 0.019466901198029518, 0.055019453167915344, -0.01297251507639885, -0.02916647121310234, 0.03680998459458351, -0.036465100944042206, -0.0508890338242054, -0.021696263924241066, -0.0075154416263103485, -0.0005896119400858879, -0.010436439886689186, 0.07197330892086029, -0.010396502912044525, -0.022793320938944817, -0.03248528018593788, 0.04080303758382797, -0.02744484134018421, 0.026869872584939003, 0.07907476276159286, -0.0010942625813186169, -0.03214367851614952, 0.0025079220067709684, -0.005088782869279385, -0.03444228693842888, 0.008785721845924854, -0.06676328927278519, 0.028236091136932373, 0.009904313832521439, -0.01369231566786766, -0.04501136392354965, -0.01995028369128704, 0.0257613155990839, 0.004954381845891476, 0.006346674636006355, -0.0026151216588914394, 0.022606071084737778, 0.015267274342477322, -0.03571305051445961, 0.022421320900321007, 0.0429912768304348, 0.021604735404253006, 0.006960262078791857, -0.010848057456314564, 0.0672517642378807, -0.016571734100580215, -0.023472324013710022, 0.013322340324521065, -0.013158414512872696, -0.03769410774111748, -0.05724894255399704, -0.055510230362415314, 0.01104783732444048, -0.004860213492065668, -0.03317701071500778, -0.01293125282973051, -0.0003246341657359153, -0.0552360936999321, 0.011929256841540337, 0.07238207012414932, -0.018422890454530716, -0.024841897189617157, 0.018272794783115387, 0.025941895321011543, 0.013354551047086716, -0.03226802498102188, -0.004347540903836489, 0.033138591796159744, 0.0003487590001896024, 0.02811684086918831, -0.04563019052147865, 0.009011796675622463, -0.02974294126033783, -0.0007302042213268578, -0.0690985843539238, -0.007353991270065308, 0.018536243587732315, -0.006970270071178675, -0.020765205845236778, 0.008024502545595169, 0.04362938925623894, -0.005995921790599823, -0.05033817142248154, 0.019290592521429062, -0.0022117693442851305, -0.008713049814105034, 0.019754020497202873, -0.04297903552651405, 0.052914347499608994, 0.08154052495956421, 0.016808273270726204, 0.019404228776693344, 0.025568483397364616, 0.06223083287477493, -0.04225503280758858, 0.0040636854246258736, -0.042532291263341904, 0.03852980211377144, -0.013630705885589123, -0.07364675402641296, -0.007403395604342222, 0.032598722726106644, -0.009175368584692478, 0.0014949771575629711, 0.03206542506814003, 0.03615376353263855, 0.016884300857782364, -0.05497089400887489, -0.022342920303344727, -0.042240019887685776, -0.011205071583390236, -0.05062149465084076, 0.0034448308870196342, 0.047953493893146515, -0.016683634370565414, 0.047423698008060455, -0.013933222740888596, 0.03683196008205414, 0.03271958604454994, 0.005708156153559685, -0.09553134441375732, -0.021863481029868126, 0.05274306610226631, -0.017955565825104713, 0.040953099727630615, 0.00014885432028677315, -0.09217491000890732, 0.012260590679943562, -0.03863927721977234, 0.006289250683039427, -0.03118814527988434, 0.03148338198661804, -0.030075686052441597, 0.001037152367644012, 0.010286557488143444, 0.02030807174742222, -0.03064829297363758, -0.01770603470504284, 0.004181671421974897, -0.048513852059841156, -0.01309858076274395, 0.09443403035402298, 0.017351143062114716, -0.008836276829242706, 0.0383928157389164, -0.014453031122684479, -0.012054084800183773, 0.05142074078321457, -0.023146819323301315, -0.0026390415150672197, 0.05170457065105438, 0.03914676606655121, 0.008698243647813797, -0.056024566292762756, 0.05150352418422699, -0.04565209895372391, -0.010077223181724548, 0.020650319755077362, 0.0017037949291989207, -0.03439682349562645, -0.003430128563195467, -0.045610424131155014, 0.03480745479464531, 0.024220183491706848, -0.04874635115265846, 0.03882838785648346, 0.05889417231082916, -0.014635905623435974, 0.011443203315138817, -0.04262673482298851, -0.007255068514496088, -0.009257332421839237, 0.05724720284342766, 0.011561465449631214, -0.011948243714869022, -0.017413217574357986, 0.018376605585217476, 0.03938806802034378, 0.0028416835702955723, -0.026936395093798637, -0.011126741766929626, -0.07836904376745224, -0.005149213597178459, -0.005395860876888037, -0.032865554094314575, 0.03833943232893944, -0.06203183904290199, 0.03733227401971817, -0.00844603031873703, -0.0026467996649444103, -0.06878894567489624, -0.0975329801440239, 0.005015703849494457, -0.01006905548274517, -0.03635438531637192, 0.03768376633524895, -0.06986081600189209, -0.03309427574276924, 0.026805303990840912, 0.030047589913010597, 0.020696178078651428, -0.054577987641096115, -0.0684681236743927, 0.011196767911314964, -0.01474194135516882, -0.020958438515663147, -0.05579813942313194, -0.05554160475730896, -0.007005693390965462, -0.06899949163198471, -0.008954312652349472, -0.05058782547712326, -0.01523948647081852, 0.013320786878466606, 0.03696766868233681, -0.021361440420150757, 0.04497355967760086, -0.020754575729370117, -0.024329595267772675, 0.0363142304122448, -0.01584538072347641, -0.01518164947628975, -0.01896633952856064, -0.033876482397317886, 0.045529428869485855, 0.032528623938560486, 0.06662286818027496, 0.07406249642372131, -0.016479576006531715, -0.04049837216734886, 0.01010407879948616, 0.016834888607263565, -0.06009456887841225, -0.02386309579014778, -0.020919745787978172, 0.0013701453572139144, -0.07347085326910019, 0.02934393286705017, 0.020523585379123688, -0.008539839647710323, -0.04673546180129051, -0.008786412887275219, -0.0409875251352787, -0.04207448288798332, 0.012190035544335842, 0.044981036335229874, -0.0337185338139534, 0.004070150200277567, 0.006011690944433212, 0.024166317656636238, -0.007910246960818768, -0.018146375194191933, 0.008168165571987629, -0.059128910303115845, 0.06387871503829956, 0.004566086921840906, -0.03827616944909096, -0.012441378086805344, -0.07019130140542984, -0.009271994233131409, -0.039184585213661194, -0.059049397706985474, -0.00512212747707963, -0.002154496032744646, 0.0052290381863713264, 0.0358332060277462, -0.04050431400537491, 0.013136502355337143, -0.01517100352793932, -0.0758880078792572, -0.02389371022582054, 0.047634754329919815, 0.0004909164272248745, 0.005481152329593897, -0.03202315792441368, -0.021423690021038055, 0.02260717563331127, 0.03814930096268654, -0.0793619230389595, 0.04418358579277992, -0.002296410733833909, -0.007862619124352932, 0.010449353605508804, 0.03820260986685753, 0.03090628609061241, 0.00230319588445127, 0.06176333874464035, 0.09913328289985657, -0.04608965292572975, -0.01937153749167919, -0.016887420788407326, 0.000929787871427834, 0.010035676881670952, 0.02947176620364189, -0.032358091324567795, -0.026958802714943886, -0.027952812612056732, 0.04382973164319992, 0.0034329681657254696, 0.04971371591091156, 0.014952118508517742, 0.014667370356619358, -0.02402411215007305, -0.04515283927321434, -0.019257720559835434, 0.0015577740268781781, 0.013390780426561832, 0.0480673722922802, 0.01885906420648098, 0.028616325929760933, 0.020285306498408318, 0.046322789043188095, -0.08816340565681458, -0.0379449836909771, 0.005890573840588331, 0.06262782216072083, -0.007751753553748131, 0.00283935503102839, 0.026232965290546417, 0.020896179601550102, -0.0335054025053978, -0.10117730498313904, 0.003602273529395461, -0.004708403255790472, 0.008201450109481812, 0.03413780778646469, 0.004716949537396431, 0.008615728467702866, -0.02252078801393509, -0.0680297315120697, 0.08160175383090973, 0.0003524523926898837, -0.05938856303691864, 0.0007810895913280547, 0.03284821659326553, -0.05549086257815361, 0.006056913640350103, -0.006329062394797802, -0.0019260388799011707, 0.03772864118218422, 0.014000273309648037, -0.10046577453613281, -0.06450033187866211, 0.04098880663514137, -0.019574901089072227, 0.01748966984450817, 0.06242142245173454, 0.022254640236496925, -0.014574475586414337, -0.002615935867652297, 0.03346424922347069, 0.06345679610967636, -0.00011432648898335174, -0.00532215042039752, 0.011216494254767895, 0.008132115006446838, 0.0025760759599506855, -0.00032380683114752173, 0.01888473890721798, 0.07285138964653015, -0.12179003655910492, 0.006577114574611187, 0.03362332284450531, 0.06279055774211884, 0.02883163094520569, 0.018455181270837784, 0.027028873562812805, 0.012971083633601665, -0.03904762119054794, 0.05949692055583, 0.008207621052861214, -0.0030329544097185135, 0.012324381619691849, -0.0049617537297308445, 0.05068396031856537, -0.008649274706840515, -0.01666334643959999, 0.01611330918967724, -0.05437607318162918, 0.014748032204806805, -0.016668977215886116, 0.02410835213959217, 0.021496940404176712, -0.0036673361901193857, -0.01564835011959076, -0.013003338128328323, -0.03614014387130737, 0.004282751120626926, -0.04049472138285637, 0.002425141865387559, 0.03211928531527519, -0.009745422750711441, -0.057684291154146194, 0.06695759296417236, 0.0034214132465422153, -0.004143052734434605, -0.00686122290790081, -0.02646501548588276, -0.058526769280433655, -0.0476982519030571, 0.05584922432899475, -0.012248500250279903, 0.032718725502491, -0.00926725473254919, -0.009883660823106766, 0.03658200055360794, -0.003924090415239334, 0.04270268976688385, -0.04038933664560318, 0.05422592535614967, -0.017648005858063698, 0.014336540363729, 0.05588185787200928, 8.473593334201723e-05, 0.011234226636588573, -0.03647337481379509, 0.008663053624331951, -0.04823913425207138, 0.0116974962875247, -0.01611044444143772, -5.179422433632869e-33, 0.037800393998622894, -0.04515046253800392, -0.01702529937028885, 0.06157981976866722, -0.010900214314460754, 0.0451471172273159, 0.013693129643797874, -0.007588833570480347, 0.03658665344119072, 0.005492900498211384, -0.009958259761333466, 0.0349651500582695, 0.04796741530299187, -0.01210654154419899, 0.0559627003967762, 0.00464814156293869, 0.04036959260702133, -0.022054867818951607, -0.03736262395977974, -0.005066437181085348, 0.03055240400135517, 0.06633491069078445, 0.023558340966701508, -0.10326694697141647, -0.05512302741408348, -0.017683640122413635, -0.024379270151257515, 0.008078938350081444, -0.053098779171705246, -0.019191373139619827, -0.00758163770660758, 0.027067366987466812, 0.02755299210548401, -0.05246509984135628, 0.007440165616571903, 0.022323384881019592, 0.009633287787437439, 0.03958003595471382, -0.04758407548069954, 0.05009240657091141, -0.04735589399933815, 0.015677213668823242, 0.03879333287477493, -0.009815298952162266, -0.033379849046468735, 0.022827785462141037, 0.04977963864803314, -0.012740750797092915, -0.033347081393003464, -0.06020936742424965, 0.019039899110794067, 0.008782274089753628, 0.0009077989961951971, 0.015682468190789223, 0.0385492667555809, -0.012567001394927502, -0.005236215889453888, 0.029142914339900017, -0.061601169407367706, 0.050162434577941895, -0.011770115233957767, 0.025381160899996758, -0.004532946273684502, 0.04186172038316727, 0.0006768616149201989, -0.0014003192773088813, 0.04129524156451225, -0.08648710697889328, -0.022279968485236168, 0.017182178795337677, -0.0050964998081326485, 0.05691928416490555, 0.04166743531823158, -0.012514844536781311, 0.05253233015537262, -0.06573911011219025, -0.010665452107787132, 0.01678386703133583, 0.07009438425302505, -0.04246347397565842, -0.039799246937036514, -0.005700807087123394, -0.006648282520473003, -0.019429150968790054, 0.00854898989200592, -0.051627643406391144, -0.012599237263202667, 0.010407986119389534, 0.012389469891786575, 0.03679991886019707, -0.026465151458978653, 0.07317347824573517, 0.004378712270408869, -0.025321993976831436, -0.04161271080374718, 0.01627424918115139, 0.05541247874498367, -0.0011150679783895612, 0.02778516709804535, -0.07173153758049011, -0.0338631272315979, -0.038904815912246704, -0.019415276125073433, -0.02415558323264122, 0.02986786887049675, -0.016211260110139847, 0.08774565160274506, 0.006281244568526745, -0.029802029952406883, 0.006929041352123022, 0.04847074672579765, -0.02492717280983925, -0.011089080944657326, 0.027414970099925995, 0.02705339714884758, -0.028776003047823906, 0.03554021567106247, 0.045934900641441345, 0.0072961291298270226, 0.02521475963294506, -0.03589412942528725, -0.05422831326723099, -0.005933681037276983, 0.009709987789392471, -0.028293617069721222, 0.013312163762748241, -0.039173126220703125, -0.02409256622195244, -0.013034642674028873, -0.008044710382819176, -0.010416004806756973, -0.019567854702472687, 2.4660533881615265e-07, -0.012066963128745556, 0.040341153740882874, -0.05749691277742386, -0.062281034886837006, -0.006783436052501202, 0.03738287463784218, 0.03560669720172882, 0.00809682346880436, -0.018190836533904076, 0.04441860690712929, 0.015326627530157566, -0.028773875907063484, 0.08461881428956985, -0.006842437665909529, -0.023149920627474785, -0.061738353222608566, -0.03652304410934448, 0.0746234804391861, -0.05556401237845421, 0.05032658204436302, 0.04241266846656799, 0.07759299129247665, 0.06348344683647156, -0.06767863035202026, 0.03016819804906845, 0.02802027389407158, -0.04393407702445984, 0.0374155193567276, 0.025008676573634148, -0.03992047160863876, 0.001960458466783166, 0.07024498283863068, 0.0047057741321623325, 0.019354145973920822, -0.0577138215303421, 0.037668079137802124, -0.027038177475333214, 0.01874421164393425, 0.004198479000478983, 0.06099342182278633, 0.02124841883778572, 0.002949234563857317, 0.020218253135681152, 0.01849166303873062, 0.016250548884272575, 0.0019468654645606875, -0.0484689399600029, -0.012064628303050995, 0.02940376102924347, -0.07511619478464127, 0.05353473499417305, 0.022996580228209496, -0.003602936863899231, 0.001909109647385776, 0.00631152605637908, -0.06477347016334534, -0.050233159214258194, -0.06335502117872238, 0.003897226881235838, 0.005586262326687574, -0.006245676893740892, 0.015101744793355465, 0.03235108405351639, 0.04891591891646385, 0.03615551441907883, 0.048282887786626816, 0.007636398077011108, 2.0886718567175525e-34, -0.024472327902913094, 0.021165668964385986, 0.0030741251539438963, 0.07807980477809906, -0.06164216622710228, -0.0009508947259746492, 0.0572933703660965, 0.0016876502195373178, -0.02688150852918625, -0.02465173788368702, 0.015274979174137115]

['Hamidreza Chitsaz', 'Elmirasadat Forouzmand', 'Gholamreza Haffari']

1301.1590v1

It has been shown that minimum free energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble based quantities such as melting temperature and equilibrium concentrations can be more reliably predicted. Even structure prediction by sampling from the ensemble and clustering those structures by Sfold [7] has proven to be more reliable than minimum free energy structure prediction. The main obstacle for ensemble based approaches is the computational complexity of the partition function and base pairing probabilities. For instance, the space complexity of the partition function for RNA-RNA interaction is $O(n^4)$ and the time complexity is $O(n^6)$ which are prohibitively large [4,12]. Our goal in this paper is to give a fast algorithm, based on sparse folding, to calculate an upper bound on the partition function. Our work is based on the recent algorithm of Hazan and Jaakkola [10]. The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is $O(MFE(n)\ell)$ for single RNA and $O(MFE(m, n)\ell)$ for RNA-RNA interaction in practice, in which $MFE$ is the running time of sparse folding and $\ell \leq n$ ($\ell \leq n + m$) is a sequence dependent parameter.

An Efficient Algorithm for Upper Bound on the Partition Function of Nucleic Acids

http://arxiv.org/pdf/1301.1590v1

Title Efficient Algorithm Upper Bound Partition Function Nucleic Acids Summary shown minimum free energy structure RNAs RNARNA interaction often incorrect due inaccuracy energy parameter inherent limitation energy model contrast ensemble based quantity melting temperature equilibrium concentration reliably predicted Even structure prediction sampling ensemble clustering structure Sfold 7 proven reliable minimum free energy structure prediction main obstacle ensemble based approach computational complexity partition function base pairing probability instance space complexity partition function RNARNA interaction On4 time complexity On6 prohibitively large 412 goal paper give fast algorithm based sparse folding calculate upper bound partition function work based recent algorithm Hazan Jaakkola 10 space complexity algorithm sparse folding algorithm time complexity algorithm OMFEnell single RNA OMFEm nell RNARNA interaction practice MFE running time sparse folding ell leq n ell leq n sequence dependent parameter Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.002672175643965602, -0.025067072361707687, 0.016400165855884552, 0.03143899515271187, 0.008016200736165047, -0.008618984371423721, 0.015521989203989506, -0.007015491835772991, 0.02143612690269947, -0.016600433737039566, 0.033112406730651855, -0.03479335457086563, 0.03922487422823906, 0.049285635352134705, 0.017380276694893837, -0.03146928921341896, -0.0037973574362695217, 0.0006347477319650352, 0.024295493960380554, -0.022896723821759224, 0.026366600766777992, -0.0022660293616354465, 0.024340856820344925, -0.027088504284620285, 0.03151978179812431, -0.00791943073272705, -0.04841502383351326, 0.023571958765387535, 0.0033087674528360367, -0.04526596888899803, -0.002144844736903906, 0.05096560716629028, -0.003353607142344117, 0.00302935391664505, 2.268871867272537e-06, -0.05392861366271973, -0.020364750176668167, 0.016728626564145088, -0.007299521937966347, -0.007397142238914967, 0.05760626122355461, 0.04156748577952385, 0.022992635145783424, 0.03534817695617676, 0.0398639440536499, -0.05596677213907242, 0.07278937101364136, 0.03596052527427673, -0.035095151513814926, -0.010384014807641506, -0.007534306962043047, -0.025585534051060677, 0.017639311030507088, 0.007904396392405033, 0.07841233164072037, -0.033561043441295624, 0.03536946326494217, 0.020199114456772804, 0.018055308610200882, -0.022253043949604034, -0.017389265820384026, 0.016307028010487556, 0.009702597744762897, 0.008938966318964958, -0.0059990426525473595, 0.06943529099225998, -0.04596014320850372, -0.028621187433600426, 0.017868492752313614, 0.03125028684735298, 0.033255115151405334, -0.04409745708107948, -0.016943009570240974, 0.028523074463009834, -0.01735405996441841, -0.025480499491095543, 0.002307451795786619, -0.018341651186347008, -0.02439839392900467, 0.03301292285323143, 0.002178341615945101, 0.03563472628593445, 0.04021582379937172, -0.036313556134700775, -0.003192767035216093, 0.05339318513870239, -0.007534571923315525, -0.045618437230587006, 0.0019708320032805204, -0.007262590806931257, -0.02038595825433731, -0.00971166044473648, -0.016794098541140556, -0.02497919648885727, 0.007628926075994968, -0.030899014323949814, 0.014747167006134987, 0.0031428183428943157, 0.06783416867256165, 0.009011118672788143, 0.03623390197753906, -0.030350932851433754, 0.06619689613580704, -0.006652156822383404, 0.0247646514326334, -0.07827027142047882, -0.04294586926698685, -0.011731987819075584, -0.027812128886580467, 0.01573706977069378, -0.02665354683995247, 0.012179072014987469, 0.021088818088173866, 0.010311763733625412, -0.010167678818106651, -0.004508072976022959, -0.0391065739095211, -0.055448856204748154, 0.021390248090028763, -0.027607304975390434, 0.03763648495078087, 0.0480332188308239, 0.014434358105063438, 0.07736331224441528, 0.01910179853439331, 0.004601610824465752, -0.03581734746694565, -0.01343639474362135, -0.005710004363209009, -0.07533340156078339, -0.012110346928238869, -0.0018951677484437823, 0.010471177287399769, -0.002250579884275794, -0.05275692790746689, 0.03581469506025314, -0.0059829819947481155, -0.01522288378328085, 0.07835650444030762, -0.019290367141366005, -0.05433513969182968, -0.021929915994405746, -0.04454723745584488, -0.06925641745328903, 0.06825794279575348, 0.031933944672346115, -0.027007892727851868, 0.022346893325448036, 0.05853693559765816, -0.04606255516409874, -0.03260933235287666, 0.07178591936826706, -0.029944296926259995, -0.01894323341548443, 0.049403369426727295, 0.02160029299557209, -0.0020483951084315777, -0.020838584750890732, 0.01084056030958891, 0.02576739713549614, -0.002123432932421565, 0.0011365205282345414, 0.010228547267615795, -0.0632789358496666, -0.0395776592195034, -0.05781221389770508, 0.05720438435673714, 0.019758794456720352, 0.011418025009334087, 0.01626608334481716, -0.03438933193683624, -0.02475154772400856, 0.030074691399931908, 0.011216162703931332, -0.020018450915813446, 0.029786642640829086, 0.008940170519053936, 0.07152096927165985, -0.048526108264923096, 0.04575382173061371, 0.01545604970306158, -0.015190278179943562, 0.02859967015683651, 0.05575747787952423, -0.0603928416967392, -0.031482990831136703, 0.08808363229036331, -0.0014653775142505765, -0.0017789212288334966, 0.02981403097510338, -0.03163078799843788, 0.034338705241680145, -0.0008024641429074109, -0.08071943372488022, -0.006318668834865093, -0.05048183724284172, -0.06739785522222519, 0.02445577271282673, 0.026525065302848816, -0.05312282219529152, -0.015839867293834686, 0.04805763438344002, 0.035940736532211304, -0.030600864440202713, -0.005048916209489107, -0.03659290820360184, -0.05267053097486496, 0.017319882288575172, -0.04417189583182335, -0.0258366446942091, -0.015623803250491619, 0.0005295206792652607, -0.0037806902546435595, -0.0280620064586401, -0.0005967162433080375, 0.001447909278795123, 0.001404834445565939, 0.028796600177884102, 0.0068416232243180275, -0.010838767513632774, 0.06594236940145493, 0.023770185187458992, -0.03467292711138725, -0.027853352949023247, -0.051763568073511124, 0.0391792431473732, -0.01578708365559578, -0.0027280650101602077, 0.05957915633916855, -0.016675487160682678, -0.0029127486050128937, 0.013105398043990135, 0.09011963754892349, -0.04324653372168541, -0.049152396619319916, -0.04595368728041649, 0.02296973206102848, -0.06851974129676819, -0.04399913549423218, -0.0037912416737526655, 0.04410375654697418, -0.0026671902742236853, -0.02074846252799034, -0.006813080981373787, 0.031839001923799515, -0.021683404222130775, -0.02434215322136879, -0.04795071855187416, -0.021289991214871407, -0.020564105361700058, 0.008171788416802883, 0.02504749968647957, 0.03685258701443672, -0.011155280284583569, 0.06525636464357376, -0.034664612263441086, -0.07232367247343063, -0.022904537618160248, -0.021947314962744713, 0.056785307824611664, -0.018220243975520134, 0.03551968187093735, -0.04383455589413643, 0.009656324982643127, -0.007663145195692778, -0.04687277600169182, -0.031152116134762764, -0.011758897453546524, -0.003389735473319888, 0.025887036696076393, 0.02840055339038372, -0.004837812390178442, 0.015542467124760151, 0.012145747430622578, 0.0404052659869194, -0.052936919033527374, -0.013876921497285366, -0.010852604173123837, -0.020348012447357178, 0.022226758301258087, -0.020122302696108818, -0.0593111477792263, -0.026606380939483643, -0.016716528683900833, -0.028997382149100304, 0.05696863308548927, 0.03271773084998131, -0.06499190628528595, -0.001729095121845603, 0.029139602556824684, -0.0044986591674387455, 0.009413041174411774, -0.0066529386676847935, -0.042004846036434174, 0.0016237864037975669, -0.05021810159087181, 0.01878311298787594, -0.009118899703025818, 0.011580579914152622, -0.06299617886543274, 0.07296349108219147, 0.04924774169921875, 0.03325372189283371, 0.022854331880807877, 0.005757058970630169, 0.06033599004149437, 0.06228360906243324, -0.026386089622974396, -0.006209854036569595, 0.026203859597444534, 0.025419214740395546, -0.010153454728424549, -0.06274055689573288, -0.05349539592862129, 0.05558142811059952, -0.07785581052303314, 0.01798885315656662, 0.00797885749489069, -0.01432937104254961, 0.0019222638802602887, 0.0013914643786847591, -0.0004118340148124844, 0.03149557113647461, -0.023806262761354446, -0.027792086824774742, -0.0022484655492007732, 0.03383955731987953, 0.03524626046419144, -0.034131985157728195, -0.008988147601485252, 0.0652189776301384, -0.08536764979362488, -0.013190073892474174, 0.023204293102025986, -0.05866902694106102, -0.022062618285417557, -0.03903328999876976, -0.0028062465135008097, 0.029297109693288803, -0.030632544308900833, 0.04023626819252968, 0.04464482516050339, 0.0055296337231993675, 0.06690959632396698, 0.03569670766592026, 0.005510797258466482, 0.09452992677688599, -0.014730381779372692, -0.0247015580534935, 0.03881387412548065, 0.05125318840146065, -0.010054763406515121, -0.028416557237505913, 0.03433281555771828, 0.003129048505797982, 0.05926794186234474, -0.056275125592947006, -0.07084354013204575, 0.015652919188141823, -0.02412073314189911, 0.05158131942152977, 0.059343766421079636, 0.0005584541941061616, 0.035105086863040924, -0.0015666016843169928, -0.018070053309202194, 0.009063253179192543, -0.012057065963745117, -0.02543463557958603, -0.016770198941230774, 0.02269195020198822, 0.007561368867754936, -0.004645780194550753, 0.07138760387897491, 0.05494384840130806, -0.044803209602832794, 0.0044955783523619175, -0.019202448427677155, -0.007513752207159996, 0.009612001478672028, 0.06937821954488754, -0.00531116034835577, -0.004381187260150909, -0.011950298212468624, 0.0005625333869829774, -0.00611836276948452, -0.07949637621641159, -0.024496186524629593, -0.012243050150573254, -0.027138901874423027, 0.014063836075365543, -0.007872830145061016, -0.039542026817798615, -0.09588033705949783, -0.04064368084073067, -0.03317864611744881, -0.06389304995536804, 0.05772942304611206, 0.026061225682497025, 0.033624742180109024, 0.020839501172304153, 0.0015169242396950722, -0.02131997048854828, 0.03339967131614685, -0.03760405629873276, -0.021233536303043365, 0.015568672679364681, 0.04923165217041969, -0.0073713576421141624, -0.019504880532622337, -0.0051622153259813786, 0.023583753034472466, -0.026597091928124428, -0.07565125077962875, 0.025068238377571106, 0.05244508385658264, -0.009643414057791233, -0.0053709992207586765, -0.025718556717038155, -0.04141522943973541, -0.00865089800208807, 0.008485683239996433, 0.0278770811855793, 0.05878517031669617, -0.05732809379696846, 0.012064740061759949, 0.015284364111721516, -0.003167711663991213, 0.001836329814977944, 0.059929803013801575, 0.044016510248184204, -0.016280926764011383, 0.03535814210772514, 0.020331988111138344, -0.02597772143781185, 0.05106305703520775, -0.0006575717125087976, -0.0455799363553524, 0.007705147378146648, -0.04432687163352966, 0.0363299697637558, 0.01454458199441433, 0.06229624152183533, -0.0036768170539289713, 0.005671869032084942, -0.02618660219013691, -0.06277791410684586, 0.00803388748317957, -0.06348440051078796, 0.030070511624217033, 0.018079975619912148, -0.04788316786289215, -0.05321064591407776, 0.047887418419122696, 0.034840043634176254, -0.0020904226694256067, 0.016815897077322006, -0.008873318322002888, -0.06645958125591278, -0.027707558125257492, 0.028187833726406097, 0.00625977898016572, -0.024618888273835182, 0.020075369626283646, -0.0034681069664657116, -0.045112498104572296, 0.03086366504430771, -0.0033187703229486942, 0.004719190299510956, -0.01937820389866829, -0.06911417841911316, -0.0018861343851312995, 0.03880887106060982, 0.018594080582261086, 0.02183327078819275, -0.04421735182404518, -0.031978800892829895, 0.008250126615166664, -0.04633548483252525, 0.024057699367403984, 0.09340178966522217, -0.00044561593676917255, 0.030965492129325867, -0.02192392572760582, 0.0003433594247326255, 0.02231545001268387, 0.0037866723723709583, -0.022885426878929138, -0.037442922592163086, -0.020871087908744812, 0.0009285721462219954, 0.01288892887532711, -0.00915580429136753, 0.10153163224458694, -0.03321022912859917, -0.034796830266714096, 0.023511767387390137, 0.06500919908285141, 0.008926725015044212, 0.055098701268434525, 0.07608063519001007, -0.0040735541842877865, -0.03990492224693298, 0.0036568287760019302, -0.010877424851059914, 0.0135120814666152, -0.013986760750412941, -0.09522243589162827, -0.008875971660017967, 0.07814665138721466, -0.05724417418241501, 0.03120291978120804, 0.027868911623954773, 0.019832666963338852, 0.017845196649432182, -0.03391863778233528, 0.004066260997205973, -0.018009290099143982, 0.03229788318276405, 0.03881717100739479, 0.009231159463524818, -0.04975711554288864, 0.04708011820912361, -0.0062034158036112785, -0.017004137858748436, 0.01998942531645298, 0.04834073781967163, -0.039485082030296326, -0.04268142208456993, 0.07815568149089813, 0.02977122738957405, -0.005525102838873863, -0.004019090905785561, -0.06376437097787857, -0.02600502409040928, 0.039523717015981674, -0.004431992769241333, -0.015215185470879078, -0.03637990355491638, -0.012745414860546589, 0.03741098567843437, -0.0002608612412586808, 0.03551013022661209, 0.01175784133374691, 0.010348688811063766, 0.08331558853387833, -0.03522353991866112, -0.020401807501912117, 0.04282831400632858, -0.040308259427547455, 0.04710818827152252, -0.014956553466618061, 0.013875612989068031, -0.061739131808280945, 0.03716197982430458, -6.516168528107066e-33, -0.0020022979006171227, -0.03189642354846001, -0.08361086994409561, -0.00015796354273334146, 0.004167402163147926, 0.006555730942636728, -0.052300672978162766, -0.011802823282778263, 0.031104009598493576, 0.014145770110189915, 0.017545338720083237, 0.016530852764844894, -0.013086085207760334, -0.0649201050400734, 0.014461029320955276, 0.017353488132357597, 0.014652598649263382, 0.06051149591803551, 0.01211857981979847, 0.00011849141446873546, 0.0370129831135273, 0.036297328770160675, 0.007025565952062607, 0.02637464553117752, 0.01211527269333601, -0.007446032017469406, 0.00912630744278431, -0.009016687050461769, -0.06256309151649475, -0.05502282828092575, 0.04575112462043762, 0.004278603009879589, -0.03600794076919556, 0.015246793627738953, -0.015091676265001297, -0.049789465963840485, -0.023662034422159195, 0.017938505858182907, 0.029771670699119568, -0.02037644013762474, -0.017839496955275536, -0.009256160818040371, -0.021690838038921356, 0.005111791659146547, -0.054435085505247116, 0.000335741468006745, 0.07401344180107117, -0.012014500796794891, -0.03561888635158539, -0.027537526562809944, 0.0245826318860054, 0.010233588516712189, 0.014461765997111797, 0.030248476192355156, 0.0011533431243151426, -0.0596829317510128, 0.004591608420014381, -0.0075974371284246445, 0.04736809432506561, 0.029215006157755852, 0.05809131637215614, 0.06515057384967804, 0.07584317028522491, -0.002268197014927864, 0.012749544344842434, -0.01956804096698761, 0.02045060135424137, 0.01071788277477026, -0.023422857746481895, -0.0061133368872106075, -0.011841933242976665, -0.018879687413573265, -0.04081093519926071, -0.022938454523682594, 0.06800615042448044, -0.029115067794919014, -0.06208448112010956, 0.06736154854297638, -0.05358625575900078, 0.04591141641139984, -0.02026638761162758, 0.0005796682089567184, 0.016724374145269394, -0.004648540634661913, -0.006627803202718496, -0.007675413507968187, -0.004555653780698776, -0.033362314105033875, -0.03555350750684738, -0.025703370571136475, -0.05323035642504692, 0.024335213005542755, -0.02506609819829464, -0.02846229262650013, 0.007250475697219372, 0.06927180290222168, 0.04014619067311287, -0.01857326179742813, -0.05518069490790367, 0.014850912615656853, 0.008427418768405914, -0.03124210610985756, 0.051924366503953934, -0.06427328288555145, -0.009263131767511368, -0.04825415462255478, 0.046832457184791565, 0.014011128805577755, -0.002707152860239148, -0.017414402216672897, -0.015764031559228897, -0.005828138440847397, 0.0025967094115912914, 0.04888840392231941, -0.025507232174277306, -0.026793720200657845, -0.007790696807205677, 0.03532116487622261, 0.03961941599845886, 0.022910576313734055, 0.05449699983000755, 0.030252739787101746, 0.005002245772629976, 0.00830923207104206, -0.058704882860183716, -0.01918923668563366, -0.09222814440727234, -0.03188609704375267, 0.007282437290996313, 0.024887222796678543, -0.06943255662918091, 0.003699904540553689, 2.907834470988746e-07, 0.06774525344371796, 0.055768758058547974, -0.010697434656322002, -0.05167294666171074, -0.0323941707611084, -0.0312609001994133, -0.0541534386575222, 0.026985032483935356, -0.10779781639575958, -0.02632989175617695, 0.004355932120233774, -0.008865118958055973, 0.03314335644245148, 0.05374867469072342, 0.00826231949031353, 0.016676614060997963, -0.0373670794069767, 0.0546436570584774, -0.012971607968211174, -0.018326107412576675, 0.0030749354045838118, 0.01341336965560913, 0.016740841791033745, 0.02930617518723011, 0.006637568585574627, 0.004241942893713713, -0.03157389163970947, -0.00808097142726183, 0.019786374643445015, 0.002641549101099372, -0.059292323887348175, -0.0660439059138298, 0.01881234161555767, -0.041488658636808395, -0.025932714343070984, -0.046134259551763535, -0.02041604369878769, 0.022388318553566933, -0.019199207425117493, 0.04846985265612602, 0.13225871324539185, 0.023524904623627663, 0.0317046232521534, 0.043747469782829285, -0.04625802859663963, 0.009430035017430782, -0.06422532349824905, 0.04272002726793289, 0.002296656370162964, 0.005978700239211321, 0.016788488253951073, 0.08323902636766434, 0.07124379277229309, 0.056052420288324356, -0.009914814494550228, -0.08739983290433884, 0.004263354931026697, 0.00486662145704031, -0.02744963951408863, -0.006236469838768244, 0.00015082121535670012, 0.015357269905507565, 0.016575977206230164, 0.018527645617723465, 0.021778734400868416, 0.006120372097939253, 0.021186957135796547, 3.4711817829791838e-34, 0.013340325094759464, -0.022834204137325287, -0.016220834106206894, 0.036302972584962845, -0.009445364587008953, -0.03364923596382141, 0.018650878220796585, -0.015858789905905724, -0.034885670989751816, -0.06995352357625961, -0.03536956384778023]

['Rita Sharma', 'David L Poole']

1301.2309v1

Collaborative filtering is the process of making recommendations regarding the potential preference of a user, for example shopping on the Internet, based on the preference ratings of the user and a number of other users for various items. This paper considers collaborative filtering based on explicitmulti-valued ratings. To evaluate the algorithms, weconsider only {em pure} collaborative filtering, using ratings exclusively, and no other information about the people or items.Our approach is to predict a user's preferences regarding a particularitem by using other people who rated that item and other items ratedby the user as noisy sensors. The noisy sensor model uses Bayes' theorem to compute the probability distribution for the user'srating of a new item. We give two variant models: in one, we learn a{em classical normal linear regression} model of how users rate items; in another,we assume different users rate items the same, but the accuracy of thesensors needs to be learned. We compare these variant models withstate-of-the-art techniques and show how they are significantly better,whether a user has rated only two items or many. We reportempirical results using the EachMovie database footnote{http://research.compaq.com/SRC/eachmovie/} of movie ratings. Wealso show that by considering items similarity along with theusers similarity, the accuracy of the prediction increases.

Symmetric Collaborative Filtering Using the Noisy Sensor Model

http://arxiv.org/pdf/1301.2309v1

Title Symmetric Collaborative Filtering Using Noisy Sensor Model Summary Collaborative filtering process making recommendation regarding potential preference user example shopping Internet based preference rating user number user various item paper considers collaborative filtering based explicitmultivalued rating evaluate algorithm weconsider em pure collaborative filtering using rating exclusively information people itemsOur approach predict user preference regarding particularitem using people rated item item ratedby user noisy sensor noisy sensor model us Bayes theorem compute probability distribution usersrating new item give two variant model one learn aem classical normal linear regression model user rate item anotherwe assume different user rate item accuracy thesensors need learned compare variant model withstateoftheart technique show significantly betterwhether user rated two item many reportempirical result using EachMovie database footnotehttpresearchcompaqcomSRCeachmovie movie rating Wealso show considering item similarity along theusers similarity accuracy prediction increase Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.008782458491623402, 0.015500392764806747, -0.003009394509717822, -0.023728370666503906, -0.03332379832863808, -0.00459327083081007, 0.028603585436940193, 0.009473216719925404, -0.007886656560003757, -0.025943433865904808, -0.04060247540473938, 0.008654385805130005, 0.007603995501995087, 0.034851767122745514, -0.012531105428934097, -0.02405894547700882, -0.0045396434143185616, 0.031039269641041756, -0.0017602104926481843, -0.038303133100271225, 0.03534635528922081, -0.03264925256371498, 0.035382747650146484, -0.022295212373137474, 0.035291220992803574, 0.029295431450009346, 0.028438139706850052, -0.04090874269604683, -0.019140956923365593, -0.042842473834753036, 0.03301041200757027, 0.000918388192076236, -0.00916687399148941, -0.0029833135195076466, 2.209487547588651e-06, -0.029980935156345367, -0.017586518079042435, -0.007284626364707947, 0.03608538210391998, -0.02640709839761257, 0.04366118460893631, 0.11048579961061478, 0.050232209265232086, 0.01956133544445038, -0.057270586490631104, -0.012005306780338287, 0.007458559703081846, 0.04171212017536163, 0.005311706103384495, -0.02810771018266678, -0.01181838009506464, -0.038691446185112, -0.03555963933467865, -0.014499505050480366, 0.0854608416557312, -0.0012428326299414039, 0.01621706411242485, -0.02655036374926567, 0.010258588008582592, 0.005445674527436495, 0.0060296026058495045, -0.04392658546566963, -0.021339569240808487, 0.0007688458426855505, 0.0772605910897255, 0.026683347299695015, 0.033021122217178345, -0.029895532876253128, 0.02443358115851879, 0.03793312981724739, 0.018700888380408287, 0.004686838481575251, -0.005494005512446165, 0.034611959010362625, -0.021037383005023003, 0.044274307787418365, -0.036343637853860855, -0.01928584650158882, -0.030347881838679314, 0.017391974106431007, -0.043821439146995544, 0.02835555374622345, 0.03821048513054848, 0.021476317197084427, 0.052165716886520386, 0.09572746604681015, -0.008855141699314117, -0.01958588697016239, 0.00789729505777359, -0.011834774166345596, 0.014510400593280792, -0.04425207898020744, 0.05861218273639679, -0.007912101224064827, -0.039347849786281586, -0.025710871443152428, 0.014655894599854946, 0.030703015625476837, 0.007000922691076994, -0.06361199915409088, 0.061319272965192795, -0.0015218546614050865, 0.024383224546909332, 0.022696709260344505, 0.004357466474175453, -0.003296274458989501, 0.012455062009394169, 0.029509983956813812, -0.004414597526192665, 0.05505372956395149, -0.03609878569841385, 0.03696736693382263, 0.056874681264162064, 0.053349025547504425, -0.0009024709579534829, -0.014146188274025917, -0.05732143297791481, 0.03071937896311283, -0.012913561426103115, 0.015800734981894493, 0.02074376493692398, 0.05533595010638237, 0.021083232015371323, 0.034639872610569, -0.06931538879871368, 0.003518938785418868, -0.05660031735897064, 0.059682488441467285, 0.0064567942172288895, 0.07480479776859283, 0.07149862498044968, -0.0021088169887661934, 0.03535661846399307, 0.016445189714431763, 0.041617102921009064, 0.013994255103170872, 0.04335853457450867, 0.025275487452745438, -0.041416943073272705, -0.0062050847336649895, 0.012593865394592285, -0.00924704223871231, -0.08653873205184937, -0.056600090116262436, 0.031889863312244415, 0.018679318949580193, -0.003174476558342576, -0.01154477708041668, 0.004580977838486433, -0.01793169230222702, -0.060257624834775925, 0.09133544564247131, 0.0003331471816636622, -0.009416192770004272, 0.02643372118473053, -0.00393587676808238, -0.0040879882872104645, -0.04606866464018822, -0.0017308086389675736, 0.040087632834911346, 0.06409961730241776, 0.01321016438305378, -0.007101544179022312, -0.023895548656582832, -0.04144067317247391, -0.005299420095980167, -0.022871797904372215, 0.03559262305498123, -0.031882040202617645, -0.008561954833567142, -0.03029322810471058, 0.032194703817367554, -0.015145724639296532, -0.030703730881214142, 0.05271031707525253, 0.02542739175260067, -0.011013375595211983, 0.043680790811777115, -0.011249208822846413, 0.04874972254037857, -0.03505634889006615, 0.021958384662866592, 0.013703522272408009, 0.05787404999136925, -0.00944625586271286, -0.04569407179951668, 0.019742326810956, -0.023389136418700218, -0.03884883224964142, -0.018810193985700607, 0.01008701790124178, -0.02998465858399868, 0.028558852151036263, 0.005983420182019472, 0.03417782858014107, -0.027849148958921432, 0.003447673050686717, -0.03963426128029823, 0.051181234419345856, -0.008599565364420414, 0.012448864988982677, -0.039539311081171036, 0.1029299795627594, 0.05674202740192413, -0.006949417293071747, -0.022447437047958374, 0.0337369479238987, -0.04749483987689018, -0.06697909533977509, -0.14401774108409882, 0.019803931936621666, -0.03144281730055809, -0.03856527432799339, -0.037411484867334366, -0.0656963661313057, 0.0350433774292469, 0.012376152910292149, 0.02816343866288662, -0.061799950897693634, 0.0018948009237647057, -0.019270537421107292, 0.02705090306699276, 0.006903712637722492, -0.016402658075094223, 0.01278337836265564, 0.041363250464200974, 0.06034516170620918, -0.010946138761937618, 0.051107920706272125, 0.013613236136734486, 0.048367492854595184, 0.0006433328962884843, 0.019751008599996567, -0.0030889876652508974, -0.061431221663951874, 0.027113866060972214, 0.022504897788167, 0.021518699824810028, 0.0331142358481884, -0.012400426901876926, 0.07462836056947708, 0.059423159807920456, 0.029462071135640144, -0.004668135195970535, 0.024143187329173088, -0.00118328258395195, -0.031543176621198654, 0.019200274720788002, 0.03457921743392944, 0.0028155618347227573, -0.017749886959791183, -0.024503521621227264, 0.01847294718027115, -0.03811594843864441, 0.01725730113685131, -0.05600845441222191, -0.02990587241947651, 0.04048933833837509, -0.008961180225014687, -0.027553362771868706, -0.01644667610526085, 0.02764740400016308, 0.03833319619297981, 0.016054699197411537, -0.021740278229117393, -0.011753917671740055, -0.02500046230852604, -0.015483925119042397, 0.011602157726883888, -0.0031671514734625816, -0.01379594299942255, 0.011589442379772663, 0.011448833160102367, 0.02263292670249939, -0.020067965611815453, -0.041983284056186676, 0.03721717745065689, -0.04204157367348671, 0.005162034649401903, 0.008844839408993721, 0.062482934445142746, 0.003316985908895731, -0.011167186312377453, -0.03595683351159096, -0.03241807967424393, 0.005737277679145336, 0.05334332585334778, -0.014946001581847668, -0.04881366714835167, -0.006554656196385622, -0.02381586655974388, -0.038254398852586746, 0.018709363415837288, 0.0013885640073567629, -0.03082932159304619, -0.0013447173405438662, -0.022967291995882988, -0.010851186700165272, -0.005515618249773979, 0.0133121432736516, 0.07067320495843887, 0.026959136128425598, -0.05502491816878319, 0.002780648646876216, -0.01693912409245968, 0.010548790916800499, -0.024036815389990807, -0.01097351498901844, -0.021442152559757233, -0.05728961154818535, 0.03274594619870186, -0.017227422446012497, 0.004582292400300503, 0.05970989912748337, -0.002434150315821171, -0.003424843307584524, -0.055148154497146606, -0.02052616886794567, 0.007375428453087807, 0.05429535359144211, 0.026423020288348198, -0.01476757787168026, 0.042480360716581345, 0.030501846224069595, 0.02500939555466175, -0.05722486227750778, -0.04853823035955429, 0.050130054354667664, -0.040427908301353455, 0.0026653872337192297, 0.012926134280860424, -0.05139750987291336, 0.030785631388425827, -0.012639293447136879, -0.0184322502464056, 0.08284566551446915, -0.039162810891866684, -0.04554443061351776, 0.04428601637482643, -0.03637774661183357, 0.016582554206252098, -0.0284791961312294, -0.007327516097575426, -0.05366695299744606, -0.004960885737091303, -0.044341787695884705, -0.02699420601129532, -0.022640390321612358, 0.0010934697929769754, 0.01126020960509777, -0.03961576893925667, 0.009974007494747639, -0.008623592555522919, -0.037323229014873505, 0.03933966904878616, 0.009451180696487427, 0.02701461873948574, -0.07728060334920883, -0.05242718383669853, -0.013339017517864704, 0.001505739986896515, 0.05885012820363045, 0.042477380484342575, -0.0038176507223397493, -0.047340843826532364, 0.03513816371560097, 0.05172991007566452, 0.030781859531998634, -0.031797926872968674, 0.032836027443408966, -0.02802937664091587, 0.024581769481301308, 0.06598798930644989, 0.05281931534409523, 0.011713368818163872, -0.13668012619018555, -0.029168792068958282, -0.03887065127491951, -0.02606832981109619, 0.05090158060193062, 0.02936164289712906, -0.0014030331512913108, 0.005151307210326195, -0.0061623407527804375, 0.051965467631816864, 0.016912490129470825, -0.05182666331529617, -0.021563293412327766, -0.022441403940320015, 0.013017762452363968, -0.024307632818818092, -0.010877583175897598, -0.001076000975444913, -0.07594922930002213, 0.020456166937947273, -0.05634824186563492, -0.011004835367202759, -0.001852816087193787, 0.021669702604413033, 0.025450820103287697, 0.0011530700139701366, -0.026216289028525352, 0.0044689360074698925, 0.04487807676196098, -0.09022895246744156, 0.04589903727173805, 0.037556130439043045, 0.026763293892145157, -0.03205656632781029, -0.029964355751872063, -0.03694275766611099, 0.03226473554968834, 0.008415143936872482, -0.02573864720761776, 0.02791522815823555, -0.00025586975971236825, 0.028492236509919167, -0.04191286861896515, 0.03058747388422489, -0.006789416540414095, 0.02249174937605858, 0.020241862162947655, 0.042138904333114624, -0.007786909118294716, -0.015294486656785011, -0.01755533367395401, 0.03148758038878441, 0.020301256328821182, 0.03088236041367054, -0.02437700144946575, -0.07191181182861328, 0.040588218718767166, -0.011409517377614975, -0.03592853993177414, 0.08011456578969955, 0.008181000128388405, 0.00894677173346281, -0.019456032663583755, -0.05944044888019562, -0.07490261644124985, 0.008832495659589767, -0.02732662856578827, 0.04502622038125992, 0.0005051639745943248, 0.049693357199430466, 0.02395595982670784, -0.03985290974378586, 0.017751282081007957, -0.04291445016860962, 0.06197219714522362, 0.00497674522921443, -0.0069204820320010185, 0.03557711839675903, 0.01731514185667038, -0.014869620092213154, -0.03170947730541229, -0.1175600066781044, -0.037554461508989334, -0.03635423257946968, -0.01386169157922268, 0.10355579853057861, 0.021133847534656525, 0.0342162549495697, -0.04764629900455475, -0.048468269407749176, -0.046978339552879333, -0.013772607780992985, -0.01701286807656288, -0.04986227676272392, 0.010822782292962074, 0.005530246067792177, 2.2167874703882262e-05, 0.02888496406376362, -0.010124456137418747, -0.011904532089829445, -0.009535654447972775, -0.06893275678157806, -0.08241179585456848, -0.05540703982114792, 0.019723674282431602, 0.00933423638343811, 0.036012765020132065, -0.01835493929684162, 0.011136802844703197, 0.004764709621667862, 0.017116034403443336, 0.005376982502639294, -0.03806327283382416, -0.03323246166110039, -0.038386739790439606, 0.054238829761743546, -0.005460655316710472, -0.023582808673381805, -0.024756357073783875, 0.013200143352150917, -0.009576072916388512, -0.0411929115653038, 0.03510052338242531, -0.0022619590163230896, 0.0030649967957288027, 0.007061460986733437, -2.8179529181215912e-05, 0.03219024837017059, -0.05027258023619652, 0.05816169083118439, 0.011494657956063747, -0.010023005306720734, 0.03018493950366974, -0.028008677065372467, -0.019890207797288895, 0.0024562899488955736, 0.03208218142390251, 0.024538863450288773, -0.01778113842010498, -0.013712815940380096, 0.01257564127445221, -0.018265599384903908, -0.0288095660507679, -0.009297562763094902, -0.0013058229815214872, 0.011413573287427425, -0.04249349236488342, 0.03037405200302601, -0.04663904011249542, 0.03275243565440178, 0.04656127467751503, 0.03244880214333534, -0.008052485063672066, 0.03949255868792534, 0.07218440622091293, -0.028790872544050217, -0.05196990817785263, -0.02943592704832554, -0.097517229616642, -0.0037023830227553844, 0.06943821907043457, 0.014707275666296482, 0.07082926481962204, -0.04553541913628578, 0.00019276139209978282, 0.025004655122756958, -0.01360792014747858, 0.005475356709212065, -0.03968717157840729, 0.08040978014469147, -0.014767423272132874, 0.01865403726696968, 0.052890706807374954, -0.022696377709507942, 0.064117431640625, -0.03536797687411308, -0.07577528804540634, 0.01938668079674244, -0.00431721331551671, -0.012725205160677433, -6.322893746944865e-33, 0.03496116027235985, -0.020368803292512894, -0.030473269522190094, 0.025990040972828865, 0.008507638238370419, -0.06699254363775253, 0.038487520068883896, 0.018389087170362473, 0.03653673082590103, -0.0010011635022237897, -0.01596919074654579, 0.006826243828982115, 0.019355488941073418, -0.01704070158302784, 0.027249380946159363, -0.02318796142935753, 0.01893114484846592, 0.011343937367200851, 0.02974748983979225, -0.007976946420967579, 0.04181923717260361, 0.033328067511320114, -0.0035871006548404694, -0.09093236923217773, 0.013664650730788708, 0.008441991172730923, -0.023990757763385773, -0.04122868925333023, -0.012286636047065258, 0.03146732598543167, 0.007147837430238724, 0.01833481527864933, -0.013026047497987747, 0.004917772952467203, -0.03180593624711037, -0.02869657799601555, -0.06877841800451279, 0.015206526033580303, -0.02554793655872345, 0.023020969703793526, 0.041093554347753525, 0.021248267963528633, 0.036491427570581436, 0.023461226373910904, -0.02929266169667244, 9.559666796121746e-05, 0.048466771841049194, -0.03520364686846733, -0.02606457844376564, 0.008171357214450836, 0.06701299548149109, 0.005852326285094023, -0.0009685870609246194, 0.024806058034300804, -0.0018263149540871382, 0.04052591696381569, -0.039439428597688675, 0.007609653752297163, -0.03484927862882614, 0.04674156382679939, -0.06961377710103989, 0.03356432914733887, -0.021852167323231697, -0.036532413214445114, 0.005852869246155024, 0.017232758924365044, 0.03541119024157524, -0.06338527798652649, 0.010168245993554592, -0.019358491525053978, -0.05567369982600212, 0.07155215740203857, 0.007291482295840979, 0.07820583134889603, 0.05993770807981491, -0.07456880807876587, -0.04167871177196503, 0.07821476459503174, 0.03335681930184364, -0.012833635322749615, 0.05369583144783974, 0.026398858055472374, -0.038178835064172745, -0.03801001235842705, 0.027628516778349876, -0.025509590283036232, -0.057294849306344986, -0.05735854431986809, 0.011628334410488605, 0.022237012162804604, -0.0006952001131139696, -0.00821855291724205, -0.02978748455643654, -0.0772099420428276, -0.041994884610176086, -0.03900543972849846, -0.017647573724389076, -0.00727651733905077, 0.0239736195653677, -0.04918818920850754, -0.017103388905525208, 0.017230279743671417, -0.052652232348918915, -0.017048710957169533, -0.042174652218818665, 0.0038308254443109035, 0.023394200950860977, 0.020164338871836662, -0.03128622844815254, -0.03171440213918686, 0.05472279340028763, -0.08026391267776489, 0.04515219107270241, 0.01473702397197485, 0.001888813218101859, -0.005077643319964409, -0.03514229506254196, 0.0884915441274643, 0.004034023731946945, 0.055624786764383316, -0.01805379055440426, -0.07676957547664642, -0.00042873225174844265, -0.009349150583148003, -0.01894025318324566, -0.04156685248017311, -0.044815581291913986, -0.03513508662581444, 0.031646907329559326, -0.020260527729988098, -0.024819517508149147, -0.053012702614068985, 2.843874256086565e-07, 0.0025766475591808558, -0.003276542294770479, -0.05523127689957619, -0.032045576721429825, 0.010785296559333801, 0.05545265972614288, -0.019151249900460243, 0.04464519023895264, 0.046844251453876495, 0.03552790731191635, 0.0034309211187064648, -0.049675799906253815, -0.00476093590259552, 0.04117661714553833, -0.014218993484973907, -0.058808110654354095, -0.03206101804971695, 0.02054143324494362, 0.007851546630263329, 0.014342742040753365, 0.006870314944535494, 0.06658560037612915, 0.08439617604017258, -0.01974680833518505, -0.007463389541953802, -0.0233776792883873, 0.026383398100733757, -0.0594673678278923, -0.029387783259153366, -0.04156560078263283, 0.05055748671293259, -0.011606685817241669, -0.01984282210469246, 0.04910951480269432, -0.0322326198220253, -0.0251570176333189, 0.03504342585802078, 0.01122556533664465, -0.017453964799642563, 0.015995895490050316, 0.03696516901254654, 0.013525759801268578, 0.01534991804510355, -0.043342724442481995, 0.04601354897022247, 0.06064213439822197, -0.04323573783040047, 0.005493542645126581, -0.016704918816685677, 0.007341769523918629, 0.03902182728052139, -0.008293412625789642, -0.019779982045292854, -0.023442070931196213, 0.00404050387442112, 0.008808352053165436, -0.004629772622138262, -0.00798154715448618, 0.0039646378718316555, -0.041311223059892654, -0.009644532576203346, -0.05633751302957535, 0.01600685715675354, 0.015340079553425312, 0.035369209945201874, 0.002671858062967658, 0.015981005504727364, 2.432994126293815e-34, 0.04344811290502548, 0.059630099684000015, -0.01279331836849451, -0.046920035034418106, 0.01088737417012453, -0.04282500222325325, 0.025547251105308533, -0.007961246185004711, 0.05751422420144081, -0.0024057026021182537, -0.036701127886772156]

['Muhammad Rafi', 'Mohammad Shahid Shaikh']

1301.2785v1

Document classification is a task of assigning a new unclassified document to one of the predefined set of classes. The content based document classification uses the content of the document with some weighting criteria to assign it to one of the predefined classes. It is a major task in library science, electronic document management systems and information sciences. This paper investigates document classification by using two different classification techniques (1) Support Vector Machine (SVM) and (2) Relevance Vector Machine (RVM). SVM is a supervised machine learning technique that can be used for classification task. In its basic form, SVM represents the instances of the data into space and tries to separate the distinct classes by a maximum possible wide gap (hyper plane) that separates the classes. On the other hand RVM uses probabilistic measure to define this separation space. RVM uses Bayesian inference to obtain succinct solution, thus RVM uses significantly fewer basis functions. Experimental studies on three standard text classification datasets reveal that although RVM takes more training time, its classification is much better as compared to SVM.

A comparison of SVM and RVM for Document Classification

http://arxiv.org/pdf/1301.2785v1

Title comparison SVM RVM Document Classification Summary Document classification task assigning new unclassified document one predefined set class content based document classification us content document weighting criterion assign one predefined class major task library science electronic document management system information science paper investigates document classification using two different classification technique 1 Support Vector Machine SVM 2 Relevance Vector Machine RVM SVM supervised machine learning technique used classification task basic form SVM represents instance data space try separate distinct class maximum possible wide gap hyper plane separate class hand RVM us probabilistic measure define separation space RVM us Bayesian inference obtain succinct solution thus RVM us significantly fewer basis function Experimental study three standard text classification datasets reveal although RVM take training time classification much better compared SVM Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.05774236470460892, -0.032632920891046524, 0.004407941363751888, -0.010359959676861763, -0.01884765923023224, 0.020488448441028595, 0.03451387211680412, 0.026344312354922295, -0.012620843015611172, -0.06945031881332397, 0.02125324122607708, 0.025510607287287712, 0.023115264251828194, -0.02499411441385746, -0.03350143879652023, -0.047315068542957306, 0.03463674709200859, -0.0010381377069279552, 0.012864393182098866, 0.005857928656041622, 0.02753102034330368, -0.018071340397000313, 0.02110537514090538, 0.000303647480905056, 0.013251636177301407, 0.03162958845496178, -0.00015031336806714535, -0.01497644279152155, -0.016548676416277885, -0.0362311489880085, 0.05656646937131882, 0.02939123846590519, 0.009168452583253384, 0.06746596097946167, 1.8497718201615498e-06, -0.05206942558288574, -0.030852578580379486, 0.012672006152570248, 0.030339520424604416, -0.03656616434454918, 0.05732562020421028, -0.03676179423928261, 0.028739970177412033, 0.021212434396147728, -0.028298957273364067, -0.033034369349479675, 0.021653398871421814, 0.09593141824007034, -0.021467868238687515, 0.05012139678001404, -0.017327697947621346, -0.06561194360256195, 0.028939243406057358, -0.007263219449669123, 0.0670226663351059, -0.0063810767605900764, 0.012330948375165462, 0.018791889771819115, 0.005560293328016996, 0.016486525535583496, -0.011424733325839043, 0.002805709606036544, -0.041089024394750595, -0.017142105847597122, 0.024702660739421844, 0.0330486036837101, -0.05753714591264725, 0.018150733783841133, 0.012064616195857525, -0.002040982013568282, -0.009308712556958199, -0.004322559107095003, 0.01247632596641779, 0.021510016173124313, -0.037104181945323944, 0.03396110236644745, -0.009588925167918205, 0.02183704450726509, -0.028927523642778397, 0.03841397166252136, 0.013334987685084343, 0.05447180196642876, -0.027307894080877304, 0.003950982820242643, 0.008186501450836658, 0.026819296181201935, -0.023941343650221825, -0.048704568296670914, 0.057425063103437424, 0.020832881331443787, 0.009305949322879314, -0.013752005062997341, 0.016270125284790993, 0.02096647210419178, -0.014358152635395527, 0.006210682913661003, -0.03892954811453819, -0.04945193976163864, 0.070583276450634, -0.0812869518995285, 0.026819908991456032, -0.0416591577231884, 0.003780860686674714, 0.042278945446014404, -0.02028803899884224, 0.01516458299010992, 0.024028509855270386, 0.01908736675977707, -0.011038664728403091, 0.03776498883962631, -0.094861701130867, -0.009593517519533634, 0.01595301926136017, 0.0583265945315361, 0.014147299341857433, -0.03654180467128754, -0.08049685508012772, 0.006853882689028978, 0.04414767399430275, 0.013351158238947392, 0.002539766253903508, -0.002939641010016203, -0.002090564463287592, 0.054980430752038956, -0.049142949283123016, -0.021881859749555588, 0.003161258064210415, 0.029399534687399864, -0.0668591782450676, 0.023646624758839607, 0.06811956316232681, 0.03219165652990341, -0.011013592593371868, 0.0006931691896170378, 0.054165348410606384, -0.02483813464641571, -0.0191267728805542, -0.014394892379641533, -0.05217115581035614, -0.013438364490866661, 0.0055199721828103065, -0.027019312605261803, 0.0010252774227410555, -0.03210653364658356, 0.002731424756348133, 0.019148696213960648, -0.03577427938580513, 0.07049724459648132, -0.006644568871706724, -0.0029315731953829527, -0.012937715277075768, 0.057204604148864746, -0.01234300248324871, 0.02540084905922413, 0.13293954730033875, -0.0016623166156932712, 0.021471237763762474, -3.8257585401879624e-05, -0.05195096507668495, -0.01640750840306282, 0.03721913322806358, -0.03159666433930397, 0.055441245436668396, -0.02311880700290203, -0.06870731711387634, -0.06273452192544937, 0.006530842278152704, 0.04859665781259537, 0.010520534589886665, -0.011163592338562012, 0.010092769749462605, 0.017764268442988396, -0.001044953940436244, -0.024255577474832535, 0.016528863459825516, 0.057653043419122696, 0.032103199511766434, 0.002981331665068865, -0.015610449016094208, 0.08271994441747665, 0.036931656301021576, 0.012455525808036327, 0.021034715697169304, -0.018514443188905716, -0.06449094414710999, -0.0038638627156615257, -0.052362922579050064, -0.06610322743654251, -0.006929134950041771, -0.049056775867938995, -0.03696295991539955, 0.002830077428370714, 0.0007043091463856399, -0.03453557938337326, 0.06790479272603989, -0.010107383131980896, -0.020198358222842216, -0.02950632944703102, 0.01679629646241665, -0.0038630247581750154, -0.06344622373580933, -0.02763347327709198, 0.036999285221099854, -0.0038618119433522224, 0.013040837831795216, -0.10993489623069763, 0.043094150722026825, 0.005247085355222225, 0.005219601560384035, -0.0055523039773106575, 0.0646858811378479, 0.014475886709988117, -0.0313284769654274, -0.0166873037815094, 0.0069569009356200695, 0.00555806141346693, 0.0023609399795532227, 0.0016887161182239652, -0.011239350773394108, 0.021676382049918175, -0.002588406903669238, -0.01357649639248848, -0.08058316260576248, 0.07304488867521286, 0.07332277297973633, -0.004507241304963827, 0.03166257590055466, 0.021008508279919624, 0.00497097335755825, -0.030142033472657204, -0.004623819142580032, -0.016387561336159706, 0.01629551686346531, -0.013031074777245522, -0.04918082058429718, -0.03410612791776657, 0.03148245811462402, -0.00965860579162836, 0.00310407392680645, -0.0006622139480896294, 0.015842556953430176, 0.03666730225086212, -0.017131390050053596, -0.018882306292653084, -0.05421553552150726, 0.0077875894494354725, 0.0035850408021360636, -0.050331760197877884, 0.06340011954307556, -0.04758082702755928, 0.013761657290160656, -0.05748496577143669, 0.059743355959653854, 0.045196399092674255, 0.06382566690444946, -0.019059786573052406, -0.042708273977041245, 0.03727135434746742, -0.0024291984736919403, -0.0296610239893198, 0.016010552644729614, -0.0520472526550293, 0.021298177540302277, 0.0036439329851418734, 0.018010493367910385, -0.028319139033555984, -0.04552936553955078, -0.0452079176902771, -0.0066752866841852665, 0.02824830263853073, 0.014147233217954636, -0.02784816548228264, -0.040343839675188065, -0.006474063731729984, -0.009949533268809319, -0.04750259965658188, -0.01711580902338028, -0.0008729484979994595, -0.02108713611960411, 0.05356438830494881, -0.023164233192801476, 0.04279528930783272, -0.03716851770877838, -0.003009821753948927, 0.025916343554854393, 0.04620137810707092, 0.04882455989718437, 0.008426741696894169, -0.03764631599187851, 0.015837114304304123, 0.0005868049920536578, 0.003206992754712701, 0.02126110903918743, -0.006020508706569672, -0.04127432033419609, -0.04003046825528145, -0.05246071144938469, 0.0006375191733241081, 0.02527463063597679, 0.02595432661473751, 0.06219010055065155, 0.06625926494598389, -0.025531645864248276, -0.0025887228548526764, -0.05094021558761597, 0.024478871375322342, 0.0012204345548525453, 0.020396551117300987, 0.05110831931233406, -0.017412468791007996, 0.001975185237824917, 0.016330618411302567, 0.03035776875913143, -0.005893034860491753, 0.008693491108715534, 0.027185602113604546, -0.03316214680671692, -0.03737497702240944, 0.01368326973170042, 0.018311774358153343, 0.013729609549045563, -0.0351194329559803, 0.02059539221227169, -0.046000946313142776, 0.01399296149611473, -0.10703546553850174, -0.02905457839369774, -0.012722483836114407, 0.016354622319340706, -0.009847118519246578, 0.007837414741516113, -0.03961984068155289, -0.008427471853792667, 0.011858288198709488, 0.030438173562288284, 0.054148949682712555, -0.023371456190943718, -0.044612787663936615, 0.01900915801525116, 0.00946843158453703, -0.04313766211271286, 0.033102646470069885, -0.018747230991721153, -0.04215525463223457, 0.012766659259796143, -0.004363503307104111, 0.02082889899611473, 0.015238014981150627, -0.03258419409394264, 0.07975753396749496, -0.011645754799246788, 0.0369991660118103, -0.04743792116641998, -0.055398836731910706, 0.04501526057720184, 0.015459515154361725, 0.004618306644260883, -0.0520646907389164, -0.06595968455076218, 0.037620801478624344, 0.024252448230981827, 0.015385320410132408, -0.015620016492903233, 0.0017137391259893775, -0.021602731198072433, 0.011427134275436401, 0.021354641765356064, -0.07330042868852615, -0.059446804225444794, -0.03642714396119118, -0.02093677595257759, -0.051346030086278915, 0.039069123566150665, 0.07683948427438736, 0.04614297300577164, -0.07981328666210175, -0.053213391453027725, -0.07670273631811142, -0.04530199617147446, 0.027037592604756355, 0.060001615434885025, 0.0060723451897501945, 0.012495449744164944, -0.019571291282773018, 0.04379605874419212, -0.012202713638544083, -0.022141991183161736, 0.02451758272945881, -0.031290795654058456, 0.020919613540172577, -0.035375580191612244, -0.11126423627138138, 0.031585242599248886, -0.06538692861795425, -0.020107902586460114, 0.016956841573119164, -0.06680338084697723, 0.00016966993280220777, -0.03743119165301323, 0.006748604588210583, 0.029686253517866135, -0.08386369049549103, -0.012323095463216305, -0.012469414621591568, -0.01682126335799694, -0.03680926561355591, 0.021952375769615173, 0.04210420325398445, -0.03788721188902855, -0.009071377106010914, -0.0203827116638422, -0.04208417236804962, 0.04137326776981354, -0.076944999396801, 0.07957670837640762, -0.0036221991758793592, 0.023023884743452072, -0.009394727647304535, -0.0022319962736219168, 0.03614339604973793, 0.024679455906152725, 0.05468866601586342, 0.012440103106200695, -0.03994382172822952, -0.048333920538425446, -0.06490366160869598, -0.006109846290200949, -0.009825955145061016, 0.02964792400598526, -0.0142205273732543, -0.030366895720362663, -0.06450071185827255, 0.03626912459731102, 0.02235795371234417, 0.04290696606040001, 0.017110399901866913, -0.010975104756653309, -0.07032332569360733, -0.0801679790019989, -0.061029646545648575, -0.0099113704636693, -0.02133728750050068, 0.03200315684080124, 0.003935950342565775, 0.04660028591752052, -0.011333766393363476, 0.023657498881220818, -0.08446361869573593, -0.05608013644814491, 0.05569153651595116, -0.0008719807374291122, -0.02901073545217514, -0.007309505250304937, 0.042368438094854355, -0.005469061434268951, -0.024311095476150513, -0.1159990057349205, 0.036985673010349274, -0.017021991312503815, -0.009660555981099606, 0.0053334422409534454, 0.015269565396010876, 0.009611524641513824, 0.0011127511970698833, -0.06395557522773743, 0.05241962522268295, 0.007159546948969364, -0.025346187874674797, -0.007669690530747175, 0.03914397582411766, -0.024368632584810257, -0.03862335532903671, -0.020675944164395332, -0.021861230954527855, 0.04203878715634346, 0.02004312537610531, -0.07046515494585037, -0.023804042488336563, 0.032418400049209595, -0.0456075593829155, 0.008334130980074406, 0.06423456221818924, 0.014489023946225643, -0.016931530088186264, 0.006121393758803606, 0.011613443493843079, 0.014887270517647266, -0.010028638876974583, 0.021022086963057518, -0.013072114437818527, 0.02353430911898613, 0.01674589328467846, -0.007842374965548515, 0.051447056233882904, -0.015885796397924423, 0.006965843960642815, -0.002017570659518242, 0.02520778402686119, 0.03569703921675682, 0.06900233030319214, -0.029017360880970955, 0.025849197059869766, -0.03144249692559242, -0.04835793748497963, 0.04998907074332237, 0.0051118964329361916, -0.02002638205885887, 0.03911101073026657, -0.000552646815776825, 0.046075623482465744, -0.005250114481896162, -0.0038412667345255613, -0.02085067145526409, 0.011781684122979641, 0.004137237090617418, 0.037299659103155136, 0.010390028357505798, -0.048888836055994034, -0.022823749110102654, -0.0064650592394173145, -0.019099393859505653, -0.024439813569188118, 0.0336858406662941, 0.03131575509905815, 0.01396576315164566, 0.04980887845158577, -0.0036390796303749084, -0.048820387572050095, 0.033028073608875275, 0.03913300856947899, 0.03357399255037308, -0.07640473544597626, -0.0010766604682430625, -0.11256074905395508, -0.03131142631173134, 0.024665679782629013, 0.07412680238485336, 0.027260396629571915, 2.7536383640835993e-05, -0.021074827760457993, -0.02010030299425125, 0.023310303688049316, 0.034870147705078125, -0.025056032463908195, 0.04241122305393219, -0.004910805728286505, -0.0011875592172145844, 0.07800683379173279, 0.04229999706149101, 0.02661452256143093, -0.041942134499549866, -0.020776202902197838, -0.03452639654278755, 0.018634377047419548, -0.02494201250374317, -5.178962154126125e-33, 0.032822079956531525, -0.05268377810716629, -0.04451347514986992, 0.04689894989132881, -0.0028329677879810333, 0.02764984220266342, 0.00667560426518321, 0.007974391803145409, 0.018386153504252434, -0.0014957882231101394, -0.005826221313327551, 0.001241017715074122, 0.01855427958071232, -0.011717154644429684, 0.04530966654419899, 0.024599861353635788, 0.022759294137358665, -0.0064378040842711926, -0.0182467233389616, 0.0023778011091053486, 0.015437561087310314, 0.031365662813186646, 0.004217870999127626, -0.09899242967367172, 0.01193955633789301, -0.019179483875632286, -0.00026173662627115846, -0.00411547627300024, 0.022461671382188797, 0.0245519932359457, 0.0006275638588704169, 0.03860565274953842, 0.034219443798065186, -0.030117059126496315, 0.029836207628250122, 0.04606026038527489, -0.01673348806798458, -0.034697383642196655, 0.0012376797385513783, 0.03646794334053993, 0.015495591796934605, 0.03458385542035103, 0.03256858512759209, 0.011366444639861584, -0.017907870933413506, 0.010980403982102871, 0.10070065408945084, -0.03624590486288071, -0.06715072691440582, -0.0991237685084343, -0.03284681588411331, 0.010492974892258644, 0.004953434225171804, 0.024369465187191963, 0.04809210076928139, -0.008503632619976997, -0.014640038833022118, 0.027266567572951317, -0.0394262969493866, 0.01340564712882042, -0.003269763197749853, 0.02105613984167576, 0.010214314796030521, 0.03933723270893097, -0.0155655387789011, 0.021645549684762955, 0.044046975672245026, -0.017053456977009773, 0.026317359879612923, -0.012426655739545822, 0.03245043009519577, 0.04604487121105194, 0.03725370764732361, 0.00907334964722395, 0.07940100133419037, -0.04103218391537666, -0.02983260154724121, 0.08204405009746552, 0.015665093436837196, -0.027637742459774017, 5.196737220103387e-06, 0.0016366890631616116, -0.026316119357943535, -0.036394063383340836, 0.0031597085762768984, -0.0001786203501978889, -0.02359817363321781, -0.011374182067811489, 0.02775360830128193, -0.0014243950136005878, -0.02187371999025345, -0.0025601410306990147, -0.027680957689881325, -0.004034085664898157, -0.06356166303157806, 0.015835363417863846, -0.014557948336005211, 0.02678213082253933, -0.02906215935945511, -0.07999326288700104, -0.005406152922660112, -0.023075319826602936, 0.026898769661784172, -0.013911177404224873, 0.015826847404241562, -0.041064441204071045, 0.06656818836927414, -0.01311543583869934, -0.03382321074604988, 0.0017439075745642185, 0.06471081078052521, -0.03006625548005104, -0.01987653784453869, 0.08011344075202942, -0.04565506428480148, -0.04630966857075691, 0.025286758318543434, 0.0635896548628807, 0.014329219236969948, 0.00644481647759676, -0.05814671888947487, -0.08507342636585236, 0.021813910454511642, 0.01111967209726572, -0.02966172620654106, 0.019986407831311226, -0.0038068112917244434, 0.0021376446820795536, 0.030834147706627846, -0.00471648620441556, -0.004099187441170216, -0.008474302478134632, 2.418038889118179e-07, 0.06650735437870026, 0.03177642822265625, -0.006684386171400547, -0.06801734864711761, 0.006615280639380217, 0.026126930490136147, 0.0023150250781327486, 0.007132981438189745, -0.016254251822829247, 0.07507798820734024, 0.02928857132792473, -0.02053092233836651, 0.06602279096841812, 0.010435285046696663, -0.032441768795251846, -0.05645294860005379, -0.06284455955028534, 0.014470024034380913, -0.05359631031751633, 0.039881546050310135, 0.08465814590454102, 0.028923429548740387, 0.019936123862862587, -0.049024976789951324, -0.04373384639620781, -0.016470300033688545, -0.01350692380219698, -0.021359700709581375, 0.05350537225604057, 0.024096820503473282, 0.04569842293858528, 0.02608116902410984, -0.025811996310949326, -0.012257822789251804, -0.007338310591876507, 0.0021479895804077387, 0.013484269380569458, 0.01873895525932312, -0.01974843628704548, 0.0365697406232357, 0.035813216120004654, 0.03387236222624779, 0.0376005694270134, -0.03474525362253189, 0.040723882615566254, -0.012980431318283081, -0.02094733528792858, 0.007477152161300182, -0.007113065104931593, -0.06791452318429947, 0.03944247588515282, 0.0025053643621504307, -0.015224142000079155, 0.01823090948164463, -0.004918529186397791, -0.03685610741376877, -0.024613618850708008, -0.04562317207455635, -0.0031969407573342323, 0.04033763334155083, 0.016930924728512764, 0.01622770167887211, 0.01436159759759903, 0.04203182831406593, 0.04649893194437027, -0.005586857907474041, 0.023736679926514626, 2.219943122046968e-34, 0.013162895105779171, 0.011057939380407333, -0.020379696041345596, -0.002785281278192997, -0.053288184106349945, 0.023180337622761726, 0.02595362439751625, 0.019563930109143257, -0.03266994655132294, -0.04920763522386551, 0.028183504939079285]

['Hugo Van hamme']

1301.3389v2

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated by the low-rank product of two matrices with non-negative entries. In this paper, the approximation quality is measured by the Kullback-Leibler divergence between the data and its low-rank reconstruction. The existence of the simple multiplicative update (MU) algorithm for computing the matrix factors has contributed to the success of NMF. Despite the availability of algorithms showing faster convergence, MU remains popular due to its simplicity. In this paper, a diagonalized Newton algorithm (DNA) is proposed showing faster convergence while the implementation remains simple and suitable for high-rank problems. The DNA algorithm is applied to various publicly available data sets, showing a substantial speed-up on modern hardware.

The Diagonalized Newton Algorithm for Nonnegative Matrix Factorization

http://arxiv.org/pdf/1301.3389v2

Title Diagonalized Newton Algorithm Nonnegative Matrix Factorization Summary Nonnegative matrix factorization NMF become popular machine learning approach many problem text mining speech image processing bioinformatics seismic data analysis name NMF matrix nonnegative data approximated lowrank product two matrix nonnegative entry paper approximation quality measured KullbackLeibler divergence data lowrank reconstruction existence simple multiplicative update MU algorithm computing matrix factor contributed success NMF Despite availability algorithm showing faster convergence MU remains popular due simplicity paper diagonalized Newton algorithm DNA proposed showing faster convergence implementation remains simple suitable highrank problem DNA algorithm applied various publicly available data set showing substantial speedup modern hardware Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04855253919959068, 0.021101033315062523, -0.013566582463681698, 0.03508944436907768, -0.01605318859219551, -0.020591752603650093, -0.005609322339296341, 0.019227951765060425, -0.06961600482463837, -0.0046234456822276115, -0.0023273027036339045, -0.012901190668344498, 0.020082810893654823, 0.015001890249550343, -0.00016312635852955282, 0.01812996342778206, -0.013309864327311516, -0.017533056437969208, -0.0699792429804802, -0.010327964089810848, -0.02170477621257305, -0.028513053432106972, -0.02352902851998806, -0.018024496734142303, -0.011999943293631077, -0.0221602451056242, -0.037957340478897095, -0.0027669642586261034, 0.01932384818792343, -0.02898504212498665, -0.05480184406042099, 0.01718108355998993, -0.0034450197126716375, 0.034697771072387695, 2.278839701830293e-06, -0.007971860468387604, 0.032896097749471664, -0.011997025460004807, 0.0654517412185669, 0.055540841072797775, 0.030390700325369835, 0.014938905835151672, -0.011972006410360336, -0.017100853845477104, -0.04723215848207474, -0.03372245281934738, 0.022662490606307983, 0.03131136670708656, 0.02460193820297718, 0.026058398187160492, 0.004737326875329018, -0.023794418200850487, -0.005863376893103123, 0.011993853375315666, -0.0027713030576705933, -0.017838921397924423, 0.02635415643453598, 0.0005926522426307201, 0.033435121178627014, 0.021044092252850533, -0.023811757564544678, 0.03207648545503616, -0.02307908982038498, -0.028998199850320816, 0.039005573838949203, 0.05051058903336525, 0.018154364079236984, 0.011886322870850563, -0.02025276981294155, 0.09324081987142563, 0.03331948444247246, -0.013331783935427666, 0.002419290831312537, 0.023014409467577934, -0.03417200595140457, 0.02631303481757641, -0.02052285149693489, -0.007818865589797497, -0.03673854470252991, 0.016689391806721687, -0.06937630474567413, -0.02752310410141945, 0.020801356062293053, 0.003806759137660265, -0.0025795313995331526, 0.1304757446050644, 0.021892564371228218, -0.02837306261062622, 0.01656058058142662, -0.047349005937576294, -0.0003139719774480909, 0.006215931382030249, 0.05467413365840912, -0.014327717944979668, -0.03755854815244675, -0.009064629673957825, -0.0018834022339433432, -0.03917064890265465, 0.006740505341440439, -0.03244656324386597, -0.009854670614004135, -0.011385715566575527, 0.04664338007569313, 0.04000992327928543, -0.018012473359704018, -0.04216761514544487, -0.06251906603574753, -0.022552035748958588, -0.026982992887496948, 0.010691322386264801, -0.06682823598384857, -0.003816784592345357, 0.05019479617476463, 0.06417956948280334, 0.008640901185572147, -0.010080404579639435, -0.03338227793574333, -0.01196919847279787, -0.02955574169754982, -0.05902424454689026, -0.020285040140151978, 0.062057945877313614, 0.06148957833647728, -0.02811037376523018, -0.03264616057276726, 0.050653427839279175, -0.022697096690535545, 0.031187379732728004, -0.046034153550863266, 0.02946520410478115, 0.00691214669495821, -0.010912894271314144, 0.028072798624634743, 0.038006652146577835, 0.007464509457349777, 0.025268128141760826, 0.00538407638669014, 0.0037721043918281794, -0.01535690575838089, 0.007864605635404587, -0.007306617219001055, -0.04230523109436035, -0.04612954333424568, -0.0461345799267292, -0.0014733858406543732, -0.005537527613341808, -0.004234932828694582, 0.04750954359769821, 0.027614925056695938, 0.0008383027161471546, -0.005472419783473015, 0.08765456080436707, -0.01591051183640957, -0.011166508309543133, 0.08400846272706985, 0.011776147410273552, 0.017125794664025307, 0.011189318262040615, -0.0159529447555542, -0.028955327346920967, 0.011694243177771568, -0.007914658635854721, -0.02734924480319023, -0.010873631574213505, -0.02637268230319023, -0.014557527378201485, -0.025540919974446297, -0.01586783677339554, -0.05454257130622864, -0.006666017230600119, -0.0060308631509542465, 0.02408754825592041, 0.01411597803235054, -0.006316182669252157, 0.009324928745627403, 0.06991797685623169, -0.014917735941708088, 0.08027993142604828, -0.006042057182639837, 0.028212394565343857, -0.021484751254320145, -0.05911192297935486, 0.03907327353954315, 0.04151083156466484, -0.06962529569864273, -0.04757342115044594, -0.005100115668028593, -0.011391148902475834, -0.05800614133477211, -0.004868440330028534, 0.025994526222348213, -0.05774691328406334, -0.013387606479227543, -0.03072306513786316, 0.054698869585990906, -0.04883546009659767, -0.042375873774290085, -0.04314058646559715, 0.016953976824879646, -0.06769625097513199, -0.03917180374264717, 0.013559230603277683, 0.04266824945807457, -0.04743572697043419, -0.000618652964476496, -0.07928375899791718, -0.021990351378917694, -0.02612168714404106, 0.014448818750679493, -0.050157058984041214, -0.08113876730203629, 0.02262594923377037, 0.002997792325913906, -0.03365553915500641, 0.005094946827739477, 0.06728856265544891, 0.005227254703640938, -0.015901263803243637, -0.03737260401248932, 0.058243073523044586, 0.004220592323690653, 0.023240119218826294, 0.010309810750186443, -0.0150592140853405, 0.006528319325298071, 0.0179002583026886, 0.09470510482788086, 0.029605098068714142, 0.04790589585900307, 0.06862452626228333, 0.04759654402732849, -0.04261975735425949, 0.07711557298898697, -0.05139504373073578, -0.05952497944235802, -0.03221530839800835, -0.0003096184227615595, -0.03639186918735504, 0.03864980489015579, -0.08556710183620453, 0.05015554651618004, 0.10850450396537781, -0.00087218132102862, -0.052994534373283386, 0.07255149632692337, -0.01435847394168377, -0.027681374922394753, -0.06123941019177437, 0.018955906853079796, -0.021434228867292404, -0.02043112926185131, 0.02328924648463726, 0.019627230241894722, -0.0293887946754694, 0.058018602430820465, 0.0042396425269544125, -0.024581391364336014, 0.027886496856808662, -0.014526593498885632, -0.024779774248600006, 0.010007830336689949, -0.05628092959523201, -0.0017624878091737628, 0.0017291131662204862, -0.0169405285269022, 0.04483649134635925, 0.02213260903954506, -0.039004135876894, 0.01411337312310934, -0.007693128194659948, -0.001772747258655727, 0.04475950822234154, -0.02030993066728115, 0.030762042850255966, 0.0022924623917788267, -0.0021660448983311653, 0.06751474738121033, -0.0271831676363945, -0.062181368470191956, 0.030285878106951714, -0.03224315494298935, 0.009069366380572319, 0.005911461543291807, -0.033733073621988297, -0.01730032078921795, 0.03280775994062424, -0.019480429589748383, -0.03312711417675018, -0.056382469832897186, 0.05156344547867775, -0.04776960611343384, -0.015995793044567108, -0.021100755780935287, 0.0032184135634452105, 0.004044943954795599, -0.02137024886906147, -0.005879982840269804, 0.010268894955515862, 0.01584729366004467, -0.021954329684376717, 0.0001542871759738773, 0.10170869529247284, 0.045349083840847015, 0.007848162204027176, 7.482736236852361e-06, 0.0415518544614315, 0.04971054568886757, -0.004739259369671345, 0.04925791174173355, 0.00572133669629693, -0.011326574720442295, -0.02145799808204174, 0.02774987369775772, -0.03169193118810654, -0.03612971305847168, -0.05117412656545639, -0.050389450043439865, 0.009710165672004223, -0.042181938886642456, -0.020588135346770287, 0.02941911295056343, -0.02066848799586296, 0.040853239595890045, -0.014714406803250313, -0.026167642325162888, 0.0008884170092642307, -0.06612536311149597, 0.006560699548572302, -0.0448836125433445, -0.005509106442332268, 0.015299559570848942, -0.06272435188293457, -0.041610900312662125, 0.08334574103355408, -0.011105585843324661, 0.030948244035243988, -0.04563398286700249, 0.005225731059908867, 0.043974049389362335, -0.008976532146334648, 0.01715649478137493, -0.011300520040094852, 0.002127572428435087, -0.031857773661613464, 0.05065329745411873, -0.005290460307151079, -0.011836856603622437, -0.026280835270881653, 0.001922964002005756, 0.04510540887713432, 0.031570035964250565, 0.00456493254750967, -0.03192254900932312, -0.009682542644441128, 0.008743379265069962, 0.06705670803785324, -0.0023945195134729147, 0.014219681732356548, -0.02185729332268238, 0.0036292097065597773, 0.07588096708059311, -0.003748436225578189, 0.033173538744449615, -0.003902239492163062, -0.022702494636178017, -0.006835849490016699, -0.01542906928807497, 0.01243130024522543, -0.028204454109072685, 0.028418269008398056, -0.016114281490445137, 0.06122194230556488, 0.015479129739105701, 0.025587741285562515, 0.05236184597015381, -0.08821654319763184, 0.008354654535651207, -0.02622431516647339, 0.001350358477793634, 0.046330418437719345, -0.03323177993297577, -0.041394270956516266, -0.006994019262492657, 0.009640165604650974, 0.03651070594787598, 0.025862528011202812, -0.06168260797858238, -0.0008528431062586606, -0.08118028193712234, 0.03266429156064987, 0.004439890384674072, -0.013620460405945778, -0.04791587218642235, -0.09050115197896957, -0.021417194977402687, -0.037543896585702896, -0.04618799686431885, 0.04594973474740982, 0.0069984993897378445, 0.019508611410856247, 0.0015994565328583121, -0.0234870295971632, -0.01797664351761341, -0.041343238204717636, -0.07062244415283203, -0.001216716947965324, -0.06178627535700798, 0.03397761285305023, -0.04002149775624275, -0.03157762438058853, 0.015270651318132877, 0.015207841992378235, -0.0013523788657039404, -0.07032670825719833, 0.029845908284187317, 0.038631267845630646, -0.0009438128327019513, -0.06860175728797913, 0.10343436896800995, -0.05171365290880203, 0.05070304498076439, 0.012146513909101486, 0.07425980269908905, 0.016133176162838936, 0.02900618128478527, -0.014980552718043327, 0.0092934500426054, 0.014724480919539928, 0.03642760589718819, -0.03628607094287872, -0.021169353276491165, -0.023213451728224754, 0.04880601540207863, 0.06017632037401199, 0.05529196187853813, -0.038362279534339905, -0.04674622416496277, 0.02258704975247383, 0.0007424037903547287, -0.05329187586903572, 0.020446613430976868, -0.008107509464025497, 0.07554779946804047, 0.002955981530249119, 0.0008782105869613588, 0.04303135350346565, 0.0013419508468359709, -0.02381417155265808, -0.05226301774382591, 0.040372516959905624, 0.024602066725492477, -0.030455658212304115, 0.053942807018756866, 0.04992350563406944, 0.02066815085709095, 0.01130759995430708, -0.04236685857176781, -0.0442378930747509, 0.005145920906215906, -0.09868825227022171, 0.030134977772831917, 0.0034493685234338045, -0.033360421657562256, -0.039141058921813965, -0.006732642184942961, -0.016465533524751663, 0.050217725336551666, -0.011640021577477455, 0.0498293973505497, -0.009744730778038502, -0.05847997963428497, 0.006136197131127119, 0.026544082909822464, 0.00848868116736412, 0.019985416904091835, 0.0021598415914922953, 0.01721893809735775, -0.011371828615665436, 0.009204866364598274, 0.013607373461127281, 0.03767866641283035, 0.07921607047319412, 0.03919285535812378, -0.020544297993183136, -0.015388165600597858, 0.03135289251804352, -0.021484678611159325, 0.027809718623757362, -0.011852467432618141, 0.021848665550351143, 0.05786275863647461, 0.0026252446696162224, -0.046848464757204056, -0.015198481269180775, 0.021669019013643265, 0.013341526500880718, 0.04392746835947037, 0.050492651760578156, 0.027756555005908012, 0.018237333744764328, -0.044420626014471054, 0.020879799500107765, 0.00525553897023201, -0.007619880605489016, 0.04950626567006111, 0.03612413629889488, -0.02451392263174057, 0.030743736773729324, -0.05971278250217438, 0.02854338474571705, -0.04258193075656891, -0.01763429120182991, -0.03668218106031418, -0.005412140395492315, 0.0053629702888429165, 0.02369348332285881, 0.04301188886165619, 0.008784914389252663, 0.0510304756462574, 0.025215590372681618, 0.00980908889323473, -0.05619144067168236, 0.04307493939995766, -0.02095578797161579, 0.051980629563331604, 0.026166504248976707, 0.012885766103863716, -0.03454071283340454, 0.05013139918446541, 0.022591544315218925, -0.0023713218979537487, -0.03950650990009308, -0.01700677163898945, -0.030778640881180763, -0.031220177188515663, 0.05151016265153885, 0.015498383902013302, 0.05640978366136551, -0.03261953219771385, -0.0059632486663758755, -0.01498956885188818, 0.00900222733616829, 0.01645050197839737, -0.050949618220329285, 0.005861115641891956, -0.02385248988866806, -0.015188283286988735, -0.01672576740384102, -0.03024192526936531, 0.0010719202691689134, -0.02634880505502224, 0.03601887822151184, -0.03182549774646759, -0.02248818799853325, -0.05927278846502304, -5.6792738556711994e-33, 0.0014030543388798833, -0.015367654152214527, -0.05421535298228264, 0.06025514751672745, -0.016074268147349358, 0.04599878564476967, 0.035130977630615234, 0.03721494972705841, 0.041248586028814316, -0.012128440663218498, -0.004237650893628597, 0.009747549891471863, -0.0005991002544760704, 0.008965443819761276, 0.018460875377058983, 0.043163102120161057, 0.014416503719985485, -0.0012365529546514153, 0.043827593326568604, -0.008086562156677246, 0.03899022564291954, 0.05009015277028084, 0.016463834792375565, -0.030049264430999756, -0.08421242982149124, -0.01651664450764656, 0.0005399028304964304, -0.000332544615957886, 0.008348315954208374, -0.02426530420780182, 0.003113152924925089, 0.01751396246254444, 0.002976137911900878, -0.050879962742328644, 0.016912858933210373, -0.04098576679825783, -0.028653059154748917, 0.005581240635365248, -0.006527159828692675, 0.007292613852769136, 0.008168754167854786, 0.03408552333712578, 0.06533772498369217, 0.02239707112312317, -0.07612112164497375, 0.0068597570061683655, 0.06278856098651886, 0.005193115212023258, -0.04691218212246895, -0.026932576671242714, -0.016054952517151833, 0.016552960500121117, -0.023405415937304497, 0.01795557700097561, 0.05057878792285919, 0.029490306973457336, -0.07407309114933014, -0.017649710178375244, -0.04343900457024574, 0.04480839520692825, 0.03908029943704605, 0.047757990658283234, 0.032247912138700485, -0.0013086217222735286, 0.022861195728182793, 0.0310685895383358, 0.09105580300092697, -0.016095779836177826, -0.011563833802938461, -0.07351551204919815, -0.017407353967428207, 0.04004821926355362, 0.03171417862176895, 0.06264643371105194, 0.07892660051584244, -0.03288307785987854, -0.05791889503598213, 0.05589451640844345, -0.02373996190726757, -0.011746060103178024, 0.0031477671582251787, 0.003548698266968131, -0.0027923928573727608, 0.008504286408424377, 0.018182672560214996, -0.010000960901379585, -0.022539231926202774, -0.002089094603434205, -0.012199418619275093, -0.031070411205291748, -0.05945524200797081, 0.02975541725754738, -0.023933548480272293, -0.05353199318051338, 0.00865753274410963, 0.01241667103022337, -0.0021227088291198015, 0.0420987494289875, -6.569518882315606e-05, -0.06445839256048203, -0.07490265369415283, -0.0017821037909016013, -0.008064720779657364, -0.023495107889175415, 0.010234401561319828, -0.056443952023983, -0.008900532498955727, 0.028632165864109993, -0.05565723404288292, -0.04940970614552498, 0.03415951132774353, -0.035515133291482925, 0.025137977674603462, 0.03578662499785423, 0.02505885437130928, -0.06893868744373322, 0.01118857879191637, 0.04883602261543274, 0.040333036333322525, 0.042740676552057266, -0.006223901640623808, -0.01607838086783886, -0.005933860316872597, -0.006195797119289637, -0.03287291154265404, -0.020673954859375954, -0.010286695323884487, 0.010872571729123592, -0.008934566751122475, -0.06573951989412308, -0.024188809096813202, -0.04070085287094116, 2.834549661656638e-07, -0.03542273864150047, 0.06576674431562424, -0.027000751346349716, -0.08308623731136322, 0.04357105866074562, 0.0068571134470403194, -0.049311742186546326, 0.010605347342789173, -0.0338866263628006, -0.016777697950601578, 0.06102919951081276, -0.022196847945451736, 0.008528420701622963, 0.046002935618162155, -0.04440302401781082, 0.031977683305740356, -0.03939269483089447, 0.004188330844044685, -0.03240741416811943, -0.029231077060103416, 0.035818759351968765, 0.027659738436341286, 0.021178293973207474, -0.02954036556184292, 0.05187297239899635, -0.051311738789081573, 0.05658547580242157, -0.0042547862976789474, 0.027678681537508965, -0.04471457749605179, 0.05685436353087425, -0.06440582126379013, 0.0022130426950752735, -0.05310888588428497, 0.018261892721056938, 0.012209094129502773, 0.029814574867486954, 0.054948851466178894, -0.03670378774404526, 0.02762429043650627, 0.02244567684829235, 0.05224495753645897, 0.02882419340312481, 0.0017762253992259502, 0.058539196848869324, 0.06789835542440414, -0.026461556553840637, -0.06064892187714577, -0.021060306578874588, 0.037110812962055206, 0.049573298543691635, -0.01198019552975893, 0.04233618825674057, -0.003259462770074606, -0.015776248648762703, -0.021396685391664505, 0.016897886991500854, 0.026199163869023323, 0.04071584343910217, 0.04332917556166649, -0.04495906084775925, -0.014859134331345558, 1.0487760846444871e-05, 0.022427042946219444, 0.06889063864946365, 0.0074567897245287895, 0.009725840762257576, 2.6403763549515694e-34, -0.008635707199573517, 0.013397918082773685, 0.022850606590509415, 0.020641284063458443, -0.04555083066225052, -0.023103605955839157, -0.050301361829042435, -0.025713063776493073, -0.0416150838136673, -0.0429283082485199, -0.0023478923831135035]

['Vamsi K. Potluru', 'Sergey M. Plis', 'Jonathan Le Roux', 'Barak A. Pearlmutter', 'Vince D. Calhoun', 'Thomas P. Hayes']

1301.3527v2

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow and other formulations for sparse NMF have been proposed such as those based on L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets.

Block Coordinate Descent for Sparse NMF

http://arxiv.org/pdf/1301.3527v2

Title Block Coordinate Descent Sparse NMF Summary Nonnegative matrix factorization NMF become ubiquitous tool data analysis important variant sparse NMF problem arises explicitly require learnt feature sparse natural measure sparsity L0 norm however optimization NPhard Mixed norm L1L2 measure shown model sparsity robustly based intuitive attribute measure need satisfy contrast computationally cheaper alternative plain L1 norm However present algorithm designed optimizing mixed norm L1L2 slow formulation sparse NMF proposed based L1 L0 norm proposed algorithm allows u solve mixed norm sparsity constraint sacrificing computation time present experimental evidence realworld datasets show new algorithm performs order magnitude faster compared current stateoftheart solver optimizing mixed norm suitable largescale datasets Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.06981907784938812, 0.05822659283876419, -0.0006703216349706054, 0.017602402716875076, 0.038129787892103195, -0.017369944602251053, 0.022350875660777092, 0.05252306908369064, -0.014975612051784992, 0.002320698695257306, -9.518376464257017e-05, -0.03089166060090065, 0.0090234549716115, 0.020047631114721298, 0.0004226025484967977, -0.011625370942056179, 0.0032221537549048662, -0.00944411102682352, -0.057486072182655334, 0.0058532520197331905, 0.016396982595324516, -0.04051153361797333, 0.011996526271104813, -0.0011608062777668238, -0.07369273900985718, -0.00028062902856618166, -0.03698120638728142, -0.009618036448955536, 0.02926011197268963, -0.028906118124723434, 0.015530552715063095, 0.05245726928114891, 0.015477851964533329, 0.007618420757353306, 2.3265854451892665e-06, -0.013399701565504074, 0.00508884945884347, -0.012336833402514458, 0.07592146098613739, 0.02727673389017582, 0.035783447325229645, -0.005417536478489637, -0.004234804771840572, -0.03863200545310974, -0.003323814831674099, -0.016130544245243073, 0.011152234859764576, 0.10111603885889053, 0.04367874935269356, 0.015128180384635925, -0.009013582020998001, 0.008521314710378647, -0.025961782783269882, -0.003716706531122327, -0.0071710036136209965, -0.046531349420547485, 0.023621926084160805, -0.009028639644384384, 0.0026370470877736807, 0.01581707037985325, -0.027088774368166924, 0.030371997505426407, -0.0035934699699282646, 0.003861241042613983, 0.05776779726147652, 0.027914416044950485, -0.004114246461540461, 0.04387178644537926, 0.011594661511480808, 0.06064571067690849, -0.0417913943529129, -0.01143365167081356, 0.022457417100667953, 0.023415690287947655, -0.047609880566596985, 0.017413122579455376, -0.027091966941952705, -0.021677166223526, -0.014485805295407772, 0.018798720091581345, -0.06160244718194008, 0.012793594039976597, 0.01743183098733425, 0.016730889678001404, -0.02265874296426773, 0.06311419606208801, 0.021458903327584267, -0.03277016058564186, -0.03867228701710701, -0.040275219827890396, -0.04852985963225365, 0.027020758017897606, 0.043857309967279434, -0.024180086329579353, -0.06354998052120209, -0.016048917546868324, 0.002434602240100503, -0.02953367680311203, 0.03901100903749466, -0.005108742043375969, 0.007994698360562325, 0.005331406835466623, 0.013379320502281189, 0.026723327115178108, -0.0018455046229064465, -0.03246631473302841, -0.036867812275886536, -0.022414574399590492, -0.0033003916032612324, 0.012326077558100224, -0.04975980520248413, -0.010806873440742493, 0.04378345236182213, 0.07177772372961044, -0.017345817759633064, 0.012773163616657257, -0.0015607585664838552, -0.007296693045645952, -0.04955798387527466, -0.04047510400414467, 0.0009152944548986852, 0.05669107288122177, 0.02540716528892517, -0.01826358772814274, -0.012158164754509926, 0.022642362862825394, -0.01130194403231144, 0.03677038848400116, -0.048579685389995575, 0.06343212723731995, 0.005783364176750183, -0.003977507818490267, 0.023485517129302025, 0.00983397476375103, 0.011517399922013283, 0.03538913652300835, -0.01810995116829872, 0.021964868530631065, -0.04307200759649277, -0.030728492885828018, 0.02251344732940197, -0.026592083275318146, -0.05643972009420395, -0.04345440864562988, -0.008917862549424171, -0.01874368265271187, 0.02379477210342884, -0.014323213137686253, 0.016149932518601418, 0.004765141289681196, -0.04775479435920715, 0.0638849288225174, -0.0034016184508800507, -0.024004772305488586, 0.03656516596674919, 0.04183611273765564, 0.003606493351981044, 0.014036227948963642, -0.03482413664460182, 0.008353665471076965, -0.004349817521870136, -0.002108536660671234, -0.04060162231326103, -0.039339132606983185, -0.002822068752720952, 0.036764148622751236, -0.03750891238451004, -0.013643745332956314, -0.003744733752682805, -0.042076848447322845, 0.02676384337246418, 0.034609995782375336, 0.030377432703971863, -0.0324397049844265, 0.031552720814943314, 0.06734546273946762, 0.017106808722019196, 0.06707465648651123, -0.030065977945923805, 0.017136596143245697, -0.04554356262087822, -0.020827919244766235, 0.03683896362781525, 0.05033115670084953, -0.10727087408304214, -0.06185237318277359, -0.010829905048012733, 0.03921651095151901, -0.06251339614391327, -0.008151965215802193, 0.010770226828753948, -0.023968208581209183, 0.009501487948000431, -0.009993051178753376, 0.03417870029807091, -0.07444059103727341, -0.006463826633989811, -0.05220525711774826, 0.0567522756755352, -0.05969155207276344, -0.0492679588496685, 0.021065378561615944, 0.03502810001373291, -0.0745357945561409, 0.0030389269813895226, -0.07937055081129074, -0.03815314546227455, -0.038958366960287094, -0.008307666517794132, -0.04487305507063866, -0.08515960723161697, 0.010739494115114212, 0.0012114538112655282, -0.02990609221160412, 0.0026168720796704292, 0.050063278526067734, 0.03521523252129555, -0.01929514668881893, -0.05713645741343498, 0.045546308159828186, 0.01441830676048994, 0.0017972741043195128, 0.001217672717757523, 0.00017371214926242828, 0.022565219551324844, 0.030210617929697037, 0.07661181688308716, 0.04706421494483948, 0.012736255303025246, 0.06388425827026367, 0.04608525335788727, -0.05729920417070389, 0.07790015637874603, -0.039926428347826004, -0.03010217659175396, -0.037589844316244125, -0.02351025678217411, -0.021084381267428398, 0.05970098078250885, -0.03763698786497116, 0.03852813318371773, 0.10070254653692245, 0.024730321019887924, -0.06335579603910446, 0.017677128314971924, 0.0017966917948797345, -0.06203615292906761, -0.043702319264411926, -0.00600117351859808, -0.04168110340833664, -0.017468543723225594, 0.028896085917949677, 0.03917912766337395, -0.02945222705602646, 0.03310304135084152, 0.018747946247458458, -0.053169135004282, 0.02077743411064148, -4.329335206421092e-05, -0.015369310975074768, 0.0013460719492286444, -0.052837032824754715, 0.022231223061680794, 0.013062051497399807, -0.0017085265135392547, 0.0412423275411129, 0.045522574335336685, -0.012137100100517273, 0.013712726533412933, -0.025289354845881462, -0.04486967623233795, 0.027690516784787178, 0.017654575407505035, 0.06194630265235901, -0.012639479711651802, -0.059666525572538376, 0.05051960051059723, 0.003114143153652549, -0.04088832437992096, 0.01861557923257351, 0.022890368476510048, -0.01406077854335308, 0.00014566516620106995, -0.036113932728767395, -0.0015140501782298088, -0.0172409825026989, -0.033789727836847305, -0.02803482860326767, -0.0250703077763319, 0.12301771342754364, -0.026282070204615593, -0.0033139551524072886, -0.025019288063049316, -0.007609383203089237, -0.03080866113305092, -0.056558381766080856, -0.021168356761336327, 0.03307412937283516, -0.015360462479293346, 0.015187936834990978, 0.03855719417333603, 0.07123103737831116, 0.0032223176676779985, 0.004337730351835489, -0.01804579421877861, 0.06889205425977707, 0.04833226650953293, 0.012926816940307617, 0.04639928787946701, 0.017549291253089905, 0.0032838736660778522, -0.046633169054985046, 0.01273279171437025, 0.02488158829510212, -0.031996216624975204, -0.05706928297877312, -0.08411643654108047, 0.05272727087140083, -0.022919094190001488, 0.02449950762093067, 0.004527597688138485, -0.04179549217224121, 0.04765445739030838, 0.01728151924908161, -0.026190271601080894, 0.00706564961001277, -0.07993382960557938, -0.011321761645376682, -0.06985151022672653, -0.019845200702548027, 0.01627449318766594, -0.07385701686143875, -0.013218001462519169, 0.030945170670747757, -0.008280787616968155, 0.010036198422312737, -0.013330472633242607, 0.03848044201731682, 0.06219471991062164, -0.022674353793263435, 0.003521866397932172, -0.035312801599502563, -0.022006534039974213, -0.04901847988367081, 0.06671701371669769, 0.02494087815284729, 0.03564302250742912, -0.004133853130042553, 0.018485672771930695, 0.03253604471683502, -0.005771447438746691, -0.0016476177843287587, 0.001517104567028582, -0.00922100804746151, 0.0051004234701395035, 0.07359004020690918, 0.00785182137042284, 0.021953849121928215, -0.009064464829862118, -0.0030636407900601625, 0.028681764379143715, 0.01962612196803093, -0.010097882710397243, -0.0688248872756958, -0.01998160034418106, 0.04183652251958847, 0.000631821108981967, 0.049084749072790146, -0.003918614238500595, -0.007803548593074083, 0.03807494789361954, 0.007784837856888771, 0.028563888743519783, 0.030274908989667892, 0.047419264912605286, -0.07753962278366089, 0.018426064401865005, -0.04127291217446327, 0.06827281415462494, 0.0461554229259491, -0.01705935038626194, -0.02264382876455784, 0.0007343480247072875, 0.005755438003689051, 0.047328636050224304, 0.02897254377603531, -0.07112050801515579, 0.04974311962723732, -0.04540581628680229, 0.020153310149908066, -0.0012741379905492067, 0.02156289480626583, 0.00023853042512200773, -0.0733860582113266, 0.016187936067581177, -0.022374644875526428, -0.0667026937007904, -0.010511131025850773, 0.003713067388162017, -0.01472141221165657, 0.004805316682904959, -0.008043463341891766, -0.02763289026916027, 0.006296847481280565, -0.0685633197426796, 0.05376620963215828, -0.06488808989524841, -0.020552512258291245, -0.042367950081825256, -0.04229980707168579, 0.0064720269292593, 0.024650676175951958, -0.03217681869864464, -0.08315242826938629, -0.02465842477977276, 0.048595767468214035, 0.011298878118395805, -0.07874206453561783, 0.09383995831012726, -0.014081995002925396, 0.030845003202557564, -0.014508713968098164, 0.12307564914226532, 0.008147305808961391, 0.04025617241859436, -0.012261904776096344, -0.023114444687962532, 0.039100345224142075, 0.02331627532839775, -0.038528986275196075, -0.00787363015115261, 0.0023561681155115366, 0.014252531342208385, 0.0027092627715319395, 0.038893405348062515, -0.033780500292778015, 0.010085188783705235, -0.004072262905538082, 0.019256776198744774, -0.04130863398313522, 0.019750798121094704, 0.04707306623458862, 0.056455276906490326, 2.4086732082650997e-05, 0.02125753089785576, -0.003693308914080262, -0.02632242441177368, -0.009118777699768543, -0.0016063045477494597, 0.03268688917160034, 0.027352280914783478, -0.020716678351163864, 0.040787212550640106, -0.0068646143190562725, -0.028531663119792938, 0.021152248606085777, -0.04274805635213852, -0.024168696254491806, -0.002138417912647128, -0.07746628671884537, 0.056180328130722046, -0.00999365746974945, -0.01609354466199875, -0.022385748103260994, 0.001668242271989584, 0.015589682385325432, 0.03612226992845535, -0.030996937304735184, 0.04428530111908913, 0.010587822645902634, -0.04906369745731354, 0.00765256118029356, 0.02991350367665291, 0.013014263473451138, 0.019969696179032326, -0.015538685955107212, 0.03369935601949692, -0.009279249235987663, -0.01255559828132391, 0.00152196257840842, 0.03847957402467728, 0.0290263369679451, 0.034150488674640656, 0.025229627266526222, -0.03931582719087601, 0.016063598915934563, -0.017311468720436096, 0.00441364012658596, -0.009715917520225048, -0.012087401002645493, 0.02498513273894787, 0.016347380355000496, -0.03569367155432701, 0.03462749719619751, 0.011051725596189499, 0.03555264323949814, -0.0038805927615612745, 0.07257559895515442, -0.007665892131626606, -0.041976362466812134, -0.00514542032033205, 0.040776923298835754, 0.004947513807564974, -0.026020720601081848, 0.06301986426115036, 0.01702747866511345, 0.005081123672425747, -0.01729518733918667, -0.04224030300974846, 0.024233782663941383, -0.10737544298171997, -0.011632535606622696, 0.012884128838777542, 0.017938844859600067, 0.011218772269785404, -0.03786500543355942, 0.04072873294353485, -0.042037468403577805, 0.04241523891687393, 0.014592379331588745, -0.005843539256602526, -0.0647510290145874, 0.0164750088006258, -0.022947467863559723, 0.05500354990363121, 0.05497250333428383, 0.007628176361322403, 0.0015735517954453826, 0.05338922515511513, 0.06568008661270142, -0.017451763153076172, -0.014332624152302742, 0.007930965162813663, -0.031677644699811935, -0.041722606867551804, 0.08577647805213928, 0.08223120123147964, 0.07013924419879913, -0.04574288800358772, 0.022568989545106888, -0.013177995570003986, -0.010562104173004627, 0.02092568948864937, -0.06922725588083267, 0.006679235026240349, -0.009832480922341347, -0.027305228635668755, -0.038515713065862656, -0.019687073305249214, 0.02655145153403282, -0.033359505236148834, -0.03310196101665497, -0.02265075221657753, -0.031010707840323448, -0.02640298753976822, -6.156418767613474e-33, 0.023567579686641693, -0.02889329008758068, -0.07191214710474014, 0.006267230492085218, -0.020097743719816208, 0.023468123748898506, 0.021466530859470367, 0.016593588516116142, 0.04440290108323097, -0.01254978310316801, -0.020524386316537857, -0.039701126515865326, -0.013073897920548916, 0.006338298786431551, 0.024054957553744316, 0.04090799018740654, 0.037804048508405685, 0.02039368264377117, 0.04227422550320625, -0.002481722505763173, 0.051900871098041534, 0.035539038479328156, -0.03531254827976227, -0.07339295744895935, -0.08550607413053513, 0.003698886139318347, 0.015096986666321754, -0.009577272459864616, 0.03542434424161911, -0.011357016861438751, -0.0025935673620551825, 0.025491705164313316, 0.031770259141922, -0.025575939565896988, -0.025228623300790787, -0.033378273248672485, -0.041283585131168365, 0.026724684983491898, -0.010764257982373238, -0.03606656938791275, -0.016768785193562508, -0.0012385767186060548, -0.003074878826737404, 0.01487474050372839, -0.0007638998795300722, -0.003120010020211339, 0.04017854481935501, -0.009633487090468407, -0.027572715654969215, -0.030666787177324295, -0.020701486617326736, 0.02760458178818226, -0.05421126261353493, 0.0033440219704061747, 0.051567308604717255, -0.0007715554675087333, -0.06388289481401443, -0.027584146708250046, -0.06193481758236885, 0.034216564148664474, -0.002563284244388342, 0.07156296819448471, 0.02632739581167698, 0.029621826484799385, 0.01002541370689869, 0.020828833803534508, 0.016684912145137787, 0.0003233427705708891, -0.0033628474920988083, 0.023487407714128494, -0.0010688784532248974, 0.052571509033441544, 0.02243630960583687, 0.022845711559057236, 0.027446001768112183, -0.03604525700211525, -0.0570361353456974, 0.05451193451881409, -0.04280465096235275, 0.01947399601340294, -0.027977230027318, 0.05011779069900513, 0.008615929633378983, -0.00313685555011034, 0.024482151493430138, 0.004853083752095699, -0.038354430347681046, -0.009773007594048977, -0.0104224169626832, 0.007849609479308128, -0.07137393206357956, 0.028961768373847008, 0.025611620396375656, -0.05409909039735794, 0.033283546566963196, -0.006478192750364542, -0.014284287579357624, 0.03412531316280365, 0.028176337480545044, -0.05954419821500778, -0.045612938702106476, -0.009170583449304104, 0.0021340048406273127, -0.03969646617770195, 0.014392819255590439, 0.0036891261115670204, 0.014899998903274536, 0.015812838450074196, -0.01651272550225258, -0.050615377724170685, 0.00964225921779871, -0.04062603414058685, 0.03833655267953873, 0.04641123116016388, 0.002017408376559615, -0.07627062499523163, 0.014529801905155182, 0.09743744879961014, 0.006399123929440975, 0.030057381838560104, -0.02891286090016365, -0.011354802176356316, -0.0006839627167209983, -0.01556293573230505, -0.033796001225709915, 0.00506946537643671, -0.049317408353090286, -0.019437922164797783, 0.06258600205183029, -0.036033060401678085, 1.605385114089586e-05, -0.0626566931605339, 2.901721813941549e-07, -0.04030246660113335, 0.0535300113260746, -0.0389128252863884, -0.045510146766901016, -0.010195394977927208, 0.016409581527113914, -0.06219719722867012, 0.0019343298627063632, -0.05620043724775314, -0.006176293361932039, 0.04445495083928108, -0.027234971523284912, -0.0017276292201131582, 0.02906494028866291, -0.02216603048145771, 0.0030754460021853447, 0.023081986233592033, -0.004812882747501135, -0.05778319016098976, -0.016791030764579773, 0.03798387944698334, 0.03146810829639435, -0.007097741588950157, -0.04856418818235397, 0.054227426648139954, -0.010376296937465668, 0.030807187780737877, 0.014458627440035343, -0.010549966245889664, -0.046780236065387726, 0.0884723961353302, -0.06649839133024216, 0.0013659970136359334, -0.039034489542245865, 0.005241064354777336, 0.0009840710554271936, 0.015943629667162895, 0.05225576460361481, -0.008883091621100903, -0.021020963788032532, 0.042298804968595505, 0.03829089552164078, 0.018658503890037537, -0.014672795310616493, 0.058969635516405106, 0.0898594856262207, -0.0300351120531559, 0.0016362980240955949, -0.010286429896950722, 0.02821098268032074, 0.02271178737282753, -0.047569144517183304, 0.0400179848074913, -0.01942431926727295, -0.02764654904603958, -0.02622435800731182, 0.012039070017635822, 0.029443275183439255, 0.08365840464830399, 0.043375469744205475, -0.059078458696603775, -0.033291563391685486, 0.011271344497799873, 0.0116909584030509, 0.05975034832954407, 0.0014938440872356296, 0.006326701492071152, 3.1889175795204244e-34, 0.009636352770030499, 0.012402350082993507, 0.032407887279987335, 0.02733812853693962, -0.0547599196434021, -0.04303959757089615, -0.06107534095644951, -0.010348386131227016, -0.008128968067467213, -0.08031261712312698, 0.0034646480344235897]

['Razvan Pascanu', 'Yoshua Bengio']

1301.3584v7

We evaluate natural gradient, an algorithm originally proposed in Amari (1997), for learning deep models. The contributions of this paper are as follows. We show the connection between natural gradient and three other recently proposed methods for training deep models: Hessian-Free (Martens, 2010), Krylov Subspace Descent (Vinyals and Povey, 2012) and TONGA (Le Roux et al., 2008). We describe how one can use unlabeled data to improve the generalization error obtained by natural gradient and empirically evaluate the robustness of the algorithm to the ordering of the training set compared to stochastic gradient descent. Finally we extend natural gradient to incorporate second order information alongside the manifold information and provide a benchmark of the new algorithm using a truncated Newton approach for inverting the metric matrix instead of using a diagonal approximation of it.

Revisiting Natural Gradient for Deep Networks

http://arxiv.org/pdf/1301.3584v7

Title Revisiting Natural Gradient Deep Networks Summary evaluate natural gradient algorithm originally proposed Amari 1997 learning deep model contribution paper follows show connection natural gradient three recently proposed method training deep model HessianFree Martens 2010 Krylov Subspace Descent Vinyals Povey 2012 TONGA Le Roux et al 2008 describe one use unlabeled data improve generalization error obtained natural gradient empirically evaluate robustness algorithm ordering training set compared stochastic gradient descent Finally extend natural gradient incorporate second order information alongside manifold information provide benchmark new algorithm using truncated Newton approach inverting metric matrix instead using diagonal approximation Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0025335242971777916, 0.01783045195043087, -0.0031706197187304497, 0.023112652823328972, 0.02420354261994362, -0.016692128032445908, -0.006562164053320885, -0.019774233922362328, 0.016454093158245087, 0.03116763010621071, -0.048457320779561996, 0.018049459904432297, -0.01140065211802721, -0.009460399858653545, 0.056492313742637634, -0.06016423553228378, -0.02286509983241558, 0.015083224512636662, -0.02535749413073063, -0.030554402619600296, -0.005908636376261711, -0.04035618156194687, -0.0014299642061814666, 0.02063189446926117, -0.06941381841897964, 0.003102205926552415, 0.003787386929616332, 0.03823016956448555, 0.0343816876411438, -0.038092903792858124, 0.06484972685575485, -0.017449162900447845, 0.012881234288215637, 0.042124733328819275, 2.351318016735604e-06, -0.01730157807469368, 0.029940202832221985, -0.009071288630366325, 0.03662240505218506, -0.02539760246872902, 0.011722375638782978, -0.020333262160420418, -0.0045929038897156715, -0.0004290170909371227, -0.06114910915493965, -0.0598229244351387, -0.008837779983878136, 0.04058727249503136, 0.04861068353056908, 0.07495883107185364, 0.0029851810541003942, -0.09197858721017838, -0.014771618880331516, -0.04151283577084541, -0.013901830650866032, -0.054264575242996216, 0.004780835006386042, -0.00982035230845213, -0.07097768783569336, -0.0008731457055546343, 0.006123831029981375, 0.051959943026304245, 0.05189492553472519, 0.001356912194751203, 0.06672272831201553, 0.07627683132886887, 0.03990490734577179, -0.009728314355015755, -0.01126179751008749, 0.10640697181224823, -0.04143545776605606, 0.033144887536764145, 0.019746921956539154, -0.011441539973020554, 0.009982881136238575, -0.04533834010362625, -0.014391111209988594, 0.0014277981827035546, 0.0066135963425040245, 0.006190879736095667, -0.032461605966091156, 0.030227575451135635, 0.03404927998781204, -0.0064177121967077255, 0.020703524351119995, 0.04739988595247269, 0.00444815494120121, 0.043636225163936615, 0.002904359018430114, -0.05750029906630516, -0.0011822192464023829, -0.008061034604907036, 0.020271293818950653, 0.026679005473852158, 0.011061854660511017, -0.033555768430233, 0.008193128742277622, -0.045389797538518906, 0.01084824651479721, -0.04442868009209633, 0.04321920871734619, -0.012698599137365818, -0.001176793361082673, 0.031156564131379128, -0.04942358285188675, 0.021315939724445343, -0.04886936396360397, 0.04608456417918205, -0.00420783506706357, -0.007411433849483728, -0.03074909746646881, -0.014735146425664425, 0.023122593760490417, 0.06974932551383972, -0.018917720764875412, 0.003453583223745227, -0.017459629103541374, -0.01946854591369629, -0.024604270234704018, -0.018633147701621056, 0.026961101219058037, 0.09419375658035278, -0.0004448088293429464, -0.024930467829108238, -0.05735384300351143, -0.005716191604733467, -0.028751494362950325, 0.06012096628546715, -0.011270628310739994, 0.00719172740355134, 0.0027379661332815886, 0.005894148256629705, 0.002267449861392379, 0.03058692254126072, 0.047134824097156525, 0.062224987894296646, 0.022872431203722954, 0.013877445831894875, -0.03452004864811897, 0.022603152319788933, -0.0078341756016016, -0.060218874365091324, 0.015104900114238262, -0.05146043375134468, 0.0003033721586689353, -0.027940841391682625, -0.022200319916009903, -0.07376191765069962, -0.01417007390409708, -0.02323920838534832, -0.03285346180200577, -0.00351940980181098, -0.011246142908930779, -0.012430421076714993, 0.07512585073709488, -0.013267907314002514, 0.015233511105179787, 0.042608100920915604, 0.02049640566110611, 0.025530995801091194, 0.010182708501815796, -0.0021007731556892395, -0.0244570504873991, 0.019374582916498184, 0.0020673624239861965, -0.02554449997842312, -0.01875283569097519, -0.02436215803027153, -0.006717522628605366, 0.07212284207344055, 0.053683504462242126, 0.035239312797784805, -0.00400486309081316, -0.07181902974843979, -0.003842416452243924, 0.0521964356303215, 0.03323797509074211, 0.045246321707963943, 0.000694300455506891, -0.013704388402402401, 0.028314244002103806, -0.03837398812174797, 0.029537426307797432, 0.03800542652606964, -0.004958783276379108, -0.06021800637245178, -0.011504268273711205, -0.03146443888545036, -0.057980623096227646, -0.028444582596421242, 0.04761487990617752, -0.026239488273859024, -0.0064710453152656555, -0.03412150219082832, 0.05141712725162506, -0.030882181599736214, -0.03332516923546791, -0.019799722358584404, -0.021278370171785355, 0.0231360774487257, -0.031870037317276, 0.009883011691272259, 0.014240335673093796, -0.06294683367013931, -0.03810472786426544, -0.07772655785083771, -0.06807000935077667, 0.007210136856883764, -0.021558038890361786, -0.013664687983691692, -0.016625072807073593, -8.158294076565653e-05, 0.05187584459781647, -0.03801461681723595, -0.019430145621299744, 0.005430035758763552, 0.0010967928683385253, 0.030188260599970818, -0.0698140412569046, 0.02465396746993065, 0.0528474785387516, 0.019861631095409393, -0.0268167145550251, 0.02587282657623291, -0.030308591201901436, -0.017972899600863457, 0.08722435683012009, 0.031415779143571854, -0.003030646126717329, -0.0019114711321890354, 0.0399971678853035, -0.019512908533215523, 0.008112506940960884, -0.03755129873752594, -0.012937352992594242, -0.04003812372684479, -0.03202715888619423, -0.02573571354150772, 0.028341328725218773, -0.06040554866194725, 0.02238336019217968, 0.08366695791482925, -0.02731284126639366, -0.06128853186964989, 0.017425255849957466, 0.009555020369589329, -0.005027218721807003, -0.026613853871822357, -0.04591382294893265, 0.004347742535173893, 0.039249487221241, 0.013180608861148357, -0.0164712592959404, -0.01832147315144539, -0.01698368228971958, -0.043463315814733505, 0.03867069631814957, 0.03566176816821098, -0.011341346427798271, -0.01768522523343563, 0.01585681177675724, -0.029862554743885994, 0.01562945358455181, 0.001967773772776127, 0.033495787531137466, 0.028467684984207153, 0.03298104181885719, -0.016307620331645012, 0.02798795886337757, -0.028339963406324387, -0.00428712647408247, 0.01593208499252796, -0.03694530576467514, 0.0001945189287653193, -0.02334287390112877, -0.012439480051398277, 0.10559642314910889, 0.005890129134058952, -0.0840815082192421, 0.06886739283800125, -0.00741987582296133, 0.015104797668755054, -0.023859813809394836, -0.04520098865032196, -0.007897605188190937, 0.03693477809429169, 0.026980459690093994, -0.022391630336642265, -0.0016380184097215533, 0.017476294189691544, -0.016682272776961327, 0.022471455857157707, -0.022087547928094864, -0.07465988397598267, -0.026828693225979805, -0.03273018077015877, 0.001141111832112074, 0.05817320570349693, 0.018828626722097397, -0.03818691521883011, -0.019785825163125992, 0.07267114520072937, -0.021037941798567772, 0.009461562149226665, -0.024951042607426643, 0.019821131601929665, 0.018138792365789413, -0.0014634487451985478, -0.005120523739606142, 0.016698025166988373, 0.014419978484511375, 0.005415203515440226, 0.0028467471711337566, 0.012607407756149769, 0.00461361650377512, -0.013715545646846294, -0.0721408799290657, 0.05849992111325264, -0.016410384327173233, -0.020651763305068016, 0.0318959504365921, -0.0022780366707593203, 0.011238700710237026, 0.0447353757917881, -0.023133449256420135, -0.014386948198080063, -0.027605252340435982, -0.0022880244068801403, -0.006540386937558651, 0.021302927285432816, -0.017470229417085648, -0.01058630459010601, -0.045840028673410416, -0.020808566361665726, -0.009336738847196102, 0.03146524727344513, -0.027446351945400238, -0.02411821484565735, -0.00196877121925354, 0.008894696831703186, -0.002676216186955571, -0.037279367446899414, -0.051020119339227676, -0.014815911650657654, 0.008414329029619694, 0.01933174952864647, -0.01455357763916254, -0.05562101677060127, 0.07598239183425903, -0.011711787432432175, 0.045420195907354355, 0.051547445356845856, -0.022516753524541855, -0.001915672910399735, 0.0009578819153830409, 0.059768564999103546, 0.005702354479581118, 7.515731704188511e-05, 0.015403255820274353, 0.041803885251283646, 0.02739727683365345, 0.019141901284456253, -0.0496705062687397, 0.03272236883640289, -0.08656913787126541, 0.036192651838064194, -0.02600153163075447, 0.027518747374415398, 0.0003148637479171157, 0.02040666900575161, -0.01676213927567005, -0.02768145129084587, 0.004881624132394791, 0.033151764422655106, -0.005160104483366013, -0.05964916944503784, -0.014070638455450535, 0.018316684290766716, -0.01332604419440031, 0.01889333687722683, 0.003236277960240841, 0.0035656713880598545, -0.013271107338368893, -0.009779703803360462, 0.024202626198530197, 0.02038761042058468, -0.030713217332959175, 0.039197731763124466, -0.03139214962720871, 0.01677452027797699, -0.017767276614904404, -0.06533918529748917, -0.017800819128751755, -0.06961090117692947, 0.003980692476034164, -0.030982714146375656, -0.012037688866257668, 0.01437962893396616, 0.01361534558236599, -0.0408540703356266, 0.028838103637099266, -0.08456991612911224, -0.05188418924808502, 0.012165804393589497, -0.07566634565591812, -0.039042260497808456, 0.024701548740267754, 0.034914761781692505, -0.06581278145313263, -0.013104096986353397, 0.03393333777785301, 0.031585536897182465, 0.002964939456433058, -0.02779085375368595, 0.0537259466946125, 0.0426931269466877, -0.038094375282526016, -0.013510648161172867, 0.12329930067062378, -0.05775201693177223, 0.06377650052309036, -0.011319608427584171, 0.04191230982542038, 0.024972056970000267, 0.0240337997674942, -0.04414469748735428, -0.017838317900896072, -0.00302422558888793, 0.0006820680573582649, -0.02304214984178543, -0.03054359182715416, -0.017686352133750916, -0.002723978366702795, 0.040051501244306564, 0.013913905248045921, -0.05569574609398842, 0.031414784491062164, 0.029283158481121063, -0.07187001407146454, -0.05157071352005005, -0.00911431573331356, -0.0563465841114521, 0.11553788930177689, 0.00424547865986824, -0.02737416885793209, 0.033483196049928665, -0.004632564727216959, -0.036511510610580444, 0.01318303868174553, 0.03254931792616844, -0.03346672281622887, 0.0034119021147489548, 0.028742831200361252, 0.07196434587240219, 0.0042184945195913315, -0.029137546196579933, -0.040375273674726486, -0.03237970173358917, -0.02105625905096531, -0.07496264576911926, 0.07590191811323166, -0.005536617711186409, -0.028113342821598053, -0.02636328712105751, -0.019820833578705788, 0.0243651382625103, 0.0730474665760994, 0.015372093766927719, -0.017166081815958023, 0.08721599727869034, -0.02970004267990589, -0.01625688001513481, 0.012533926405012608, -0.002417094074189663, 0.053650885820388794, 0.0032840720377862453, -0.008063229732215405, 0.04269558563828468, 0.04141218960285187, 0.026491861790418625, 0.0016633643535897136, 0.05096878111362457, 0.016024453565478325, -0.057035259902477264, -0.04382707551121712, 0.007811447139829397, 0.01429898664355278, -0.008568541146814823, -0.012912196107208729, 0.07278311997652054, 0.013962502591311932, 0.04558902978897095, -0.032824959605932236, -0.022182408720254898, 0.07665236294269562, -0.011227115988731384, -0.03845341131091118, 0.0258676428347826, -0.0053864698857069016, 0.05985945463180542, -0.018499203026294708, 0.015820220112800598, -0.02757350355386734, -0.022477708756923676, 0.01229161024093628, -0.004119097255170345, -0.004962570499628782, 0.0018668585689738393, 0.020251190289855003, 0.024204950779676437, -0.0699504166841507, 0.003940884955227375, -0.003099245484918356, -0.03067607246339321, -0.07183562964200974, 0.03418967127799988, 0.08650930225849152, -0.002971712965518236, -0.04126888886094093, -0.007165616378188133, 0.011174970306456089, -0.02520834282040596, 0.0014916366199031472, -0.04953877255320549, -0.00481501966714859, 0.03514770418405533, -0.04454522579908371, -0.017779376357793808, 0.036705728620290756, 0.046972453594207764, 0.0010564335389062762, -0.03705959394574165, -0.01694842427968979, 0.036612994968891144, -0.03513779491186142, 0.04605892300605774, 0.03481048345565796, -0.007206578738987446, -0.009949850849807262, 0.018216153606772423, 0.008817588910460472, -0.021373240277171135, 0.018136125057935715, -0.020086804404854774, -0.008480037562549114, 0.01729264110326767, 0.03601599484682083, 0.02366556227207184, 0.0028791704680770636, -0.014573449268937111, -0.0011343765072524548, 0.004963137209415436, -0.013045764528214931, -0.016684776172041893, -0.050066545605659485, -6.491726327133624e-33, 0.048609402030706406, -0.0006946137291379273, -0.06579776853322983, -0.00616766232997179, -0.007276164833456278, 0.048466913402080536, -0.013497970998287201, -0.03482821583747864, 0.0005302603240124881, 0.004797865636646748, -0.03509880602359772, 0.031206240877509117, -0.015039344318211079, 0.03693513572216034, 0.004285862669348717, -0.020982863381505013, -0.017254985868930817, -0.018888667225837708, 0.04399389401078224, 0.04013001546263695, 0.024912141263484955, 0.07443965971469879, 0.07806702703237534, -0.06398586183786392, -0.043519508093595505, 0.03576759994029999, 0.0025061944033950567, -0.019875282421708107, -0.014351101592183113, -0.011405443772673607, -0.060385216027498245, 0.016294846311211586, 0.004520902875810862, -0.033757638186216354, -0.005753427278250456, -0.05668870732188225, -0.012859159149229527, -0.019924979656934738, -0.08134861290454865, 0.024419553577899933, -0.06756722182035446, 0.011359354481101036, 0.07616551220417023, -0.0011279082391411066, -0.07773507386445999, 0.012804320082068443, 0.058233801275491714, 0.013850241899490356, -0.031503841280937195, -0.032218217849731445, 0.0021776470821350813, 0.008813559077680111, -0.023129118606448174, -0.017878280952572823, -0.017766257748007774, 0.010381187312304974, -0.015389639884233475, -0.009283076971769333, -0.04835076630115509, -0.01370937004685402, -0.03088100627064705, 0.028104260563850403, -0.016022251918911934, 0.02021866664290428, 0.059533555060625076, 0.0305043775588274, 0.06345514953136444, -0.0016961029032245278, -0.056005485355854034, -0.016445262357592583, 0.01894836500287056, 0.0021846084855496883, 0.033876217901706696, 0.03673478215932846, 0.058928169310092926, -0.02389374189078808, -0.08379600197076797, 0.03791017830371857, -0.018169568851590157, -0.0013513024896383286, -0.025334013625979424, 0.02207697555422783, -0.01748736761510372, 0.021190695464611053, 0.0014779330231249332, -0.059395529329776764, 0.014783932827413082, 0.016623500734567642, 0.02197335846722126, -0.027501245960593224, 0.023930875584483147, -0.010815605521202087, -0.022507088258862495, -0.03142429143190384, 0.0227153692394495, 0.012323331087827682, 0.014312553219497204, 0.04784046486020088, 0.04149613529443741, 0.008172925561666489, -0.024520305916666985, -0.02705775760114193, -0.034483976662158966, 0.022313596680760384, 0.043340008705854416, 0.005525026936084032, -0.03964044526219368, 0.023508556187152863, 0.01982155442237854, -0.037609249353408813, -0.022511368617415428, -0.03551420569419861, -0.007822919636964798, 0.006773876957595348, 0.04530904069542885, -0.036513201892375946, 0.012632127851247787, 0.1333257555961609, 0.010126114822924137, 0.03931232541799545, -0.060168471187353134, -0.0016536007169634104, 0.01370401494204998, 0.04096223786473274, -0.02156687155365944, 0.01890937238931656, -0.007792193442583084, -0.04364385828375816, -0.007554817479103804, -0.07085104286670685, 0.005408542696386576, -0.02061772719025612, 2.9649157795574865e-07, -0.0567086860537529, -0.0009129177778959274, 0.014061914756894112, -0.06152836233377457, -0.0034343546722084284, 0.022701682522892952, -0.0037850867956876755, 0.014246324077248573, -0.05575643107295036, -0.04009018838405609, 0.06742940098047256, -0.026330970227718353, 0.010555694811046124, 0.013745755888521671, -0.08465034514665604, 0.033542096614837646, -0.04616105929017067, 0.014690939337015152, 0.0016577662900090218, 0.008320012129843235, -0.02050728164613247, 0.10252275317907333, 0.0453215092420578, -0.03686745464801788, 0.048994340002536774, 0.01656150259077549, 0.03867439180612564, 0.01375084463506937, 0.06836456060409546, -0.04267542064189911, 0.08571215718984604, 0.021976513788104057, -0.00424638157710433, -0.040887556970119476, 0.002496941713616252, 0.06317786127328873, 0.03153805807232857, 0.024873308837413788, -0.019127069041132927, -0.04182770103216171, 0.008936643600463867, 0.05050120875239372, 0.033934224396944046, -0.020779922604560852, 0.037426263093948364, 0.019334353506565094, -0.009291698224842548, -0.02345895953476429, -0.004461945034563541, 0.07097330689430237, 0.07278129458427429, -0.04047920182347298, 0.012381239794194698, -0.001513024209998548, 0.028510013595223427, -0.054411232471466064, 0.021804746240377426, -0.07252463698387146, 0.0656033307313919, 0.09185410290956497, -0.04933777451515198, -0.0020254235714673996, -0.009839857928454876, 0.04910796880722046, 0.08691012114286423, 0.03540574386715889, 0.0032487602438777685, 2.1944851745682707e-34, -0.04573998600244522, -0.031884029507637024, 0.005750453565269709, 0.012122075073421001, -0.03962681442499161, -0.0005760702770203352, -0.046341996639966965, -0.009586474858224392, 0.023369556292891502, -0.01593996025621891, -0.040393419563770294]

['John S. Breese', 'David Heckerman', 'Carl Kadie']

1301.7363v1

Collaborative filtering or recommender systems use a database about user preferences to predict additional topics or products a new user might like. In this paper we describe several algorithms designed for this task, including techniques based on correlation coefficients, vector-based similarity calculations, and statistical Bayesian methods. We compare the predictive accuracy of the various methods in a set of representative problem domains. We use two basic classes of evaluation metrics. The first characterizes accuracy over a set of individual predictions in terms of average absolute deviation. The second estimates the utility of a ranked list of suggested items. This metric uses an estimate of the probability that a user will see a recommendation in an ordered list. Experiments were run for datasets associated with 3 application areas, 4 experimental protocols, and the 2 evaluation metrics for the various algorithms. Results indicate that for a wide range of conditions, Bayesian networks with decision trees at each node and correlation methods outperform Bayesian-clustering and vector-similarity methods. Between correlation and Bayesian networks, the preferred method depends on the nature of the dataset, nature of the application (ranked versus one-by-one presentation), and the availability of votes with which to make predictions. Other considerations include the size of database, speed of predictions, and learning time.

Empirical Analysis of Predictive Algorithms for Collaborative Filtering

http://arxiv.org/pdf/1301.7363v1

Title Empirical Analysis Predictive Algorithms Collaborative Filtering Summary Collaborative filtering recommender system use database user preference predict additional topic product new user might like paper describe several algorithm designed task including technique based correlation coefficient vectorbased similarity calculation statistical Bayesian method compare predictive accuracy various method set representative problem domain use two basic class evaluation metric first characterizes accuracy set individual prediction term average absolute deviation second estimate utility ranked list suggested item metric us estimate probability user see recommendation ordered list Experiments run datasets associated 3 application area 4 experimental protocol 2 evaluation metric various algorithm Results indicate wide range condition Bayesian network decision tree node correlation method outperform Bayesianclustering vectorsimilarity method correlation Bayesian network preferred method depends nature dataset nature application ranked versus onebyone presentation availability vote make prediction consideration include size database speed prediction learning time Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.02695382945239544, -0.0007963916286826134, -0.011771568097174168, -0.022246195003390312, -0.040704306215047836, -0.03852296993136406, 0.025240015238523483, 0.023012332618236542, 0.008438303135335445, -0.003246479667723179, -0.029594676569104195, 0.011260870844125748, 0.023833410814404488, 0.05154035985469818, -0.038913775235414505, -0.04027744382619858, -0.028605489060282707, 0.028184430673718452, -0.016280189156532288, -0.009736943058669567, 0.041379060596227646, 0.006288974080234766, 0.03744466230273247, -0.004769563674926758, 0.041688669472932816, 0.007690145168453455, 0.00037561156204901636, -0.026249753311276436, -0.008413221687078476, -0.043196626007556915, 0.0507013238966465, 0.004068550653755665, -0.04369251802563667, -0.003999569918960333, 2.124937509506708e-06, -0.02441530115902424, -0.056746695190668106, -0.026933355256915092, 0.052876971662044525, -0.03515278548002243, 0.01668136939406395, 0.09032753854990005, 0.03723630681633949, 0.04905475676059723, -0.048090238124132156, 0.012961333617568016, 0.010280191898345947, 0.06727766245603561, -0.012051680125296116, -0.020978357642889023, -0.01498821098357439, -0.03300939500331879, 0.000756352674216032, 0.013066032901406288, 0.03278833255171776, 0.013712451793253422, 0.01790217123925686, 0.006688527297228575, 0.004560887813568115, -0.007696152199059725, -0.0021813989151269197, -0.0611567497253418, -0.023463236168026924, 0.012603707611560822, 0.06153768301010132, 0.04264690354466438, -0.008749319240450859, -0.04584791511297226, -0.017184877768158913, 0.042034976184368134, 0.013689090497791767, -0.03299976885318756, -0.007738627027720213, 0.008378950878977776, -0.029597165063023567, 0.052426401525735855, -0.021079203113913536, -0.029375901445746422, -0.029427919536828995, 0.0329396054148674, -0.01965145766735077, 0.022834140807390213, 0.014313653111457825, 0.01875520683825016, 0.06569063663482666, 0.09267961233854294, 0.013608931563794613, -0.03302506357431412, 0.00031400774605572224, -0.007179178763180971, 0.052847590297460556, -0.057138919830322266, 0.041151128709316254, -0.004268845543265343, -0.039086584001779556, -0.023628342896699905, 0.02024124003946781, -0.01284746266901493, 0.028589598834514618, -0.02253234200179577, 0.04889494553208351, -0.01737457886338234, 0.02578410878777504, 0.013439479283988476, 0.014224993996322155, -0.021730594336986542, 0.007264855317771435, -0.009302031248807907, -0.008593076840043068, 0.04347892105579376, -0.04479805752635002, 0.01595824584364891, 0.026309693232178688, 0.04286259040236473, 0.0033328107092529535, -0.026906916871666908, -0.0625726506114006, 0.015370912849903107, -0.0011442824034020305, 0.016495373100042343, 0.05574854835867882, 0.06608881056308746, 0.02741597779095173, 0.026263635605573654, -0.05602201074361801, -0.004265148192644119, -0.0654749646782875, 0.06364106386899948, -0.02100549265742302, 0.06375965476036072, 0.08889488875865936, 0.009795812889933586, 0.0350777842104435, -0.0035562405828386545, 0.040034469217061996, -0.0009372032363899052, 0.03613646700978279, -0.0002011421020142734, -0.03188176080584526, -0.019933316856622696, 0.02805507928133011, -0.010435990057885647, -0.06568826735019684, -0.03802591562271118, 0.0038889278657734394, 0.014322742819786072, -0.004588422831147909, 0.024048490449786186, 0.002795731881633401, -0.020088735967874527, -0.017442410811781883, 0.0789160281419754, 0.00702079851180315, -0.0013545486144721508, 0.0500238798558712, 0.013220611959695816, 0.00033971460652537644, -0.049964457750320435, -0.05217684432864189, 0.07228772342205048, 0.0477832593023777, 0.014260909520089626, -0.004298198036849499, -0.045248229056596756, -0.03911583870649338, -0.025046331807971, -0.017176758497953415, 0.030059099197387695, -0.0010563991963863373, 0.0340753048658371, -0.049675069749355316, 0.03733394294977188, -0.023615214973688126, -0.010477987118065357, 0.03313508257269859, 0.008066723123192787, 0.055478326976299286, 0.05096599832177162, 0.010190511122345924, 0.04636862128973007, -0.021376313641667366, -0.04038950428366661, 0.02475157380104065, 0.05352218449115753, -0.03212063014507294, -0.04462755098938942, 0.020799165591597557, 0.01747627928853035, -0.029521692544221878, -0.019209275022149086, 0.023868968710303307, -0.018263673409819603, 0.0022805274929851294, -0.02653012052178383, 0.03593674674630165, -0.02127353474497795, -0.026271222159266472, -0.04401402920484543, 0.019369835034012794, -0.004498779308050871, -0.02864811196923256, -0.008443063125014305, 0.07200103253126144, 0.07603413611650467, 0.018241995945572853, -0.00688670901581645, 0.03735260292887688, -0.007112658582627773, -0.043360717594623566, -0.14807231724262238, 0.004019056912511587, -0.019431615248322487, -0.04163147509098053, -0.027713848277926445, -0.05991294980049133, 0.04837090149521828, -0.01414351537823677, 0.026564590632915497, -0.024904126301407814, 0.04119471460580826, 0.0031520051416009665, 0.0264901090413332, 0.02170724980533123, -0.00822496972978115, 0.010260472074151039, 0.03153323754668236, 0.07098785787820816, -0.007254965603351593, 0.06284070760011673, 0.00705058453604579, 0.05052945017814636, -0.00031282129930332303, 0.009084971621632576, 0.006374858319759369, -0.06614643335342407, 9.668549319030717e-05, 0.043259937316179276, 0.02801433764398098, 0.041321273893117905, -0.03268745541572571, 0.10128062963485718, 0.04786950349807739, 0.029776575043797493, -0.01961529068648815, 0.031579405069351196, 0.01863372139632702, -0.016098789870738983, 0.007501618005335331, 0.03386111930012703, -0.013837555423378944, -0.01041564904153347, 0.013163761235773563, 0.028527792543172836, 0.018957095220685005, 0.03160468488931656, -0.009906521998345852, -0.052256762981414795, 0.026203246787190437, 0.029701847583055496, -0.006230154540389776, -0.008264206349849701, 0.009826773777604103, 0.016227561980485916, 0.0030711358413100243, 0.0006980547914281487, -0.03524000570178032, 0.006255424581468105, -0.04400287941098213, 0.01161395013332367, 0.015095522627234459, -0.007183600217103958, -0.01666363701224327, -0.0019445987418293953, 0.013693687506020069, -0.02022884413599968, -0.037801165133714676, 0.03313165158033371, -0.0640648603439331, -0.0011245844652876258, -0.012415065430104733, 0.06881152093410492, 0.0026677767746150494, -0.011323525570333004, -0.03682829812169075, -0.013207134790718555, 0.0030273394659161568, 0.02495162934064865, -0.008866439573466778, -0.0017768664984032512, 0.0022091621067374945, -0.03427450731396675, -0.044412463903427124, 0.006287821568548679, 0.025853652507066727, -0.052250273525714874, 0.001844964106567204, -0.008992856368422508, -0.04303361847996712, 0.00013705187302548438, -0.01519021950662136, 0.091117262840271, 0.02376989834010601, -0.047425057739019394, -0.026593944057822227, -0.022498100996017456, 0.01741243153810501, 0.03323986008763313, 0.006486833095550537, -0.02263798378407955, -0.02475341223180294, 0.02136821672320366, -0.012863969430327415, 0.0015817934181541204, 0.023551244288682938, 0.004619059152901173, 0.03632023558020592, -0.06609933078289032, -0.03296816721558571, -0.026347331702709198, 0.04941769689321518, 0.037197113037109375, -0.013894113712012768, 0.07012124359607697, 0.020218675956130028, 0.036405298858881, -0.05537191033363342, -0.056398313492536545, 0.03246759623289108, -0.03331368789076805, 0.004132377915084362, -0.004925826098769903, -0.047995079308748245, 0.019326411187648773, -0.004439292475581169, 0.023661673069000244, 0.08364293724298477, -0.034305259585380554, -0.0552508719265461, 0.029635347425937653, -0.052383843809366226, 0.033996324986219406, 0.0015795445069670677, -0.01376393623650074, -0.045468900352716446, -0.014515936374664307, -0.023203028365969658, 0.0014650762313976884, -0.013315970078110695, -0.006804557982832193, -0.026368800550699234, -0.051468685269355774, 0.02246982418000698, -0.011523283086717129, -0.04238663613796234, 0.05949362739920616, 0.02029982954263687, 0.0131874680519104, -0.09982134401798248, -0.05096356198191643, 0.02786668762564659, 0.018374983221292496, 0.0406327024102211, -0.007259788457304239, -0.057402968406677246, -0.06309308111667633, -0.00737405102699995, 0.042199548333883286, -0.024872630834579468, -0.02932448871433735, 0.05503558740019798, -0.046426206827163696, 0.026659205555915833, 0.06159712001681328, 0.0377802699804306, 0.04827922582626343, -0.12002716958522797, -0.038610175251960754, -0.05786937475204468, -0.01252223365008831, 0.04930907487869263, 0.027587315067648888, -0.018689248710870743, 0.012619179673492908, -0.0031538880430161953, 0.04096628352999687, 0.008476600982248783, -0.056890275329351425, -0.011292275972664356, -0.030062953010201454, 0.018870573490858078, -0.03191642835736275, 0.023711541667580605, 0.01734520122408867, -0.0864061638712883, -0.006080022547394037, -0.0260971337556839, -0.04145830124616623, -0.008635763078927994, 0.008939855732023716, 0.013313953764736652, 0.020405203104019165, -0.06298238039016724, 0.0033860900439321995, 0.03927680477499962, -0.028938211500644684, 0.012196660973131657, 0.025615891441702843, 0.05134383961558342, -0.01822289265692234, -0.023335890844464302, -0.0568791925907135, -0.022679585963487625, 0.007490011863410473, -0.021241910755634308, 0.04112755507230759, 0.008278800174593925, 0.05145220085978508, -0.030879629775881767, 0.028509654104709625, 0.014933643862605095, 0.013136708177626133, 0.06393824517726898, 0.08069567382335663, -0.035582199692726135, -0.0309172160923481, -0.04913066327571869, 0.04867703467607498, 0.010652603581547737, -0.00442438293248415, 0.003055734559893608, -0.037175267934799194, 0.02370867319405079, 0.014848625287413597, -0.01135305780917406, 0.03550459071993828, 0.020477434620261192, -0.030485725030303, 0.00026675211847759783, -0.02096855826675892, -0.062288716435432434, 0.018082141876220703, -0.010541308671236038, 0.017956571653485298, 0.01548275351524353, 0.06662342697381973, -0.03037613444030285, -0.040008604526519775, -0.007970643229782581, -0.05274911969900131, 0.07814447581768036, 0.03835957869887352, -0.034144144505262375, 0.021230019629001617, 0.0012201518984511495, -0.05736607685685158, -0.014659070409834385, -0.08394652605056763, -0.020552577450871468, -0.02644425444304943, -0.04257870838046074, 0.09466073662042618, 0.01260381005704403, 0.016853829845786095, -0.049454085528850555, -0.044457949697971344, -0.035296596586704254, -0.027920693159103394, -0.024937713518738747, -0.06654272228479385, -0.014805742539465427, 0.012942414730787277, 0.017594680190086365, 0.02679304964840412, -0.03146117553114891, 0.02089354395866394, -0.03097774088382721, -0.06946434825658798, -0.023686673492193222, -0.03007940761744976, 0.022916482761502266, 0.017084717750549316, 0.045929767191410065, -0.03851622715592384, 0.027773771435022354, 0.021326875314116478, 0.02072739414870739, -0.016260644420981407, -0.02944975160062313, 0.007872682996094227, -0.005229884292930365, 0.05394848436117172, -0.002396328141912818, -0.014416733756661415, -0.020076150074601173, 0.0015945867635309696, -0.0376933254301548, 0.0009585010702721775, 0.05229867622256279, -0.01464773342013359, 0.027844535186886787, 0.013017546385526657, 0.03795560821890831, 0.04205130413174629, -0.06508929282426834, 0.07142513245344162, 0.041992515325546265, -0.010668818838894367, 0.05067146569490433, -0.02154706045985222, -0.017502032220363617, -0.01045440323650837, 0.03476378321647644, 0.033143140375614166, -0.01725197397172451, -0.007024776190519333, 0.025385024026036263, -0.01714465580880642, -0.033436380326747894, -0.041474610567092896, -0.03053598292171955, 0.009789110161364079, -0.0430099219083786, 0.030183622613549232, -0.07024706155061722, -0.004458987154066563, 0.0353633314371109, 0.014581174589693546, -0.017017457634210587, 0.06432455778121948, 0.07785765826702118, -0.020890871062874794, -0.0789264589548111, 0.003014097921550274, -0.08478894084692001, -0.00902543030679226, 0.06614601612091064, 0.0015350992325693369, 0.06940877437591553, -0.054801177233457565, -0.013264516368508339, 0.017668666318058968, -7.525202090619132e-05, 0.029823003336787224, -0.05617643520236015, 0.05225735902786255, -0.016451647505164146, 0.03448253497481346, 0.05261624604463577, -0.017550339922308922, 0.058902841061353683, -0.045371249318122864, -0.044766783714294434, -0.006434164475649595, 0.009670198895037174, -0.041058249771595, -6.071134815751394e-33, 0.05511876940727234, -0.03849411755800247, -0.02215895988047123, 0.016073226928710938, 0.0319729782640934, -0.020173294469714165, 0.021569691598415375, 0.012266542762517929, 0.04786820337176323, 0.0034555899910628796, 0.0008947491296567023, 0.010464849881827831, 0.006592613644897938, -0.021664602681994438, 0.057354193180799484, -0.005462973844259977, -0.0004400778270792216, 0.04034173861145973, 0.02006370760500431, 0.005321192089468241, 0.018153594806790352, 0.05704852193593979, -0.018933620303869247, -0.06394335627555847, 0.017480015754699707, -0.014541346579790115, -0.023511867970228195, -0.022284917533397675, -0.005295127164572477, 0.028330039232969284, 0.002874627709388733, 0.02438957430422306, -0.015591655857861042, -0.019640488550066948, -0.00014622313028667122, -0.016830792650580406, -0.04036090150475502, -0.030949724838137627, -0.008420244790613651, -0.003040095092728734, -0.003515106625854969, 0.027246851474046707, -0.0010671804193407297, 0.04130616784095764, -0.03710125386714935, 0.0009895131224766374, 0.06866569817066193, -0.02503041923046112, -0.057194557040929794, -0.019213948398828506, 0.037133872509002686, 0.002335597528144717, -0.005631151609122753, 0.022753223776817322, 0.02360844612121582, 0.06417081505060196, -0.03928704187273979, 0.01605496183037758, -0.030176497995853424, 0.030190983787178993, -0.0529954768717289, 0.03228183835744858, -0.010258881375193596, -0.04246359318494797, -0.0018409923650324345, 0.023111088201403618, -0.017737610265612602, -0.05464885011315346, 0.019178740680217743, -0.013747015036642551, -0.04541483148932457, 0.07552652806043625, -0.0017433392349630594, 0.029416056349873543, 0.03321249037981033, -0.037940263748168945, 0.01876584254205227, 0.09466241300106049, 0.021706121042370796, -0.029313037171959877, -8.71807787916623e-06, 0.017010919749736786, -0.0274835042655468, -0.04148256778717041, 0.04430721700191498, 0.013219698332250118, -0.03987482562661171, -0.07365680485963821, -0.0040529025718569756, 0.02311813458800316, 0.009332766756415367, -0.006943638902157545, -0.05286596342921257, -0.06811164319515228, -0.0426725335419178, 0.006158303003758192, -0.02997128665447235, -0.01946604624390602, 0.012995652854442596, -0.00981014221906662, -0.06804404407739639, 0.04101463779807091, -0.05969038978219032, -0.05142733082175255, -0.027455804869532585, -0.022791337221860886, 0.028557803481817245, -0.009823903441429138, -0.030655108392238617, -0.022864343598484993, 0.056657228618860245, -0.09038534760475159, 0.013028956949710846, 0.0235886313021183, -0.007331321947276592, 0.031626299023628235, -0.018751563504338264, 0.06695228070020676, 0.026957988739013672, 0.053446657955646515, -0.027504757046699524, -0.10442157834768295, 0.022342931479215622, -0.031033148989081383, -0.045113928616046906, -0.049828238785266876, -0.05002211034297943, -0.006786524783819914, 0.04145350307226181, -0.03497207164764404, -0.03771732375025749, -0.05251738801598549, 2.802561596126907e-07, 0.008599618449807167, 0.025496961548924446, -0.06054763123393059, -0.0659390389919281, 0.005295328330248594, 0.015091176144778728, -0.0012707056012004614, 0.02752208337187767, 0.023330986499786377, 0.04957558959722519, 0.06529417634010315, -0.062214307487010956, 0.008093507960438728, 0.04616744816303253, -0.040327735245227814, -0.03124546818435192, -0.0804184302687645, -0.011636263690888882, -0.04758763685822487, -0.026073899120092392, -0.0011467229342088103, 0.05289487913250923, 0.07784391939640045, 0.0009181065834127367, 0.001962285954505205, 0.0397939495742321, -0.012008662335574627, -0.055404528975486755, -0.01474522240459919, -0.04654980078339577, 0.05379212647676468, -0.00926990807056427, -0.030533628538250923, 0.03680736944079399, -0.06760194152593613, -0.018721697852015495, 0.015574438497424126, -0.020608769729733467, -0.042193908244371414, 0.02663915976881981, 0.026347031816840172, 0.006235224660485983, 0.0033354214392602444, -0.025339791551232338, 0.04811631888151169, 0.05872616544365883, -0.02728724479675293, 0.012136650271713734, -0.03585205227136612, -0.016334693878889084, 0.05253572016954422, 0.0034713493660092354, 0.013898170553147793, -0.005591767840087414, 0.006301266141235828, -0.003315137466415763, -0.0047850157134234905, 0.0029762357007712126, 0.015196873806416988, 0.013100091367959976, 0.004966313019394875, -0.035370007157325745, -0.01375534012913704, 0.006100471131503582, 0.032317522913217545, -0.007274577394127846, 0.03662601858377457, 2.1679185430622063e-34, 0.027792247012257576, 0.05563880130648613, -0.0049635241739451885, -0.03298163786530495, 0.011803814209997654, -0.05538540333509445, 0.0024657752364873886, 0.011710938066244125, 0.04855707660317421, 0.00574649590998888, -0.016528623178601265]

['Chao Zhang', 'Lei Zhang', 'Jieping Ye']

1304.1574v1

In this paper, we provide a new framework to obtain the generalization bounds of the learning process for domain adaptation, and then apply the derived bounds to analyze the asymptotical convergence of the learning process. Without loss of generality, we consider two kinds of representative domain adaptation: one is with multiple sources and the other is combining source and target data. In particular, we use the integral probability metric to measure the difference between two domains. For either kind of domain adaptation, we develop a related Hoeffding-type deviation inequality and a symmetrization inequality to achieve the corresponding generalization bound based on the uniform entropy number. We also generalized the classical McDiarmid's inequality to a more general setting where independent random variables can take values from different domains. By using this inequality, we then obtain generalization bounds based on the Rademacher complexity. Afterwards, we analyze the asymptotic convergence and the rate of convergence of the learning process for such kind of domain adaptation. Meanwhile, we discuss the factors that affect the asymptotic behavior of the learning process and the numerical experiments support our theoretical findings as well.

Generalization Bounds for Domain Adaptation

http://arxiv.org/pdf/1304.1574v1

Title Generalization Bounds Domain Adaptation Summary paper provide new framework obtain generalization bound learning process domain adaptation apply derived bound analyze asymptotical convergence learning process Without loss generality consider two kind representative domain adaptation one multiple source combining source target data particular use integral probability metric measure difference two domain either kind domain adaptation develop related Hoeffdingtype deviation inequality symmetrization inequality achieve corresponding generalization bound based uniform entropy number also generalized classical McDiarmids inequality general setting independent random variable take value different domain using inequality obtain generalization bound based Rademacher complexity Afterwards analyze asymptotic convergence rate convergence learning process kind domain adaptation Meanwhile discus factor affect asymptotic behavior learning process numerical experiment support theoretical finding well Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.02683868259191513, -0.013475160114467144, -0.029621655121445656, -0.002311290707439184, -0.02140357345342636, 0.0006741327233612537, 0.014079621061682701, 0.026455461978912354, -0.07217492163181305, 0.006727173458784819, -0.019683586433529854, -0.010879438370466232, -0.021331781521439552, 0.012868561781942844, -0.01737295649945736, -0.06381439417600632, -0.005599536467343569, -0.006428318563848734, -0.03177805617451668, -0.03327576443552971, -0.001483599073253572, -0.06762958317995071, 0.009008548222482204, 0.016048895195126534, 0.036214809864759445, 0.03756583482027054, 0.03810655698180199, -0.017649365589022636, 0.03352198377251625, -0.039459727704524994, 0.017233166843652725, 0.005928517319262028, 0.021960144862532616, 0.026017360389232635, 2.0467555259529036e-06, -0.08410514146089554, -0.02590026892721653, -0.006137861870229244, 0.04892537370324135, -0.0386427603662014, 0.012513586319983006, -0.0652221143245697, -0.002352812560275197, 0.007091530133038759, 0.0051211705431342125, -0.043552663177251816, 0.02861756458878517, 0.0622594989836216, 0.0124416034668684, 0.05474940687417984, -0.01253855787217617, -0.038915712386369705, -0.0023995779920369387, -0.02918819896876812, -0.009044484235346317, -0.04960019886493683, 0.032970864325761795, 0.0017783342627808452, -0.02321418933570385, -0.033298954367637634, -0.05603552237153053, 0.01041329838335514, 0.02975982055068016, 0.014042078517377377, 0.012275868095457554, 0.0336511991918087, 0.00933227501809597, 0.04736530780792236, -0.004996595438569784, 0.04048505052924156, -0.012374181300401688, 0.010654270648956299, -0.0357799232006073, -0.0070415702648460865, -0.004014768172055483, 0.04657093435525894, -0.05230604112148285, -0.04249061644077301, -0.010180357843637466, 0.02681848034262657, -0.09926050901412964, 0.05498414859175682, 0.006295232567936182, -0.02359595149755478, -0.026040637865662575, 0.043569885194301605, -0.005501557141542435, -0.03208422660827637, 0.038807280361652374, 0.0025996246840804815, -0.06097998097538948, 0.031134340912103653, -0.029865147545933723, 0.0007339845760725439, -0.01996050402522087, -0.027738889679312706, -0.06286714226007462, -0.08112937957048416, -0.008960715495049953, -0.027716046199202538, 0.03021816723048687, -0.01760835200548172, 0.002657670294865966, 0.02778308093547821, 0.017799625173211098, 0.044051989912986755, -0.03964836895465851, 0.03935261070728302, -0.022142287343740463, 0.01665356196463108, -0.07303072512149811, 0.026978081092238426, -4.2168150685029104e-05, 0.05489467829465866, -0.00041278768912889063, 0.014005918987095356, -0.05235709249973297, 0.04198777303099632, 0.009050152264535427, -0.015083868987858295, 0.03008691966533661, -0.011002209968864918, -0.012105287984013557, -0.0018017912516370416, -0.03542255237698555, 0.008035150356590748, -0.0520278625190258, 0.04783659055829048, 0.017024574801325798, 0.017107587307691574, 0.010318560525774956, -0.011286280117928982, 0.03467991575598717, 0.008640600368380547, -0.01726534590125084, 0.130362406373024, -0.0033818776719272137, 0.0050977980718016624, -0.07141729444265366, 0.015283549204468727, 0.01273997500538826, 0.018109427765011787, 0.03306295722723007, -0.04528495669364929, -0.020046750083565712, -0.03809178248047829, -0.01644453965127468, -0.037285853177309036, -0.03826771676540375, -0.07163621485233307, 0.0030400357209146023, 0.058374322950839996, 0.001857911003753543, -0.015774188563227654, 0.09918487071990967, -0.006022383458912373, -0.026119373738765717, 0.09161058813333511, -0.006228893529623747, -0.055018793791532516, 0.030188776552677155, -0.025655023753643036, 0.005865264683961868, -0.012751073576509953, 0.005104463081806898, 0.0017619263380765915, 0.03661219775676727, 0.000931978749576956, 0.0051239728927612305, 0.009662817232310772, 0.019509494304656982, -0.026755301281809807, -0.0345175564289093, -0.07931993901729584, 0.020416641607880592, 0.041199758648872375, 0.04571108520030975, -0.03127763792872429, -0.027746034786105156, -0.010871666483581066, -0.005940950009971857, 0.07136915624141693, -0.022754743695259094, 0.018181344494223595, -0.01700383611023426, -0.02984037809073925, 0.0021144049242138863, 0.0007665622979402542, -0.04235205054283142, -0.053062934428453445, 0.0076761734671890736, -0.026473186910152435, -0.03192657232284546, -0.0658278539776802, 0.08849627524614334, 0.011752113699913025, -0.01848801039159298, -0.04061635211110115, 0.028855619952082634, 0.012912378646433353, -0.016592444851994514, -0.02460552006959915, 0.009055349044501781, -0.07262948155403137, -0.01972177065908909, -0.08787688612937927, 0.04687200114130974, -0.007761267013847828, -0.010741389356553555, -0.04871676489710808, 0.02842060662806034, 0.028883418068289757, 0.030896451324224472, -0.01978696510195732, -0.007609965279698372, 0.04638043791055679, 0.0038264405447989702, -0.015957044437527657, 0.0043306718580424786, -0.005857191048562527, 0.011500827036798, -0.011081459932029247, 0.011343110352754593, 0.011422228999435902, -0.001070058555342257, -0.03139089420437813, 0.049889154732227325, 0.03850435093045235, 0.041167739778757095, -0.041186973452568054, -0.048317089676856995, -0.01364982035011053, 0.003393664490431547, -0.031401775777339935, -0.0759095847606659, 0.07091876864433289, 0.020561804994940758, -0.011959746479988098, 0.009862160310149193, -0.04596363380551338, 0.06734830886125565, 0.007736848201602697, -0.011570954695343971, -0.02420162223279476, 0.06069236993789673, 0.03289254754781723, 0.015972815454006195, -0.012805962935090065, 0.04570421949028969, -0.02570837177336216, 0.07875873148441315, -0.019293230026960373, 0.022653644904494286, 0.01674935594201088, -0.0031951293349266052, -0.05082426220178604, -0.016643986105918884, 0.029277563095092773, -0.0017457354115322232, 0.02656969428062439, -0.0030954063404351473, -0.04990046098828316, 0.02476862445473671, 0.01922304928302765, 0.006775423418730497, 0.010563232004642487, 0.04106448218226433, 0.033574845641851425, -0.0008795657777227461, -0.01839044690132141, 0.041358307003974915, 2.3097036319086328e-05, 0.02047828771173954, 0.007199610583484173, 0.02115752547979355, 0.023110806941986084, 0.045799966901540756, -0.011474807746708393, 0.006697177421301603, 0.03651531785726547, -0.005473040509968996, 0.007878883741796017, -0.017028683796525, -0.04026022180914879, 0.007962589152157307, 0.08093678206205368, 0.022303106263279915, -0.012759714387357235, -0.012894073501229286, 0.07200382649898529, 0.005391314625740051, 0.037426140159368515, -0.01097007468342781, -0.024584125727415085, -0.041366755962371826, -0.037918999791145325, 0.011134941130876541, 0.06148358806967735, 0.007338089868426323, 0.010527842678129673, 0.04028315469622612, 0.07174541056156158, -0.027646787464618683, -0.0029065280687063932, -0.03370851278305054, -0.022909395396709442, -0.012555488385260105, 0.010095741599798203, 0.07769283652305603, 0.03793668374419212, 0.0015581983607262373, -0.0573076494038105, -0.01779787614941597, 0.0032541214022785425, -0.010185949504375458, -0.024442559108138084, -0.04595781862735748, 0.045005738735198975, -0.0003165542148053646, -0.0016475057927891612, -0.01938597857952118, -0.0555848702788353, 0.030472546815872192, 0.053544387221336365, 0.0572412945330143, -0.06832372397184372, -0.057058148086071014, 0.005443384870886803, 0.0049201915971934795, 0.018821772187948227, 0.03845873475074768, 0.042966730892658234, -0.029597396031022072, -0.02345225401222706, -0.0014508716994896531, 0.024594411253929138, 0.0015558620216324925, 0.03905612975358963, -0.02577829174697399, 0.010844935663044453, -0.004738804884254932, 0.00300781917758286, 0.004580583889037371, 0.022301193326711655, 0.04663129895925522, -0.008012533187866211, -0.04003537818789482, -0.06373314559459686, -0.034171245992183685, -0.03476737067103386, -0.0031568759586662054, 0.02178325317800045, -0.005533970892429352, -0.05618220195174217, 0.018275752663612366, 0.0494692325592041, 0.012521381489932537, 0.007732609286904335, -0.06509324908256531, -0.02567969635128975, 0.03354139253497124, 0.003203724045306444, 0.038671039044857025, 0.016961975023150444, -0.055571917444467545, -0.008661209605634212, 0.0005973833031021059, -0.02011600136756897, -0.03832674399018288, 0.00031194050097838044, 0.047625549137592316, 0.028696928173303604, 0.03157943859696388, 0.06612362712621689, -0.015639537945389748, -0.03028089925646782, -0.0052005634643137455, -0.035195622593164444, 0.00023487882572226226, 0.018232977017760277, 0.019036073237657547, -0.0028533865697681904, -0.020410388708114624, -0.020510615780949593, 0.01309772115200758, -0.03502514585852623, -0.03121860697865486, 0.0034861473832279444, -0.0628807544708252, -0.014509943313896656, 0.006164892576634884, -0.10185428708791733, -0.08496810495853424, -0.020949460566043854, 0.024211043491959572, -0.021788155660033226, -0.026860011741518974, -0.0024852959904819727, 0.01129116676747799, -0.04162032902240753, 0.047297462821006775, -0.0231093131005764, -0.054445430636405945, -0.04109148681163788, -0.09690917283296585, -0.024800622835755348, 0.06479695439338684, 0.0024303575046360493, -0.020310483872890472, -0.01086732279509306, 0.017118297517299652, 0.008748902007937431, 0.01649479754269123, 0.0009914765832945704, 0.09327495843172073, 0.06071116402745247, 0.0038775154389441013, 0.034489817917346954, 0.05766242742538452, -0.017794838175177574, 0.05856010317802429, 0.04923945292830467, 0.03455835208296776, 0.028535641729831696, -0.0455680713057518, -0.020569227635860443, -0.028850257396697998, 0.015104652382433414, 0.0030357232317328453, -0.009094096720218658, -0.045438434928655624, 0.019712043926119804, -0.03349253907799721, 0.0050545320846140385, 0.02949630282819271, 0.001473618671298027, 0.020703714340925217, -0.019411657005548477, -0.07953707873821259, -0.08428362756967545, 0.07337287813425064, -0.04105914384126663, 0.1095593199133873, 0.03338427469134331, -0.019490361213684082, -0.016997484490275383, 0.030915310606360435, -0.02551339380443096, -0.059618908911943436, 0.041235845535993576, 0.021718284115195274, -0.053047165274620056, 0.060351330786943436, 0.034938257187604904, -0.031499363481998444, -0.0532865971326828, -0.02540348283946514, -0.03360587731003761, -0.06606253981590271, -0.021329516544938087, -0.010048157535493374, 0.022755226120352745, -0.001268716063350439, -0.004041070118546486, -0.06491624563932419, 0.015590853989124298, 0.012037196196615696, 0.02642960473895073, 0.05920863896608353, 0.10024398565292358, -0.029862193390727043, 0.012721835635602474, 0.004136307165026665, -0.010215462185442448, 0.060664158314466476, -0.005965434480458498, -0.07898061722517014, -0.00144578714389354, -0.029884029179811478, -0.019279904663562775, 0.03378499671816826, 0.03366893157362938, 0.05785735324025154, -0.058064624667167664, -0.014901233837008476, 0.03287336230278015, 0.038889240473508835, 0.008835973218083382, -0.0324724018573761, -0.02788481116294861, 0.05580327659845352, 0.04273829981684685, -0.007089488673955202, 0.01888245716691017, 0.077262744307518, -0.0338701494038105, -0.024969419464468956, 0.007364039774984121, 0.03648911044001579, 0.09900135546922684, 0.003908430691808462, 0.018072642385959625, 0.023357702419161797, -0.0500325933098793, 0.04823944345116615, -0.004823713563382626, 0.021095767617225647, 0.03074073977768421, -0.026400147005915642, 0.013329492881894112, 0.01027560792863369, -0.04140494018793106, -0.06059839949011803, 0.004925321321934462, -0.011407875455915928, 0.03638577088713646, -0.0003780358238145709, 0.003077870002016425, -0.0015714281471446157, -0.015599916689097881, 0.003894589375704527, -0.057349689304828644, 0.04839249700307846, -0.028072623535990715, 0.02857479825615883, 0.060038816183805466, -0.04064212366938591, 0.0022826518397778273, 0.024211037904024124, 0.05721716955304146, 0.013003869913518429, 0.021883493289351463, -0.06072087213397026, -0.0038918941281735897, -0.0341903455555439, 0.023095907643437386, 0.025492865592241287, -0.0003165976668242365, 0.026972169056534767, 0.02952868863940239, -0.00250431802123785, -0.023372314870357513, 0.008253472857177258, -0.03234253078699112, 0.08421237021684647, 0.03780467063188553, -0.015344042330980301, 0.02812219224870205, -0.040270205587148666, 0.019131671637296677, 0.014871462248265743, -0.027722999453544617, -0.015076755546033382, 0.01810264028608799, -0.010271523147821426, -5.49473630361347e-33, -0.03179710730910301, 0.016201289370656013, -0.07098527252674103, 0.030219750478863716, -0.009507540613412857, -0.026585567742586136, 0.027084704488515854, 0.0003104064962826669, -0.00882499199360609, -0.043926406651735306, 0.009727380238473415, 0.004461752250790596, -0.0007707244367338717, 0.02031402289867401, -0.02271018922328949, -0.02729111723601818, 0.046181537210941315, -0.0241111870855093, 0.0018543784972280264, -0.027358191087841988, 0.040350381284952164, 0.023383034393191338, 0.01373535580933094, -0.057761821895837784, -0.0365653820335865, 0.07700402289628983, -0.021814478561282158, -0.006329966243356466, 0.026937121525406837, 0.010036461055278778, 0.033497899770736694, 0.079281285405159, -0.01656116172671318, -0.046469006687402725, -0.0200729351490736, -0.0070569515228271484, -0.03833195939660072, -0.051287468522787094, -0.03354503586888313, 0.016034450381994247, -0.004639216233044863, -0.046477172523736954, 0.063707634806633, 0.008348206989467144, -0.03601507842540741, -0.05176619067788124, 0.05693276599049568, -0.025497211143374443, -0.030432509258389473, -0.017613211646676064, -0.025996286422014236, 0.026332370936870575, -0.015450157225131989, 0.04242309182882309, -0.012351217679679394, 0.03357234597206116, 0.028996702283620834, 0.0007458112086169422, -0.014966171234846115, 0.054308224469423294, 0.028904447332024574, 0.059894949197769165, 0.0022540162317454815, 0.0006135865114629269, 0.041493672877550125, 0.04848632588982582, 0.035813625901937485, -0.03467525541782379, 0.036159466952085495, -0.06957406550645828, 0.01565958559513092, 0.020098324865102768, -0.0382685549557209, 0.06039643660187721, 0.06078889220952988, -0.08005165308713913, -0.08067827671766281, 0.05593176186084747, -0.04962734505534172, -0.020712874829769135, -0.014022810384631157, 0.01862155646085739, -0.02742011286318302, 0.00217865826562047, 0.007065321784466505, 0.049575868993997574, 0.012140830978751183, -0.010044965893030167, 0.035238154232501984, -0.01974979043006897, 0.02102038636803627, -0.014949980191886425, -0.04302539303898811, -0.06051399186253548, 0.031182268634438515, 0.017763685435056686, -0.011886685155332088, 0.02766367234289646, 0.0036994016263633966, -0.0185839980840683, 0.024237317964434624, -0.04546770080924034, 0.0007236023666337132, 0.051068078726530075, 0.02061188593506813, -0.014411411248147488, 0.04768618941307068, 0.028735870495438576, -0.0584452748298645, -0.017011158168315887, -0.010020256042480469, -0.03365083038806915, 0.061322640627622604, 0.05053485557436943, 0.019280459731817245, -0.05813955143094063, -0.021424220874905586, 0.04790522903203964, -0.002872436074540019, -0.06108197942376137, -0.043951865285634995, 0.08734139055013657, 0.01979701966047287, 0.015372148714959621, -0.026574665680527687, -0.008856753818690777, -0.006473101209849119, -0.04816685616970062, 0.025506438687443733, -0.05191309377551079, -0.02745502069592476, -0.011877776123583317, 2.7459228135739977e-07, -0.04027063399553299, 0.006131144240498543, -0.033063776791095734, -0.03227374330163002, 0.040502093732357025, 0.03787915036082268, -0.02910315804183483, 0.04917800426483154, -0.006677243858575821, 0.021315351128578186, 0.02007112093269825, -0.04312346875667572, 0.02679823711514473, -0.014279220253229141, -0.038734205067157745, -0.053627077490091324, 0.030971435829997063, 0.06856384873390198, 0.01706843264400959, 0.009797230362892151, 0.02982257679104805, 0.0632895678281784, 0.019831016659736633, -0.020562423393130302, 0.038497813045978546, -0.048995260149240494, 0.022837167605757713, -0.05095967650413513, 0.08813737332820892, 0.012403936125338078, -0.01888919807970524, -0.004816338885575533, 0.007566396147012711, 0.01964261382818222, -0.021437186747789383, 0.050571221858263016, 0.02227117493748665, -0.0023781952913850546, 0.012829985469579697, 0.032936520874500275, 0.0409812405705452, 0.03034735471010208, 0.020031776279211044, 0.0005555673851631582, 0.05328652635216713, -0.07056227326393127, -0.03682858496904373, -0.00671246275305748, 0.006890187971293926, 0.017342370003461838, 0.0014026936842128634, 0.0088847940787673, 0.03292302042245865, -0.053913746029138565, -0.016739847138524055, 0.011697839014232159, 0.02061275765299797, -0.015188248828053474, 0.020445406436920166, 0.025818893685936928, -0.012225423939526081, -0.03230057284235954, -0.015825074166059494, -0.013818630948662758, 0.055118314921855927, -0.032476797699928284, -0.0011903035920113325, 2.615851226525097e-34, 0.004378801211714745, -0.011359506286680698, 0.051137205213308334, 0.0009331433102488518, -0.0488787442445755, -0.041012316942214966, -0.015175849199295044, -0.03540531173348427, 0.018964922055602074, -0.01309917587786913, 0.031958840787410736]

['Jialu Liu']

1304.5168v1

This article gives a survey for bag-of-words (BoW) or bag-of-features model in image retrieval system. In recent years, large-scale image retrieval shows significant potential in both industry applications and research problems. As local descriptors like SIFT demonstrate great discriminative power in solving vision problems like object recognition, image classification and annotation, more and more state-of-the-art large scale image retrieval systems are trying to rely on them. A common way to achieve this is first quantizing local descriptors into visual words, and then applying scalable textual indexing and retrieval schemes. We call this model as bag-of-words or bag-of-features model. The goal of this survey is to give an overview of this model and introduce different strategies when building the system based on this model.

Image Retrieval based on Bag-of-Words model

http://arxiv.org/pdf/1304.5168v1

Title Image Retrieval based BagofWords model Summary article give survey bagofwords BoW bagoffeatures model image retrieval system recent year largescale image retrieval show significant potential industry application research problem local descriptor like SIFT demonstrate great discriminative power solving vision problem like object recognition image classification annotation stateoftheart large scale image retrieval system trying rely common way achieve first quantizing local descriptor visual word applying scalable textual indexing retrieval scheme call model bagofwords bagoffeatures model goal survey give overview model introduce different strategy building system based model Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03355765715241432, 0.006209368817508221, 0.015437208116054535, 0.0559346042573452, -0.022280246019363403, 0.008382871747016907, 0.010226242244243622, 0.07734803855419159, 0.02126234769821167, -0.053723689168691635, 0.017564138397574425, 0.008907069452106953, -0.0395185612142086, 0.0575808510184288, -0.01026826724410057, -0.04656678065657616, 0.03732238709926605, 0.016952870413661003, 0.006995038595050573, -0.008360984735190868, 0.03929892182350159, -0.006358129438012838, 0.03510219231247902, 0.021916335448622704, -0.024632209911942482, 0.03307859227061272, -0.02019992284476757, 0.018189119175076485, -0.03457309678196907, -0.027494069188833237, -0.0041033802554011345, 0.015224963426589966, 0.04054710268974304, 0.009468421339988708, 1.804454086595797e-06, -0.04840771108865738, -0.08075717091560364, 0.005076628644019365, 0.020762667059898376, -0.0898074060678482, 0.07325734198093414, 0.004936462268233299, 0.01585293561220169, -0.048653844743967056, -0.022333553060889244, -0.005564970429986715, 0.07347354292869568, 0.0530763603746891, -0.007024879101663828, 0.03683978691697121, -0.029908370226621628, -0.08191186189651489, -0.009139256551861763, 0.02481262758374214, 0.012753237038850784, -0.023511191830039024, 0.002074961317703128, 0.03547489643096924, 0.05081886425614357, 0.05277473106980324, -0.024517951533198357, 0.051885660737752914, -0.034319549798965454, -0.000923926243558526, 0.06744328141212463, 0.013615336269140244, -0.06583403050899506, -0.01420105155557394, 0.004523396957665682, -0.0014206483028829098, -0.07005143910646439, -0.032939065247774124, 0.010821491479873657, 0.01136360876262188, -0.04791407659649849, 0.04053608700633049, -0.04608747735619545, 0.03230977803468704, -0.00522828521206975, -0.007830374874174595, -0.05043535307049751, 0.041983772069215775, -0.04072028398513794, 0.013125168159604073, 0.018064696341753006, -0.04113607481122017, 0.005131767597049475, -0.019043173640966415, -0.02860168367624283, -0.045422423630952835, -0.03934973105788231, -0.014456916600465775, 0.02239568531513214, 0.0409717783331871, 0.04562864825129509, -0.005990639794617891, -0.009334463626146317, -0.041881587356328964, 0.05349615216255188, -0.06749608367681503, -0.013600501231849194, -0.023894211277365685, -0.03902537003159523, 0.07016205042600632, 0.0029015899635851383, 0.02409350499510765, 0.01230640895664692, 0.023978084325790405, -0.03788578882813454, 0.0001166722213383764, -0.050607830286026, -0.04945739358663559, -0.05461817607283592, 0.07107001543045044, -0.013246281072497368, -0.07658298313617706, -0.012365826405584812, -0.02855062484741211, 0.01371854543685913, -0.05089571699500084, 0.02110799215734005, 0.019012054428458214, -0.039281364530324936, -0.026863321661949158, -0.01549419667571783, -0.0011393135646358132, 0.006041451822966337, -0.02895312011241913, -0.025480521842837334, 0.01240201573818922, 0.051284436136484146, 0.03276562690734863, 0.05164892598986626, -0.011580155231058598, 0.04394448921084404, -0.02701093815267086, -0.02495867945253849, -0.03836072236299515, -0.028606930747628212, -0.017586426809430122, -0.03039563074707985, 0.027904994785785675, 0.010449543595314026, -0.04685653746128082, -0.005041973199695349, -0.020674055442214012, -0.0159235168248415, 0.005779245402663946, -0.0035613144282251596, 0.045426301658153534, -0.04462229833006859, 0.0793275237083435, -0.01737086847424507, -0.010100259445607662, 0.1045934334397316, 0.019285904243588448, 0.061087604612112045, 0.023525262251496315, -0.03495325520634651, 0.0892878994345665, 0.06094301864504814, -0.0037224357947707176, 0.05462457612156868, 0.02702372707426548, -0.058920226991176605, -0.0649503618478775, -0.053696077316999435, 0.01794591173529625, 0.020595258101820946, -0.0241899061948061, -0.027309799566864967, 0.04517323151230812, -0.01760302111506462, 0.03881339356303215, -0.0010552280582487583, 0.12954919040203094, 0.030590010806918144, -0.017810659483075142, -0.037713244557380676, 0.05348104611039162, -0.020817354321479797, -0.04373086988925934, 0.04288772866129875, 0.05711273103952408, -0.009451345540583134, -0.050669752061367035, 0.00023731165856588632, -0.012731806375086308, -0.018499087542295456, 0.01294967345893383, 0.011724882759153843, 0.028065837919712067, -0.008122258819639683, 0.021225418895483017, 0.03941929712891579, -0.03412207216024399, 0.010913752019405365, -0.003059015143662691, -0.026878779754042625, -0.0375303290784359, -0.048855531960725784, -0.04655175656080246, 0.017695678398013115, -0.006425515748560429, 0.031727515161037445, -0.009019549004733562, 0.07781623303890228, 0.03824501857161522, -0.0013180472888052464, -0.01906628906726837, -0.004759081173688173, -0.009451457299292088, -0.032148487865924835, -0.055336013436317444, -0.02117701806128025, 0.03009953163564205, -0.03398868441581726, -0.030360005795955658, 0.026656072586774826, 0.0412830151617527, 0.026419619098305702, 0.010404415428638458, -0.014990738593041897, 0.019476598128676414, 0.06680423021316528, -0.029542775824666023, -0.023708263412117958, 0.04398728534579277, -0.01174409594386816, -0.027894403785467148, -0.009740940295159817, 0.013941643759608269, 0.0379084013402462, 0.017931180074810982, -0.013908888213336468, -0.01065079215914011, 0.06493940204381943, 0.048930130898952484, 0.02845653146505356, 0.014443092048168182, 0.03200272470712662, 0.017673533409833908, 0.013536625541746616, -0.050140634179115295, -0.03042418509721756, -0.01298430934548378, -0.02242080494761467, -0.0548861026763916, 0.04264893755316734, -0.040868982672691345, 0.030123328790068626, -0.09265284985303879, 0.04969213902950287, 0.016708165407180786, 0.011872028931975365, -0.10873245447874069, 0.005973947234451771, 0.04612031579017639, -0.05134802684187889, -0.03330385312438011, 0.06985100358724594, -0.0022234099451452494, 0.03318069502711296, 0.07154510170221329, 0.03719281032681465, -0.006600984837859869, -0.02026446908712387, -0.08629133552312851, -0.0033447835594415665, 0.02879716083407402, -0.051644280552864075, -0.027892647311091423, 0.0008408647263422608, 0.017863143235445023, -0.024545816704630852, -0.032955825328826904, 0.004178183153271675, -0.0033223030623048544, 0.004214766900986433, 0.0297994464635849, 0.008136950433254242, 0.012911432422697544, -0.037349261343479156, -0.03748554363846779, 0.02656075544655323, 0.029214905574917793, 0.04227034002542496, -0.11587647348642349, 0.020320989191532135, 0.007294585462659597, -0.031899452209472656, 0.0034619455691426992, 0.005089971702545881, 0.018998753279447556, 0.0041383602656424046, -0.07710320502519608, -0.012174652889370918, 0.06906337291002274, 0.04016827419400215, -0.013982916250824928, -0.026775352656841278, -0.006241164170205593, -0.04048192501068115, -0.006264862138777971, -0.02222980186343193, -0.007350055500864983, 0.0644020140171051, 0.0011609268840402365, 0.02561667002737522, -0.07489946484565735, -0.016750149428844452, 0.02722867578268051, -0.007117437664419413, -0.00966205820441246, -0.010143059305846691, 0.014226687140762806, -0.09960541874170303, 0.001291880034841597, 0.022128935903310776, 0.04619726166129112, -0.04467478767037392, -0.04859386011958122, -0.00451473705470562, 0.010774954222142696, -0.005947742145508528, -0.014010012149810791, -0.014044213108718395, -0.01955287903547287, 0.11739225685596466, -0.015176637098193169, 0.043096207082271576, -0.015033668838441372, 0.02361910790205002, 0.027451103553175926, -0.018259339034557343, 0.023814145475625992, -0.08212539553642273, 0.007346723694354296, -0.002222789218649268, 0.049673836678266525, -0.03081352449953556, -0.03793634846806526, 0.012161258608102798, -0.029379932209849358, -0.03061118721961975, -0.03923693299293518, 0.0007757760467939079, -0.022532613947987556, -0.013810183852910995, 0.08622992038726807, 0.03468504920601845, 0.02221590094268322, 0.00350402994081378, -0.009842906147241592, 0.036545105278491974, 0.03268229216337204, 0.04584924876689911, -0.06806506961584091, -0.04977816343307495, 0.04245290160179138, -0.018759338185191154, 0.031664155423641205, 0.01688934490084648, -0.021787289530038834, -0.04346959665417671, 0.04720912501215935, 0.04273798316717148, 0.006931667681783438, -0.025640802457928658, -0.013474873267114162, 0.040790993720293045, -0.017515692859888077, 0.020471394062042236, 0.004126173909753561, 0.01163860596716404, -0.07621632516384125, -0.06212509423494339, -0.009140663780272007, -0.09576792269945145, 0.026224061846733093, 0.04327966272830963, -0.018839480355381966, -0.022157341241836548, -0.01293193455785513, -0.014713256619870663, -0.010512232780456543, -0.0019129018764942884, -0.024585962295532227, -0.052069321274757385, 0.07087919116020203, 0.011623241007328033, 0.010281560011208057, -0.016701823100447655, -0.0032901542726904154, -0.04045344889163971, 0.0022928749676793814, -0.08413611352443695, 0.03264112025499344, -0.012397528626024723, -0.028390102088451385, 0.007076925132423639, 0.04633217304944992, 0.05667458847165108, 0.023198334500193596, -0.031227804720401764, -0.031421586871147156, 0.008933709934353828, 0.045944537967443466, -0.03420402854681015, -0.053045161068439484, -0.018763935193419456, 0.0277458056807518, -0.009609068743884563, -0.034781668335199356, 0.004258269444108009, -0.030583232641220093, -0.009209245443344116, -0.006420523393899202, -0.02364477328956127, 0.042830705642700195, -0.0013940214412286878, -0.02481335774064064, -0.009866549633443356, -0.006360158324241638, 0.04491608962416649, -0.07492976635694504, -0.01759091019630432, -0.028397612273693085, -0.041478514671325684, -0.03966346010565758, 0.01756320521235466, -0.0169296246021986, -0.0028623987454921007, -0.015378058888018131, 0.034244608134031296, -0.03514331951737404, -0.01033554133027792, -0.06189773976802826, -0.03973836451768875, -0.050975650548934937, 0.04323617368936539, -0.00264030322432518, 0.055496882647275925, -0.02109948918223381, 0.014968027360737324, -0.012176268734037876, 0.03552490100264549, -0.10209646821022034, 0.025432057678699493, -0.030191002413630486, 0.02707533910870552, -0.03884254768490791, 0.05450155958533287, 0.02392033115029335, -0.028201110661029816, -0.02026134729385376, 0.011840892024338245, -0.019185030832886696, -0.014901532791554928, 0.02568509615957737, 0.04701580852270126, 0.015302513726055622, -0.07739780843257904, 0.014793621376156807, -0.1101442500948906, 0.004555223044008017, -0.005666649900376797, 0.029801519587635994, -0.023542389273643494, -0.025573397055268288, -0.007020390592515469, -0.03474454581737518, -0.011243240907788277, -0.037015967071056366, 0.09735404700040817, -0.015361427329480648, -0.026681261137127876, -0.052161701023578644, 0.0055892979726195335, -0.02094360813498497, 0.03840598836541176, 0.04722072184085846, 0.021603714674711227, 0.0014696998987346888, -0.01839001104235649, -0.016636978834867477, 0.010707718320190907, -0.05550800636410713, -0.01749846525490284, 0.0009025789331644773, -0.007945751771330833, -0.0005319949123077095, 0.01375412568449974, 0.014871563762426376, 0.00687361229211092, 0.008823065087199211, 0.049632515758275986, -0.018936796113848686, -0.01475113071501255, 0.008710993453860283, -0.04643593356013298, 0.0038045120891183615, 0.006474691443145275, -0.010806354694068432, -0.0005791180883534253, 0.06294188648462296, -0.0022302246652543545, 0.03185482695698738, 0.0006556347943842411, -0.005484453868120909, -0.06337830424308777, 0.018413441255688667, -0.019851084798574448, -0.020661570131778717, -0.01688399165868759, 0.0011104989098384976, 0.04504035785794258, -0.06238861754536629, -0.03585831820964813, 0.0057030790485441685, 0.004588063340634108, -0.012461964040994644, 0.00561141362413764, -0.006742212455719709, -0.025877464562654495, 0.016494447365403175, 0.03298824653029442, -0.00613576453179121, 0.026603994891047478, 0.002913001924753189, -0.01833384484052658, -0.08395722508430481, -0.004247103817760944, -0.04246753081679344, -0.006141060963273048, 0.03261284902691841, 0.029021549969911575, 0.01489295344799757, 0.0028134959284216166, 0.012251535430550575, -0.00760043365880847, 0.037147652357816696, 0.045888807624578476, 0.00207883445546031, 0.013445534743368626, 0.05536779388785362, 0.030768144875764847, 0.05915284901857376, 0.03039618767797947, 0.017771609127521515, -0.03446579724550247, -0.013528604060411453, -0.0471503883600235, 0.0044102841056883335, -0.012533916160464287, -5.737469642244534e-33, 0.02121083065867424, -0.05636610463261604, 0.021386589854955673, 0.016859086230397224, 0.01219245046377182, 0.011211024597287178, 0.023008253425359726, -0.01898609660565853, -0.011889799498021603, -0.04481794685125351, -0.03753098100423813, 0.016480350866913795, 0.03581785410642624, 0.02397719770669937, 0.021516427397727966, 0.01985776610672474, -0.0113320117816329, -0.0038817350286990404, 0.02740325592458248, -0.02704273909330368, 0.0340995192527771, 0.022417452186346054, 0.025793137028813362, -0.03243458643555641, -0.019346894696354866, 0.000801773217972368, -0.018382180482149124, 0.01980893686413765, 0.064130999147892, 0.007124630268663168, -0.03491073101758957, -0.009959964081645012, -0.002868467941880226, -0.01173835527151823, 0.01594032719731331, 0.011414599604904652, -0.00585305318236351, 0.004021508619189262, -0.0422249361872673, 0.027752095833420753, 0.04408698529005051, 0.04182754456996918, 0.010415746830403805, -0.04454327002167702, -0.012671210803091526, 0.02832205221056938, 0.03290634974837303, -0.016612745821475983, -0.06777283549308777, -0.03577616810798645, -0.006333500146865845, 0.020216461271047592, 0.0318458154797554, 0.02257952094078064, 0.07202925533056259, -0.034985337406396866, 0.02255283109843731, 0.020265383645892143, 0.0007521364605054259, 0.02589457482099533, -0.04862656071782112, 0.03974045440554619, 0.012765644118189812, 0.027027033269405365, 0.04536006599664688, 0.0556405708193779, 0.043250732123851776, -0.03718702495098114, 0.04182392358779907, -0.03299489617347717, 0.009808413684368134, 0.029207978397607803, 0.04533053934574127, 0.04112176224589348, 0.10180813819169998, -0.017144182696938515, 0.019396843388676643, 0.01378837414085865, -0.024894794449210167, 0.0700707733631134, -0.014431323856115341, 0.05753263458609581, -0.048506539314985275, -0.0035837427712976933, 0.019960744306445122, 0.022297538816928864, -0.041443049907684326, 0.003435823367908597, 0.0064126369543373585, 0.05610087886452675, -0.03306274488568306, 0.10006621479988098, 0.03888950124382973, -0.0010148282162845135, 0.013553093187510967, -0.05903036892414093, 0.03138779476284981, 0.034742213785648346, -0.004000531043857336, 0.022099247202277184, -0.007122389040887356, -0.03819231316447258, 0.006801504176110029, 0.0354793407022953, -0.020518427714705467, 0.015613487921655178, 0.01406004000455141, 0.027777457609772682, -0.05794660001993179, -0.014925497584044933, 0.030612310394644737, -0.03556942567229271, -0.012511632405221462, 0.020078934729099274, -0.01717083714902401, 0.005113928113132715, 0.016649002209305763, 0.02334464341402054, 0.010315289720892906, -0.0028315444942563772, -0.019189143553376198, -0.09026080369949341, 0.011677386239171028, -0.0036739795468747616, 0.0005122023867443204, 0.07085935026407242, -0.07066456973552704, -0.02309693582355976, 0.0365120954811573, -0.024305272847414017, 0.010862082242965698, 0.06821401417255402, 2.451411091897171e-07, 0.04214344173669815, 0.04035761579871178, 0.03137441352009773, -0.013342780992388725, -0.03407695144414902, -0.015038038603961468, 0.022049419581890106, 0.010217609815299511, -0.02506321854889393, 0.03297637775540352, 0.007646000012755394, 0.008493258617818356, 0.030154507607221603, 0.01800440065562725, -0.056621748954057693, -0.002667935099452734, -0.03055645525455475, -0.012859592214226723, -0.06979109346866608, 0.015826193615794182, 0.014145237393677235, 0.056100618094205856, -0.0013089592102915049, -0.03191714733839035, -0.0080219442024827, -0.07873498648405075, 0.04365796223282814, -0.0065739392302930355, 0.03029758110642433, -0.031846512109041214, 0.016063863411545753, 0.058169174939394, 0.0061151194386184216, -0.011402055621147156, 0.004542517010122538, 0.032058436423540115, 0.07257185876369476, 0.035974226891994476, -0.06262274831533432, -0.023508233949542046, -0.011849747970700264, 0.00010248972830595449, -0.023491397500038147, -0.025247830897569656, 0.047869328409433365, 0.030587488785386086, 0.01389994565397501, -0.034674935042858124, 0.006914730649441481, -0.013132642023265362, 0.023844731971621513, -0.017720626667141914, -0.04395236074924469, 0.03735619783401489, 0.02687363140285015, -0.021909208968281746, 0.0004227719909977168, -0.11030986905097961, 0.030228322371840477, -0.01329142414033413, 0.009187715128064156, 0.05440249294042587, -0.028264185413718224, -0.035349734127521515, 0.026292378082871437, 0.00769623089581728, -0.01987338438630104, 2.024706367344848e-34, 0.01940324902534485, 0.02719035930931568, -0.013412708416581154, -0.007944042794406414, -0.011300371959805489, 0.0009142219787463546, -0.0018306626006960869, 0.022161167114973068, -0.014946216717362404, -0.0455196388065815, -0.012534840032458305]

['Rami Abousleiman', 'Guangzhi Qu', 'Osamah Rawashdeh']

1304.7851v2

The North Atlantic right whale (Eubalaena glacialis) is an endangered species. These whales continuously suffer from deadly vessel impacts alongside the eastern coast of North America. There have been countless efforts to save the remaining 350 - 400 of them. One of the most prominent works is done by Marinexplore and Cornell University. A system of hydrophones linked to satellite connected-buoys has been deployed in the whales habitat. These hydrophones record and transmit live sounds to a base station. These recording might contain the right whale contact call as well as many other noises. The noise rate increases rapidly in vessel-busy areas such as by the Boston harbor. This paper presents and studies the problem of detecting the North Atlantic right whale contact call with the presence of noise and other marine life sounds. A novel algorithm was developed to preprocess the sound waves before a tree based hierarchical classifier is used to classify the data and provide a score. The developed model was trained with 30,000 data points made available through the Cornell University Whale Detection Challenge program. Results showed that the developed algorithm had close to 85% success rate in detecting the presence of the North Atlantic right whale.

North Atlantic Right Whale Contact Call Detection

http://arxiv.org/pdf/1304.7851v2

Title North Atlantic Right Whale Contact Call Detection Summary North Atlantic right whale Eubalaena glacialis endangered specie whale continuously suffer deadly vessel impact alongside eastern coast North America countless effort save remaining 350 400 One prominent work done Marinexplore Cornell University system hydrophones linked satellite connectedbuoys deployed whale habitat hydrophones record transmit live sound base station recording might contain right whale contact call well many noise noise rate increase rapidly vesselbusy area Boston harbor paper present study problem detecting North Atlantic right whale contact call presence noise marine life sound novel algorithm developed preprocess sound wave tree based hierarchical classifier used classify data provide score developed model trained 30000 data point made available Cornell University Whale Detection Challenge program Results showed developed algorithm close 85 success rate detecting presence North Atlantic right whale Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.01751120761036873, 0.06920649111270905, -0.028089627623558044, -0.03919942304491997, 0.03211040794849396, 0.038661107420921326, 0.012041755020618439, 0.011163006536662579, -0.04414597153663635, -0.053507328033447266, -0.022613264620304108, 0.02521703951060772, 0.04146800935268402, 0.022461796179413795, -0.007533074822276831, -0.008279390633106232, 0.021887727081775665, -0.008475217036902905, 0.06346842646598816, 0.010044202208518982, -0.016847025603055954, -0.012597898952662945, -0.03803982958197594, 0.006987274624407291, -0.03102712333202362, 0.005623802077025175, -0.02595161832869053, -0.03239865601062775, 0.021900640800595284, -0.06589532643556595, 0.07475058734416962, -0.0076786186546087265, 0.0352201946079731, 0.06584256887435913, 2.0505249267444015e-06, -0.01260827574878931, 0.02263147383928299, -0.020372701808810234, 0.029518932104110718, -0.02458353340625763, 0.04632087051868439, -0.010527164675295353, -0.014577295631170273, -0.007001556921750307, 0.0223502479493618, -0.05424099788069725, 0.024504167959094048, -0.055233679711818695, 0.012132978066802025, 0.019205842167139053, -0.004013463854789734, -0.009564615786075592, -0.04285541549324989, 0.03626047074794769, 0.022526731714606285, 0.02797509729862213, 0.00911282654851675, -0.007699919398874044, -0.035909269005060196, -0.018561476841568947, 0.007683258503675461, 0.045021865516901016, 0.0061895097605884075, -0.0036701527424156666, 0.02391873113811016, 0.07941934466362, -0.06210656091570854, -0.01620115153491497, -0.006058140192180872, 0.023165710270404816, -0.008696855045855045, 0.011828376911580563, 0.017178975045681, 0.027199851348996162, -0.016332019120454788, -0.06797951459884644, -0.005461215041577816, 0.00980188138782978, -0.0168761033564806, -0.053650882095098495, -0.011854637414216995, 0.07591859251260757, -0.05964837968349457, -0.0037799770943820477, -0.015108030289411545, -0.02555840089917183, -0.001336828339844942, 0.010194671340286732, -0.011236070655286312, -0.027939487248659134, 0.021768588572740555, 0.00694539537653327, 0.02848503552377224, 0.02013879083096981, -0.047598131000995636, -0.038957785815000534, 0.041547615081071854, -0.05150192230939865, 0.04915976524353027, -0.05045618489384651, 0.0019496568711474538, -0.026328662410378456, -0.04280829057097435, 0.005161545239388943, 0.05451216921210289, -0.07940416038036346, -0.030621672049164772, -0.06020720303058624, 0.009041836485266685, 0.04755321145057678, -0.02087852545082569, 0.006757729221135378, -0.017546173185110092, 0.0037454082630574703, -0.002673668786883354, 0.0008904608548618853, 0.00735061289742589, -0.060208600014448166, 0.020503085106611252, -0.05415327847003937, -0.04946290701627731, -0.006201740819960833, 0.016916226595640182, 0.0663193017244339, 0.02958279848098755, 0.023403458297252655, 0.012587158940732479, 0.047562889754772186, 0.00024057102564256638, 0.018923088908195496, 0.0231443103402853, 0.026071807369589806, 0.011050923727452755, -0.024531379342079163, 0.00166305189486593, -0.01740645430982113, 0.0072540235705673695, -0.0018890626961365342, -0.06211424246430397, 0.014254871755838394, -0.010240459814667702, -0.005527735687792301, -0.056033745408058167, -0.025962477549910545, -0.00900320615619421, -0.06711442768573761, -0.05799524486064911, 0.13056400418281555, -0.016504617407917976, -0.03826049342751503, 0.02770586870610714, 0.04692324995994568, -0.03579475358128548, 0.03479098528623581, 0.08846691250801086, 0.0007680894923396409, 0.10587935894727707, 0.028962232172489166, 0.0370427742600441, -0.031892552971839905, 0.030117183923721313, -0.06664340198040009, -0.020992005243897438, 0.008862447924911976, -0.0521099679172039, -0.01847599633038044, -0.00600854167714715, 0.004426491912454367, -0.0454038567841053, 0.013063322752714157, 0.07409952580928802, -0.01952572539448738, 0.003155308775603771, -0.03143402561545372, 0.030066071078181267, -0.0012076442362740636, -0.0072940136305987835, -0.01910860650241375, 0.04932596534490585, 0.032033972442150116, -0.0770065039396286, -0.022719597443938255, 0.0006674889009445906, -0.005847877357155085, -0.08301001787185669, -0.05924336984753609, -0.025853324681520462, -0.002512918785214424, -0.023212408646941185, -0.03963298723101616, 0.013215546496212482, -0.0423494428396225, -0.11263053119182587, 0.003156420309096575, -0.004083719570189714, -0.03589779883623123, 0.01092543639242649, -0.01620946265757084, -0.012633153237402439, 0.004581559915095568, -0.006664977874606848, -0.0034179091453552246, 0.14930620789527893, -0.04485181346535683, -0.03829675167798996, -0.028866881504654884, 0.03812183439731598, -0.03635198995471001, -0.007036449853330851, -0.01298773754388094, -0.006412873975932598, -0.005505607463419437, 0.02687256596982479, 0.011327283456921577, -0.033212970942258835, 0.06131405010819435, 0.01299822237342596, -0.006740950513631105, 0.02045232616364956, 0.049953773617744446, 0.026864100247621536, -0.004102574195712805, -0.0223139189183712, 0.028496431186795235, 0.07063082605600357, 0.024877427145838737, -0.01731593906879425, 0.019580069929361343, 0.060106150805950165, 0.00512089254334569, 0.013509330339729786, 0.012765366584062576, 0.024629978463053703, -0.026343686506152153, -0.023986605927348137, 0.021013524383306503, 0.005209286231547594, 0.027473514899611473, -0.0181754007935524, -0.03651578724384308, 0.022108593955636024, 0.01201624609529972, -0.009552669711411, -0.0066797141917049885, -0.00584734883159399, -0.08497098088264465, 0.03852109983563423, 0.015445416793227196, 0.0036990807857364416, -0.007804591208696365, 0.006409491412341595, 0.03423474356532097, 0.03463713452219963, 0.03039257600903511, 0.006826093420386314, -0.0830041915178299, 0.007242685183882713, 0.051230091601610184, -0.056710384786129, 0.005104553420096636, 0.010305057279765606, -0.032648716121912, -0.07747598737478256, 0.009329589083790779, 0.05442964658141136, -0.03133942186832428, 0.01506731379777193, -0.007356029003858566, -0.014551480300724506, 0.004646604880690575, 0.009899397380650043, -0.028166741132736206, -0.04204589128494263, -0.00757021876052022, 0.01266846340149641, 0.038407452404499054, -0.0033143197651952505, -0.04089868813753128, -0.010423482395708561, -0.02007194049656391, -0.043124664574861526, -0.06163156405091286, -0.03012850508093834, -0.024299023672938347, 0.0061250547878444195, 0.005860817618668079, 0.03377263993024826, -0.10817455500364304, -0.04725169017910957, -0.006287524942308664, -0.014260409399867058, -0.017331378534436226, 0.0055184559896588326, -0.05382454767823219, 0.010533114895224571, 0.023673295974731445, -0.006674984935671091, 0.031981904059648514, 0.06057197228074074, -0.01138010062277317, -0.018899759277701378, 0.05420887470245361, -0.028618289157748222, 0.036213986575603485, -0.016506198793649673, -0.010551255196332932, 0.027518443763256073, 0.0077391439117491245, -0.030111076310276985, 0.0476798415184021, -0.04811175540089607, 0.0017595369135960937, 0.04664527624845505, 0.0006887147901579738, 0.017179984599351883, -0.027773775160312653, -0.03784104064106941, -0.01785392314195633, 0.005346385296434164, -0.002353365533053875, 0.012725531123578548, -0.04467153549194336, -0.04813450947403908, 0.04312780871987343, -0.038288768380880356, -0.02386302687227726, -0.046396929770708084, 0.028980297967791557, 0.059401582926511765, 0.0026193258818238974, -0.004164859652519226, 0.008367839269340038, -0.053210869431495667, 0.07555297017097473, -0.05304659903049469, 0.0362100787460804, -0.015166299417614937, -0.07096904516220093, -0.02473459392786026, 0.03154749050736427, 0.005968352779746056, 0.0196191668510437, -0.061311859637498856, 0.06576565653085709, -0.01619134098291397, -0.01677580736577511, -0.008725166320800781, -0.028455451130867004, 0.011163952760398388, 0.03118487447500229, 0.02801096811890602, -0.009430053643882275, 0.04210108518600464, -0.00276445341296494, -0.021464375779032707, 0.04023769125342369, 0.04365524649620056, 0.026396898552775383, 0.035873714834451675, 0.07778936624526978, 0.057481758296489716, -0.01268021110445261, -0.07126840949058533, 0.027069145813584328, -0.04987604543566704, 0.03853446990251541, 0.04183139652013779, 0.018268348649144173, -0.005413101054728031, 0.007386527024209499, 0.06045955419540405, 0.008223324082791805, 0.0017640774603933096, 0.014215289615094662, 0.018157267943024635, -0.014077440835535526, 0.008910097181797028, -0.005907396785914898, 0.016720149666070938, 0.048998404294252396, -0.008096570149064064, 0.05356281250715256, 0.018534841015934944, -0.016107795760035515, 0.003536528442054987, -0.011713583022356033, -0.0003195038007106632, 0.0028640255331993103, -0.07919572293758392, 0.05547323450446129, 0.0065618460066616535, -0.05404726788401604, -0.0077027385123074055, -0.08122114092111588, -0.017717786133289337, -0.05052288994193077, 0.007674665190279484, 0.048497460782527924, 0.028976554051041603, -0.027876947075128555, 0.014687729068100452, -0.07653846591711044, 0.04144718870520592, -0.002179940929636359, -0.03983476385474205, 0.028461046516895294, 0.02077605575323105, 0.05915209278464317, -0.07037869095802307, -0.08653391897678375, -0.005140143912285566, 0.010250016115605831, 0.0044319164007902145, 0.015111313201487064, -0.030737314373254776, 0.01499045081436634, 0.011699924245476723, -0.020160814747214317, 0.045435551553964615, -0.012568938545882702, 0.02743516117334366, 0.07609501481056213, 0.03851030766963959, -0.014988926239311695, -0.012240554206073284, -0.043317705392837524, 0.09811592102050781, 0.02477889508008957, 0.02501828595995903, 0.025748008862137794, 0.008831645362079144, -0.030441107228398323, 0.03916440159082413, 0.014936156570911407, 0.02639579400420189, 0.06773663312196732, 0.05021534487605095, -0.025419287383556366, -0.09756296873092651, -0.08047962933778763, 0.015888415277004242, 0.0070328665897250175, 0.002541434485465288, 0.024322405457496643, 0.06754940748214722, 0.005783480126410723, -0.01752440072596073, -0.014076021499931812, 0.03185654804110527, 0.011418960988521576, 0.04387926310300827, -0.028264224529266357, 0.010533333756029606, 0.0067344531416893005, 0.03230707347393036, -0.006325238849967718, 0.027600008994340897, 0.008603420108556747, 0.003508326131850481, 0.025592222809791565, 0.010722288861870766, 0.0038874056190252304, -0.0050300611183047295, -0.04579082876443863, -0.030165042728185654, -0.11677180230617523, 0.08583366870880127, -0.06633064895868301, -0.01133231446146965, 0.041581686586141586, 0.014221458695828915, 0.01124532613903284, -0.03020837903022766, -0.005333213601261377, 0.07523434609174728, -0.021394478157162666, -0.025391671806573868, -0.07415087521076202, -0.017651833593845367, 0.011823699809610844, 0.02459547482430935, 0.053197335451841354, -0.04146679863333702, -0.05723695456981659, 0.0009162289788946509, 0.017169177532196045, 0.037434305995702744, 0.017118927091360092, -0.011529886163771152, 0.026644267141819, 0.00010337220737710595, 0.04709073156118393, -0.026943005621433258, 0.013626440428197384, -0.03454968333244324, -0.0011930534383282065, 0.007778318598866463, 0.08789071440696716, 0.06347967684268951, -0.020653080195188522, -0.023965127766132355, -0.04060482978820801, -0.0076743499375879765, 0.020555146038532257, 0.010437184013426304, 0.03310208022594452, 0.03545570746064186, -0.026158014312386513, 0.0028819239232689142, -0.02568744868040085, 0.004072298761457205, -0.03274855017662048, 0.024982910603284836, 0.010498963296413422, 0.036200184375047684, 0.02596534602344036, 0.01863870583474636, -0.02801324427127838, -0.04859485104680061, 0.018730726093053818, -0.026172839105129242, 0.0012098223669454455, 0.020318729802966118, -0.028910411521792412, 0.005719655193388462, 0.0037134287413209677, 0.0526050366461277, -0.04265681281685829, 0.023913536220788956, -0.042798880487680435, -0.015420805662870407, 0.020920073613524437, 0.001444474677555263, -0.025201957672834396, -0.0032601782586425543, 0.009091158397495747, 0.10413596779108047, 0.05887226760387421, -0.02554774284362793, 0.023133238777518272, -0.01225376222282648, -0.028310200199484825, -0.010850395075976849, 0.01950385980308056, 0.034204259514808655, 0.02074350416660309, 0.03259953111410141, -0.031418658792972565, -0.010874575935304165, -0.0414365716278553, 0.031201645731925964, -0.023686222732067108, 0.03051813133060932, 0.025238148868083954, -0.007421333342790604, -4.9443445019615356e-33, -0.04083390533924103, -0.032768312841653824, -0.01722087524831295, -0.022905582562088966, -0.03778965026140213, 0.03976234793663025, 0.04977944493293762, -0.008222514763474464, 0.056685466319322586, -0.007147257681936026, 0.023630771785974503, -0.01204158365726471, 0.0004861367342527956, -0.011832892894744873, 0.002513783285394311, 0.037989623844623566, -0.006374094635248184, -0.03003538027405739, 0.02844061516225338, -0.05143514648079872, 0.014808434061706066, 0.0259122084826231, 0.018738187849521637, -0.0453459732234478, -0.031686365604400635, 0.01642831601202488, -0.037669118493795395, -0.014894651249051094, -0.06554247438907623, 0.03183884918689728, 0.0002451301261316985, 0.03273186832666397, -0.0380864143371582, 0.011663009412586689, 0.009984875097870827, -0.0028374933172017336, -0.060471873730421066, -0.028523974120616913, 0.02535560168325901, 0.01786886528134346, 0.05454448238015175, 0.04161154478788376, 0.048700835555791855, -0.010337036103010178, -7.135181658668444e-05, 0.0008582787704654038, 0.04579827934503555, -0.05858100205659866, 0.018365012481808662, -0.047999005764722824, -0.027896985411643982, 0.0062636639922857285, -0.031321022659540176, -0.044413939118385315, -0.00833221897482872, -0.0006611383869312704, -0.034351740032434464, 0.007741790264844894, -0.06274043023586273, 0.05592985823750496, 0.04933743551373482, 0.0211823508143425, -0.02794153057038784, 0.002336455974727869, -0.0091312937438488, 0.015653155744075775, 0.051976535469293594, -0.04115508869290352, -0.012304394505918026, 0.01860211230814457, -0.008345452137291431, 0.06869454681873322, 0.024214034900069237, 0.020600615069270134, 0.058333564549684525, -0.03161712363362312, -0.03873790428042412, 0.03060169145464897, 0.03741266950964928, -0.02973567135632038, -0.037670958787202835, 0.02889828383922577, -0.033931270241737366, 0.017946725711226463, 0.01014601532369852, -0.04536721110343933, 0.012197447940707207, 0.0480431467294693, 0.0030131719540804625, -0.017933376133441925, 0.00732334004715085, -0.0472608245909214, -0.009780306369066238, -0.0057762302458286285, 0.04657050222158432, -0.07484310865402222, 0.04731136932969093, -0.027638010680675507, 0.03519449755549431, -0.02328687720000744, 0.04119974002242088, -0.009368810802698135, 0.09092456102371216, -0.050670504570007324, 0.03048940934240818, -0.04604911059141159, 0.06664519011974335, 0.0054717459715902805, -0.016160935163497925, -0.02303583174943924, 0.016696788370609283, -0.020541531965136528, 0.011846842244267464, 0.007893006317317486, 0.0013886060332879424, -0.06232867389917374, 0.012172939255833626, -6.873694474052172e-06, 0.026029853150248528, 0.007852362468838692, -0.028557127341628075, 0.006339184939861298, -0.08810723572969437, 0.053598858416080475, -0.037631768733263016, -0.028869209811091423, 0.00774502893909812, -0.022861825302243233, -0.012834766879677773, 0.003830940928310156, -0.024916667491197586, 0.0010459879413247108, 2.638790874698316e-07, -0.05207168683409691, -0.05336473882198334, 0.011534688994288445, -0.04550493508577347, 0.06898923218250275, -0.0027225336525589228, 0.025196678936481476, -0.030068915337324142, -0.00823300238698721, -0.042833033949136734, 0.03702133148908615, -0.05381748080253601, 0.002450420521199703, -0.01740914396941662, -0.03619625046849251, -0.020439306274056435, -0.01619870774447918, -0.0842999741435051, -0.06440181285142899, 0.0008796884212642908, 0.010191667824983597, 0.017758917063474655, 0.027440514415502548, -0.0643407329916954, 0.0072411722503602505, 0.041821349412202835, -0.04235813394188881, -0.08756225556135178, -0.007084723096340895, -0.05287226289510727, 0.020451899617910385, -0.002032789634540677, 0.015128693543374538, 0.052705179899930954, 0.0022082084324210882, -0.05108796805143356, 0.007602296769618988, 0.039466552436351776, -0.008068240247666836, 0.057937100529670715, -0.008863902650773525, 0.08243574947118759, -0.006851990707218647, -0.04132605716586113, 0.050039201974868774, -0.006231749430298805, 0.012794389389455318, -0.0351984016597271, -0.017590312287211418, -0.005196256097406149, 0.031218182295560837, -0.035973407328128815, 0.029399968683719635, -0.039607927203178406, 0.03338875621557236, -0.015732290223240852, -1.6297452020808123e-05, 0.0492553673684597, 0.05468299984931946, 0.01737235113978386, 0.013312086462974548, -0.017775824293494225, 0.005869738757610321, 0.007445594761520624, 0.034436289221048355, -0.02836170606315136, -0.023226836696267128, 1.8136120331380173e-34, -0.0016893239226192236, 0.014321528375148773, -0.0060313488356769085, 0.005303673911839724, -0.006742139812558889, 0.0224298145622015, 0.027668297290802002, -0.0038129014428704977, 0.030181169509887695, 0.008770755492150784, 0.002411173190921545]

['Aleksandrs Slivkins']

1306.0155v1

We consider an application of multi-armed bandits to internet advertising (specifically, to dynamic ad allocation in the pay-per-click model, with uncertainty on the click probabilities). We focus on an important practical issue that advertisers are constrained in how much money they can spend on their ad campaigns. This issue has not been considered in the prior work on bandit-based approaches for ad allocation, to the best of our knowledge. We define a simple, stylized model where an algorithm picks one ad to display in each round, and each ad has a \emph{budget}: the maximal amount of money that can be spent on this ad. This model admits a natural variant of UCB1, a well-known algorithm for multi-armed bandits with stochastic rewards. We derive strong provable guarantees for this algorithm.

Dynamic Ad Allocation: Bandits with Budgets

http://arxiv.org/pdf/1306.0155v1

Title Dynamic Ad Allocation Bandits Budgets Summary consider application multiarmed bandit internet advertising specifically dynamic ad allocation payperclick model uncertainty click probability focus important practical issue advertiser constrained much money spend ad campaign issue considered prior work banditbased approach ad allocation best knowledge define simple stylized model algorithm pick one ad display round ad emphbudget maximal amount money spent ad model admits natural variant UCB1 wellknown algorithm multiarmed bandit stochastic reward derive strong provable guarantee algorithm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.06592494249343872, 0.042505376040935516, -0.03081665188074112, -0.07167617976665497, 0.008459684439003468, -0.03762124478816986, 0.02816993184387684, -0.012552228756248951, -0.00460441317409277, -0.04229958355426788, -0.028953485190868378, -0.04189458116889, -0.0351698100566864, 0.08391334116458893, 0.007550724782049656, -0.06983302533626556, -0.02055998332798481, -0.050566934049129486, 0.014674431644380093, -0.02291836403310299, 0.07454033941030502, -0.06294231116771698, -0.019921395927667618, -0.0048958053812384605, 0.04826228320598602, -0.004216285888105631, -0.035133469849824905, -0.012813284061849117, 0.0015568943927064538, -0.0700889304280281, 0.03546705096960068, 0.005045596044510603, 0.029098888859152794, 0.019547756761312485, 2.049865997832967e-06, -0.06347744166851044, -0.02186237834393978, -0.028846291825175285, -0.012873202562332153, 0.0653238371014595, 0.0265219584107399, 0.04151296615600586, 0.05545227229595184, 0.037879638373851776, 0.009456736035645008, 0.06862088292837143, -0.0021436873357743025, 0.04692201316356659, -0.031225884333252907, 0.004110634792596102, 0.011517145670950413, -0.03404443711042404, -0.005603516474366188, -0.04002540931105614, -0.002140628406777978, -0.06805983930826187, -0.0042249769903719425, -0.0376538448035717, -0.03724652901291847, -0.05886799842119217, 0.017738377675414085, 0.018411338329315186, -0.032256193459033966, -0.030662070959806442, 0.022922804579138756, -0.0016934899613261223, 3.986642695963383e-05, -0.03321566432714462, -0.035914577543735504, -0.035408616065979004, 0.007435020990669727, 0.040997035801410675, 0.05402806028723717, 0.001842948840931058, -0.01569526642560959, -0.00304254493676126, -0.017507966607809067, 0.044707633554935455, -0.028257127851247787, 0.009680897928774357, 0.0016931922873482108, 0.004208646714687347, 0.00607983348891139, 0.04072254151105881, 0.006536458618938923, 0.026240529492497444, -0.056151825934648514, -0.011729373596608639, -0.016216130927205086, 0.024189069867134094, -0.01786968857049942, -0.014296614564955235, 0.01858874224126339, -0.03701359033584595, -0.023634236305952072, 0.02049524523317814, 0.017049865797162056, 0.007665400393307209, 0.040401894599199295, 0.008585178293287754, 0.10208798944950104, -0.04737521708011627, 0.03117178939282894, 0.02127174101769924, 0.011653394438326359, 0.021454516798257828, -0.07102397829294205, -0.009347815997898579, 0.02317493036389351, 0.06971020996570587, -0.0025739187840372324, -0.002930565970018506, -0.009827612899243832, 0.03318604454398155, 0.02663361094892025, -0.0014943378046154976, -0.07723408192396164, 0.06628584116697311, -0.0036143737379461527, 0.013027197681367397, 0.03482578694820404, -0.003533699316903949, 0.026951521635055542, 0.010952148586511612, -0.018533790484070778, -0.05067266896367073, -0.05969393625855446, 0.015391649678349495, 0.01357631292194128, 0.03348762169480324, 0.028031855821609497, 0.054868292063474655, -0.04599611088633537, -0.04695103317499161, -0.028414053842425346, 0.07234612852334976, 0.011446250602602959, 0.05055663362145424, -0.07833704352378845, -0.06795695424079895, -0.03358011692762375, 0.032343316823244095, -0.0414445735514164, -0.02727215737104416, -0.011399507522583008, -0.017504755407571793, -0.039965156465768814, 0.0433342345058918, -0.02556021697819233, -0.02943381667137146, -0.02383919432759285, -0.0017407466657459736, 0.07929801195859909, 0.01405518688261509, -0.0026107316371053457, -0.026577185839414597, -0.018105508759617805, -0.0033916498068720102, 0.024294286966323853, 0.09550837427377701, 0.055072981864213943, 0.022822823375463486, -0.03474117070436478, -0.006030348129570484, 0.01945686526596546, 0.04024669528007507, 0.012855947017669678, 0.008587946183979511, 0.023874381557106972, -0.0013988318387418985, -0.012088315561413765, -0.027988102287054062, -0.01212356984615326, -0.005785031709820032, 0.049092479050159454, -0.04593563452363014, 0.05880014970898628, -0.060280464589595795, 0.024193808436393738, -0.0004187529266346246, -0.040145520120859146, -0.042653102427721024, -0.01320667378604412, 0.017706619575619698, -0.035501353442668915, -0.01893349550664425, 0.01773923821747303, -0.010138762183487415, -0.020308738574385643, 0.021134620532393456, 0.003701648907735944, 0.021188700571656227, -0.014220373705029488, 0.07043332606554031, 0.015816237777471542, -0.03565056994557381, -0.0007489578565582633, -0.03859119489789009, -0.00570566114038229, 0.07672793418169022, 0.014818040654063225, -0.051738157868385315, 0.029656464233994484, -0.0100273247808218, 0.02213462069630623, -0.01923922449350357, 0.03301212564110756, -0.036785975098609924, 0.00032097173971123993, -0.030498269945383072, 0.07889341562986374, -0.009445346891880035, 0.003453081240877509, 0.016017816960811615, -0.02611173503100872, -0.014449878595769405, 0.01397704891860485, 0.04554001986980438, -0.00022162155073601753, 0.03730262070894241, -0.026036715134978294, 0.01775682531297207, 0.07376936078071594, -0.01836550235748291, 0.03144213184714317, -0.0468013696372509, 0.0537012480199337, -0.012365961447358131, 0.044073499739170074, -0.04955263435840607, 0.0037156420294195414, -0.01511411927640438, 0.011055738665163517, -0.0016393166733905673, -0.02306663617491722, -0.027808725833892822, 0.0796632245182991, 0.014541990123689175, 0.02004264108836651, -0.0027724471874535084, 0.02734866738319397, 0.020636912435293198, -0.01159836258739233, -0.024620039388537407, 0.0817796066403389, -0.028853805735707283, -0.006760390475392342, -0.0004225489974487573, 0.017095061019062996, 0.024485468864440918, 0.022348470985889435, -0.018773164600133896, 0.029400916770100594, 0.04331601783633232, -0.013173237442970276, 0.011832614429295063, 0.000547239207662642, 0.0036099334247410297, -0.10539279133081436, 0.05123244971036911, -0.06381721794605255, 0.0008332070428878069, -0.004390368703752756, -0.006971925962716341, 0.010352361015975475, -0.0011371925938874483, -0.013769222423434258, 0.020315561443567276, 0.036552947014570236, 0.030314819887280464, 0.027733976021409035, 0.0008157403208315372, -0.019687986001372337, -0.003256655763834715, -0.02836603857576847, 0.004445964004844427, -0.02836558222770691, -0.02599409967660904, 0.02134281024336815, 0.020757803693413734, 0.017735159024596214, 0.014203512109816074, 0.02663576602935791, -0.02031986601650715, -0.009285654872655869, 0.00047642452409490943, 0.07930794358253479, -0.039018917828798294, -0.02401500940322876, -0.0561765618622303, -0.022771431133151054, 0.011105081997811794, -0.007252924609929323, -0.013788961805403233, -0.06120216101408005, 0.005566115025430918, -0.05285511538386345, 0.03933315724134445, 0.02204953506588936, 0.0077547053806483746, -0.006928902119398117, 0.003763052634894848, -0.055009566247463226, -0.002252088626846671, 0.025699874386191368, 0.01691882126033306, 0.010513978078961372, -0.015705881640315056, 0.07931022346019745, 0.07824263721704483, 0.04557094722986221, 0.022987645119428635, 0.026354625821113586, 0.02523791790008545, 0.03335192799568176, -0.035740867257118225, -0.09225146472454071, 0.04145001247525215, -0.01786266267299652, 0.0649886503815651, 0.0011445553973317146, -0.02639808878302574, 0.07794204354286194, 0.0447096973657608, 0.015483962371945381, 0.055727943778038025, -0.049042895436286926, 0.000914186704903841, -0.09296369552612305, -0.01060902513563633, 0.048470329493284225, -0.005030592437833548, -0.020211482420563698, -0.022568779066205025, -0.003333129221573472, 0.11325891315937042, -0.016985103487968445, -0.0020327535457909107, 0.05803941562771797, -0.03055170737206936, -0.03747796267271042, -0.045547954738140106, -0.03226735070347786, -0.0994039997458458, 0.04524792358279228, -0.03857167437672615, 0.029105165973305702, -0.007149599492549896, -0.10182780772447586, 0.025429222732782364, 0.02295440435409546, 0.0340307392179966, -0.011310495436191559, -0.004998143762350082, 0.0388212651014328, 0.07367949187755585, -0.005400797817856073, -0.05298950523138046, -0.03667393699288368, -0.0381750762462616, 0.003658395493403077, 0.011788574978709221, 0.02625029720366001, 0.03498366102576256, -0.0019315878162160516, 0.07328306138515472, 0.04699789360165596, -0.05358733609318733, -0.022492697462439537, 0.016705503687262535, -0.026766855269670486, 0.0028844624757766724, 0.056601278483867645, 0.008564350195229053, 0.010697921738028526, -0.03292585536837578, -0.022385070100426674, -0.016125135123729706, 0.04018064960837364, -0.010932724922895432, 0.04740700498223305, -0.05999673902988434, -0.014809216372668743, -0.01570744253695011, 0.08273040503263474, -0.0209009051322937, -0.05656074360013008, -0.006719999015331268, -0.04105180874466896, 0.025259489193558693, -0.0299160685390234, 0.01844961754977703, 0.05541049689054489, -0.0709637776017189, -0.008559409528970718, -0.06445781886577606, -0.04586204141378403, 0.05602949857711792, -0.005811858922243118, 0.015558705665171146, 0.028818275779485703, -0.013033442199230194, 0.03898687660694122, -0.024452820420265198, -0.04093669727444649, 0.018287593498826027, 0.024602454155683517, -0.000984800048172474, -0.006090281996876001, -0.004629954230040312, -0.051092904061079025, 0.0009337210794910789, -0.026543378829956055, 0.0508127324283123, 0.06274483352899551, 0.0007012537680566311, 0.0302065908908844, 0.004536045249551535, -0.0010734148090705276, -0.010314320214092731, 0.016132518649101257, 0.07740621268749237, 0.033340852707624435, 0.03059549815952778, -0.028832830488681793, -0.030266843736171722, -0.012630895711481571, 0.02266792580485344, 0.022006776183843613, -0.029129235073924065, -0.04833959415555, -0.015105433762073517, -0.024143580347299576, -0.040591076016426086, -0.05559445917606354, 0.025083379819989204, 0.0030928219202905893, -0.003958370536565781, 0.02217916212975979, -0.06703691929578781, 0.03695688024163246, -0.06449978053569794, 0.053384553641080856, 0.015141638927161694, -0.012561886571347713, -0.09262387454509735, -0.0020359326153993607, -0.01050653401762247, -0.040763914585113525, 0.007581356912851334, -0.007863931357860565, -0.04454166069626808, 0.04979381337761879, 0.01823534071445465, -0.10313735157251358, -0.0640312135219574, 0.00398826040327549, -0.05402158945798874, -0.03387569263577461, -0.02428162842988968, 0.024112971499562263, 0.011994333937764168, 0.012388573959469795, -0.04382302984595299, 0.011248638853430748, -0.015481249429285526, -0.016753124073147774, 0.09237446635961533, -0.029040426015853882, 0.0020807108376175165, 0.06175472214818001, -0.012190887704491615, -0.009568103589117527, -0.039889857172966, 0.01159766223281622, 0.025088028982281685, -0.057955551892519, -0.027506941929459572, 0.02153516560792923, 0.0011878875084221363, 0.021706292405724525, 0.0076500182040035725, 0.0003030872903764248, -0.027401257306337357, 0.017241433262825012, 0.020337289199233055, 0.05535764992237091, -0.03666236996650696, -0.046159565448760986, -0.005658354144543409, 0.046649131923913956, 0.012722603045403957, 0.04939786344766617, -0.001538642100058496, 0.007645462639629841, -0.0732211321592331, 0.010224082507193089, -0.014637377113103867, 0.01046680100262165, 0.06637711077928543, 0.0005287434905767441, 0.027504708617925644, 0.0613076277077198, 0.04616347700357437, 0.025118175894021988, 0.05959289148449898, -0.02830752357840538, -0.01695355772972107, -0.001327452715486288, 0.0064936126582324505, 0.015371630899608135, -0.036995068192481995, 0.023087723180651665, -0.01933404430747032, -0.01822545751929283, 0.0021467634942382574, 0.0006624784437008202, -0.002074015326797962, 0.02365076169371605, -0.013409142382442951, 0.019762763753533363, 0.033813875168561935, -0.002431736560538411, -0.032318539917469025, -0.00635013310238719, 0.0028471543919295073, 0.05007642135024071, 0.018582480028271675, 0.04057183489203453, 0.05008822679519653, 0.03726653382182121, -0.007506181951612234, -0.07609960436820984, -0.0827726274728775, -0.006820414215326309, 0.009062782861292362, 0.04609993100166321, 0.05501743033528328, -0.021748526021838188, 0.003001877572387457, -0.009251931682229042, 0.016193240880966187, -0.025596503168344498, -0.049174048006534576, 0.07321988046169281, 0.005108978133648634, 0.0005827967543154955, -0.014971848577260971, -0.004172328393906355, 0.07831637561321259, -0.04628853127360344, -0.011857683770358562, -0.02962806075811386, 0.002710670465603471, -0.0625392347574234, -6.1195280814648245e-33, 0.031104495748877525, -0.021536752581596375, -0.05117041617631912, -0.08007410913705826, -0.021254578605294228, -0.02635456994175911, 0.047194402664899826, -0.029424337670207024, 0.05140729993581772, -0.0658135786652565, -0.027825387194752693, -0.028281813487410545, 0.036919206380844116, 0.020405247807502747, 0.04167892783880234, 0.013817074708640575, -0.027131808921694756, -0.0029549666214734316, -0.06801121681928635, 0.004553348757326603, 0.01955629512667656, 0.030799254775047302, -0.020095815882086754, 0.009696808643639088, -0.0011691802646964788, 0.02440507337450981, -0.0337747223675251, 0.006764269899576902, 0.023753603920340538, 0.033272698521614075, 0.014593592844903469, 0.0005294897709973156, -0.003863613586872816, -0.00816752016544342, 0.0271136537194252, -0.026929954066872597, -0.0007332778768613935, -0.009173563681542873, 0.019718201830983162, 0.02453562244772911, 0.02010492794215679, 0.0014815712347626686, 0.03694881126284599, -0.013162520714104176, -0.008598423562943935, 0.01382233202457428, 0.044787295162677765, -0.030524099245667458, -0.002290976932272315, 0.0051634241826832294, 0.01893523707985878, 0.005388099234551191, -0.0325302854180336, 0.043887846171855927, -0.010270546190440655, 0.038671959191560745, -0.019268393516540527, 0.02429375611245632, -0.0220013540238142, 0.043977975845336914, -0.00021878663392271847, 0.017755672335624695, 0.0026254181284457445, 0.03898235782980919, 0.01733868010342121, 0.017217179760336876, -0.010176941752433777, -0.018461652100086212, 0.022141147404909134, -0.05107184126973152, -0.06560607999563217, -0.014458687044680119, -0.0018831705674529076, 0.06639232486486435, 0.07102701812982559, 0.004211912397295237, 0.04101775586605072, 0.021065589040517807, 0.08806423842906952, -0.05815025791525841, 0.02202901989221573, 0.005755497608333826, -0.009716430678963661, -0.00875591579824686, 0.004535345360636711, -0.061691686511039734, -0.017569182440638542, -0.07160082459449768, 0.06635967642068863, 0.03318174555897713, 0.01565403677523136, 0.019417058676481247, -0.0068547665141522884, -0.02738090045750141, -0.01691688597202301, -0.034796860069036484, 0.03532429039478302, 0.04230305552482605, -0.01782969944179058, -0.02113531343638897, -0.003677129512652755, -0.04169953614473343, -0.045471832156181335, 0.024914618581533432, -0.03774559870362282, 0.003958761692047119, 0.00019152356253471226, 0.009986622259020805, 0.007323183584958315, 0.04375399649143219, 0.03197868913412094, -0.03479541093111038, 0.01680922880768776, 0.04295515641570091, -0.00944141112267971, -0.06903699785470963, -0.029211312532424927, -0.021798713132739067, 0.03497948497533798, -0.04803086072206497, 0.009716923348605633, -0.05731505528092384, -0.06713946908712387, 0.0020720320753753185, -0.026239948347210884, 0.005003883969038725, -0.043651651591062546, -0.033207233995199203, -0.022985853254795074, -0.054434917867183685, -0.001937044900842011, -0.06926650553941727, 2.705095596411411e-07, -0.021549027413129807, 0.016504526138305664, -0.07269768416881561, 0.00043825802276842296, 0.030659522861242294, 0.01043691486120224, -0.026657624170184135, 0.01927756518125534, 0.004400619771331549, 0.04012851044535637, 0.011765437200665474, -0.03550514578819275, 0.007462659385055304, 0.01626557484269142, -0.020437592640519142, 0.004995324183255434, -0.04402986913919449, 0.05881112068891525, 0.0025848406367003918, 0.013096623122692108, -0.05878602713346481, 0.03672712668776512, 0.07432616502046585, -0.015410220250487328, 0.013736982829868793, -0.047424230724573135, -0.00949182640761137, 0.01436226349323988, -0.022863689810037613, -0.00863428320735693, -0.014605981297791004, 0.019295956939458847, -0.04173162579536438, -0.013695571571588516, -0.031174279749393463, 0.020984305068850517, 0.03286721929907799, 0.026764070615172386, 0.06913776695728302, 0.021292198449373245, -0.0006753308116458356, -0.05354740843176842, 0.03147001191973686, -0.04447494447231293, -0.006436290219426155, 0.0009428602643311024, -0.02176676318049431, 0.006054998841136694, -0.0028111315332353115, -0.08708883076906204, 0.011519890278577805, -0.03684027120471001, 0.0179933849722147, -0.006804150529205799, -0.03908388689160347, 0.007286240812391043, 0.0008606518968008459, 0.0002117209369316697, -0.0006923917098902166, 0.037422437220811844, -0.017199335619807243, 0.008593734353780746, 0.01358458586037159, 0.06384695321321487, 0.01936078444123268, -0.09642860293388367, 0.012787464074790478, 2.6868942479979575e-34, 0.031351376324892044, -0.0012926248600706458, -0.026843931525945663, -0.030552130192518234, 0.007984030060470104, 0.018697883933782578, 0.017188986763358116, -0.010456826537847519, 0.08612110465765, -0.003326170612126589, -0.026452312245965004]

['Marina Danilevsky', 'Chi Wang', 'Nihit Desai', 'Jingyi Guo', 'Jiawei Han']

1306.0271v1

We introduce KERT (Keyphrase Extraction and Ranking by Topic), a framework for topical keyphrase generation and ranking. By shifting from the unigram-centric traditional methods of unsupervised keyphrase extraction to a phrase-centric approach, we are able to directly compare and rank phrases of different lengths. We construct a topical keyphrase ranking function which implements the four criteria that represent high quality topical keyphrases (coverage, purity, phraseness, and completeness). The effectiveness of our approach is demonstrated on two collections of content-representative titles in the domains of Computer Science and Physics.

KERT: Automatic Extraction and Ranking of Topical Keyphrases from Content-Representative Document Titles

http://arxiv.org/pdf/1306.0271v1

Title KERT Automatic Extraction Ranking Topical Keyphrases ContentRepresentative Document Titles Summary introduce KERT Keyphrase Extraction Ranking Topic framework topical keyphrase generation ranking shifting unigramcentric traditional method unsupervised keyphrase extraction phrasecentric approach able directly compare rank phrase different length construct topical keyphrase ranking function implement four criterion represent high quality topical keyphrases coverage purity phraseness completeness effectiveness approach demonstrated two collection contentrepresentative title domain Computer Science Physics Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.07744073122739792, -0.015339476056396961, -0.022575434297323227, 0.0005857402575202286, -0.03937961533665657, 0.011276140809059143, 0.0292917862534523, 0.023563673719763756, 0.0008438429213128984, -0.04994796961545944, 0.013494095765054226, 0.058537885546684265, 0.0057024587877094746, 0.057303693145513535, -0.0038511152379214764, -0.0782884955406189, 0.03433912992477417, 0.005674820858985186, 0.006808317732065916, 0.009866097010672092, 0.004540320951491594, -0.0006214979803189635, -0.005884692072868347, 0.014325795695185661, 0.06551388651132584, -0.017789719626307487, 0.0030870852060616016, -0.05450572073459625, 0.004440180491656065, -0.06395295262336731, 0.05722907930612564, 0.02889852598309517, -0.021476371213793755, 0.009635820984840393, 2.084343577735126e-06, -0.06611832976341248, -0.052227672189474106, 0.005975829437375069, 0.05538375675678253, 0.06772151589393616, 0.08951658755540848, -0.00981888547539711, 0.006881904322654009, -0.009335767477750778, -0.0016518778866156936, 0.02517513744533062, -0.0012200138298794627, 0.02674289420247078, -0.006825582589954138, -0.003111328464001417, -0.011459670029580593, -0.03957851976156235, -0.006947232410311699, 0.008917135186493397, 0.00859940703958273, -0.032082244753837585, 0.005861507263034582, 0.026367202401161194, 0.028429623693227768, 0.05937420576810837, 0.002810758538544178, 0.026295281946659088, -0.048962224274873734, -0.02490866370499134, 0.07235918939113617, 0.047543320804834366, -0.08332771062850952, -0.027586840093135834, 0.008894609287381172, 0.035569511353969574, 0.055673982948064804, 0.0001399262109771371, 0.08288078010082245, -0.00884395744651556, -0.02528262883424759, 0.06379933655261993, -0.06652738153934479, 0.004208222031593323, -0.022473229095339775, -0.04957166686654091, -0.0014735645381733775, 0.044878676533699036, -0.04088914394378662, 0.019631685689091682, -0.004520272370427847, 0.010782831348478794, 0.022652583196759224, -0.0485152006149292, 0.03332417830824852, -0.030619025230407715, 0.00744264991953969, -0.046571049839258194, 0.023032870143651962, -0.025417501106858253, 0.0914115160703659, 0.004018883220851421, 0.022908607497811317, -0.035755548626184464, 0.11376764625310898, -0.10337919741868973, -0.014756026677787304, -0.042467933148145676, 0.003689749399200082, 0.042352404445409775, 0.026746710762381554, 0.001914396183565259, 0.026864612475037575, -0.02725788578391075, -0.006429388653486967, 0.044079143553972244, -0.05524115264415741, -0.050315603613853455, -0.0035500742960721254, 0.040341656655073166, 0.026720134541392326, -0.038227375596761703, -0.05114603042602539, -0.006594853010028601, 0.0323592834174633, 0.016418561339378357, -0.037092071026563644, 0.03907741978764534, -0.042321816086769104, -0.030019069090485573, 0.016923466697335243, 0.01051715575158596, -0.01414176169782877, 0.007689537014812231, -0.004021083936095238, 0.007157627027481794, 0.014158463105559349, 0.011521903797984123, 0.03386509791016579, 0.005836171563714743, 0.014320041052997112, -0.006047689821571112, 0.006697888020426035, -0.059851083904504776, 0.02493194490671158, -0.03618541359901428, -0.02483770251274109, 0.04724293202161789, 0.033875949680805206, -0.05639170482754707, 0.03198661655187607, 0.006997774355113506, 0.004705762956291437, 0.010610803961753845, 0.003109210403636098, 0.024220528081059456, -0.04059045389294624, 0.031369827687740326, -0.03588557615876198, -0.010888497345149517, 0.08296506851911545, 0.02906966395676136, 0.02037705108523369, -0.038914356380701065, -0.03276332840323448, 0.050063442438840866, 0.06386886537075043, -0.030125800520181656, 0.02890593931078911, -0.03461208567023277, -0.011115341447293758, 0.002693351125344634, 0.031599465757608414, 0.04474937543272972, -0.0190290417522192, -0.021699177101254463, -0.05758272856473923, 0.007467729039490223, -0.02787155844271183, 0.053846534341573715, -0.00509867025539279, 0.10730729252099991, 0.01625124365091324, 0.04520991072058678, -0.04034416005015373, 0.04596702381968498, 0.0428837314248085, 0.004682294093072414, 0.04936737194657326, 0.012857072986662388, 0.0008752583526074886, 0.01838046684861183, -0.016948580741882324, 0.023769758641719818, 0.017594585195183754, -0.04079105332493782, -0.025089040398597717, 0.04975186660885811, -0.03843013197183609, -0.05399521067738533, 0.06267524510622025, 0.019362425431609154, 0.0043702865950763226, -0.009341374970972538, 0.029454009607434273, -0.021036744117736816, -0.023034321144223213, -0.0005741628119722009, 0.00575332110747695, 0.0018620892660692334, 0.0386827327311039, -0.031258609145879745, -0.05443524569272995, 0.014752484858036041, 0.017361458390951157, 0.024759016931056976, 0.00165325659327209, -0.01981792040169239, -0.039601366966962814, -0.05813717842102051, -0.011832655407488346, -0.021939339116215706, 0.009126182645559311, 0.014595866203308105, -0.03766319900751114, 0.041160956025123596, 0.032112061977386475, 0.02796322852373123, -0.022152753546833992, 0.021980294957756996, 0.003541206242516637, -0.027890611439943314, 0.0021506426855921745, -0.02630326896905899, 0.014666372910141945, -0.008106164634227753, -0.008875594474375248, 0.02584027871489525, 0.04753812402486801, -0.004682582803070545, -0.027653202414512634, 0.035031456500291824, 0.04299836605787277, 0.057625219225883484, -0.0031749613117426634, -0.07124032080173492, 0.037622399628162384, -0.008400741033256054, 0.0037158799823373556, -0.01945381425321102, -0.0027419724501669407, -0.0025482941418886185, -0.0009287160937674344, -0.008132090792059898, 0.008768411353230476, -0.024994149804115295, 0.005986510775983334, -0.027685334905982018, 0.05753272771835327, 0.016979342326521873, 0.04754577577114105, -0.009122464805841446, -0.07768217474222183, 0.020331179723143578, 0.01001033466309309, -0.013859880156815052, 0.02848392352461815, -0.019682031124830246, -0.02035059779882431, 0.0529310517013073, -0.003950872924178839, -0.038613151758909225, -0.018698349595069885, -0.05586099997162819, 0.008195091038942337, 0.028226787224411964, 0.004683593288064003, 0.020090248435735703, -0.0004343943437561393, -0.01599694974720478, -0.0028428819496184587, 0.031119072809815407, -0.07814496755599976, -0.01375177688896656, -0.03497183695435524, 0.04725310206413269, 0.013495652005076408, 0.018475443124771118, -0.04884949326515198, -0.016618769615888596, -0.042032390832901, 0.039800938218832016, 0.071342833340168, -0.03628125786781311, -0.0010668045142665505, 0.07169812172651291, 0.013833604753017426, -0.054049041122198105, -0.014958280138671398, -0.014533923007547855, -0.020303037017583847, -0.022501865401864052, 0.01182225625962019, 0.022213175892829895, 0.049580108374357224, 0.017994653433561325, 0.03516712039709091, -0.0492824912071228, -0.013651547953486443, -0.028301674872636795, -0.026068970561027527, 0.0022582905367016792, 0.06447480618953705, -0.02452411688864231, 0.12329379469156265, -0.006030149292200804, 0.03228108212351799, 0.024891942739486694, -0.013293785974383354, -0.003276658244431019, -0.04447689279913902, 0.026284197345376015, -0.0685306042432785, 0.008423153311014175, 0.014363418333232403, 0.053240686655044556, 0.01357294525951147, 0.02921816147863865, 0.020747363567352295, -0.006098720245063305, 0.017954958602786064, -0.10376374423503876, -0.0068750581704080105, -0.023487353697419167, 0.03901346027851105, -0.040621381253004074, 0.015077388845384121, 0.010653048753738403, -0.021514641121029854, 0.021276535466313362, -0.0009257502388209105, 0.03526431694626808, -0.02079256810247898, -0.02972879633307457, -0.03406628221273422, -0.01727611944079399, -0.019288411363959312, 0.008898359723389149, 0.008790838532149792, -0.022766536101698875, 0.058391258120536804, -0.02757970429956913, 0.038417913019657135, -0.011427631601691246, 0.008482195436954498, 0.041571758687496185, 0.05168404430150986, 0.017226966097950935, -0.04436291754245758, -0.013846466317772865, 0.005637289956212044, 0.041390325874090195, 0.07118023931980133, -0.04115808382630348, -0.027609793469309807, 0.01712871715426445, 0.018964197486639023, 0.04123115912079811, 0.024348599836230278, -0.008947940543293953, 0.004776502959430218, -0.0307048037648201, -0.0012840701965615153, -0.10258429497480392, -0.0311252623796463, -0.029637733474373817, -0.023285189643502235, -0.049392540007829666, 0.020476950332522392, 0.07191050797700882, 0.062347620725631714, -0.04624075070023537, -0.03602605685591698, -0.04641829431056976, -0.08965853601694107, -0.007290310226380825, 0.030969969928264618, -0.031355246901512146, 0.061608023941516876, -0.01781647838652134, 0.024585315957665443, -0.03581669554114342, -0.014201648533344269, -0.022121913731098175, -0.012474862858653069, 0.024216631427407265, -0.014802425168454647, -0.011593851260840893, -0.031540434807538986, -0.02573608048260212, -0.03166753798723221, 0.014433705247938633, -0.08606700599193573, 0.034525346010923386, -0.04799247160553932, 0.029368212446570396, 0.013626137748360634, -0.07996125519275665, -0.03697507083415985, 0.029099056497216225, -0.007779937237501144, -0.029768608510494232, 0.02984381839632988, 0.07377895712852478, -0.0751914381980896, -0.008250674232840538, -0.04585302621126175, -0.05841461569070816, -0.027157321572303772, -0.01681150682270527, 0.0003368502948433161, -0.009171415120363235, 0.012654068879783154, -0.005272633861750364, 0.03743850439786911, 0.007588047068566084, 0.016784578561782837, 0.09742619097232819, 0.009710797108709812, -0.031983353197574615, 0.013873357325792313, -0.09040170162916183, 0.04416356608271599, -0.02854233980178833, 0.01274543534964323, 0.005617267452180386, 0.02237263135612011, -0.0031962392386049032, -0.010492577217519283, 0.022543884813785553, 0.00948733277618885, -0.02490064688026905, -0.04629974439740181, -0.09178265184164047, -0.00315670482814312, -0.09099385887384415, -0.03125748410820961, 0.005670290905982256, 0.019130727276206017, 0.027286333963274956, 0.015519512817263603, 0.0010239894036203623, -0.01607268862426281, -0.06755787134170532, -0.020246446132659912, 0.0550101138651371, -0.06268125027418137, -0.027432486414909363, -0.012344645336270332, 0.09575126320123672, 0.002230151789262891, -0.05494129657745361, -0.036405958235263824, 0.04315120354294777, -0.033557992428541183, 0.010551591403782368, 0.010740992613136768, 0.017674891278147697, -0.019717177376151085, -0.014628457836806774, -0.04692641273140907, 0.04006870836019516, 0.042439039796590805, -0.019270265474915504, 0.0003729987074621022, -0.004004409536719322, 7.195042417151853e-05, -0.03140873461961746, -0.03047301061451435, -0.04531846195459366, 0.04920348897576332, -0.04617476463317871, -0.0357990488409996, -0.03979380428791046, -0.0013261683052405715, 0.012193441390991211, 0.03337988629937172, 0.05357486009597778, -0.027126535773277283, -0.008566958829760551, 0.00730391638353467, -0.0016422533662989736, -0.0023295774590224028, -0.010815508663654327, 0.0008416367927566171, 0.03409033641219139, 0.010253723710775375, -0.001330793951638043, -0.02448936738073826, 0.05271618440747261, -0.029578544199466705, 0.03587140515446663, -0.02582871913909912, 0.04176211357116699, -0.004949549678713083, 0.041107092052698135, -0.0028402728494256735, -0.016180049628019333, -0.023564495146274567, -0.011257162317633629, -0.036598481237888336, 0.01251891441643238, -0.026246292516589165, 0.0005531900678761303, 0.027473585680127144, -0.02592652663588524, -0.04098545014858246, 0.06282327324151993, -0.06894760578870773, -0.005052377004176378, -0.016340792179107666, 0.040611814707517624, 0.016111409291625023, -0.008674991317093372, 0.00173121877014637, -0.03401002287864685, -0.02731850929558277, 0.02115532197058201, 0.04412706196308136, -0.005401260685175657, 0.02815377153456211, 0.019149616360664368, 0.0200754776597023, -0.022108135744929314, -0.038647931069135666, 0.05229407548904419, 0.01860085316002369, -0.06053202226758003, 0.018834175541996956, -0.047169625759124756, -0.020599424839019775, 0.028522692620754242, 0.036834895610809326, 0.022286375984549522, 0.0018213298171758652, -0.012504338286817074, -0.04467517137527466, 0.02539287693798542, 0.03209977224469185, 0.028449982404708862, 0.051194820553064346, -0.030301515012979507, 0.01935311034321785, 0.08194169402122498, 0.013588991016149521, -0.020312462002038956, -0.05582820996642113, 0.009250873699784279, -0.06451068818569183, -0.01504431664943695, 0.01854109950363636, -6.287976421937658e-33, -0.013681993819773197, -0.029388269409537315, -0.01674615778028965, 0.10231903195381165, -0.00037752900971099734, 0.02435942366719246, -0.03141810745000839, -0.03002316877245903, 0.030821243301033974, 0.019027896225452423, -0.03832244127988815, 0.03457586094737053, 0.012515280395746231, -0.035312358289957047, 0.09101339429616928, 0.05186254531145096, 0.0044520203955471516, 0.008349059149622917, -0.008772160857915878, 0.03989092633128166, 0.008181416429579258, 0.030450500547885895, 0.04175374656915665, -0.03542022407054901, 0.042785536497831345, -0.022599510848522186, 0.013765980489552021, -0.06880398094654083, 0.05412904918193817, 0.019773036241531372, -0.016378050670027733, -0.022839047014713287, 0.03146171569824219, -0.03369416296482086, 0.025778237730264664, -0.013843675144016743, -0.048603761941194534, -0.04946570470929146, 0.013228391297161579, -0.029886843636631966, 0.04576848819851875, -0.030018193647265434, 0.034078773111104965, 0.0026962088886648417, -0.007943835109472275, 0.019992031157016754, 0.08967146277427673, 0.006778953596949577, -0.060042984783649445, -0.07618970423936844, -0.0421668104827404, 0.018359607085585594, -0.020184816792607307, 0.056409213691949844, 0.016948455944657326, -0.015402811579406261, -0.01278573926538229, 0.06927140802145004, 0.005833557806909084, 0.03528495132923126, 0.028696231544017792, 0.06886444240808487, 0.023801397532224655, -0.020305082201957703, 0.029639605432748795, 0.019582662731409073, -0.05123823136091232, 0.021478788927197456, 0.02303978241980076, 0.02641126699745655, 0.03131984919309616, 0.04019065946340561, 0.008264652453362942, 0.028672032058238983, 0.05327024310827255, -0.059727951884269714, -0.0013188025914132595, 0.06120508909225464, 0.0038578403182327747, 0.0037804844323545694, -0.013345998711884022, -0.02625599130988121, -0.023730721324682236, 0.011309768073260784, 0.037126604467630386, 0.023687608540058136, 0.0005404490511864424, -0.044653598219156265, -0.0034968717955052853, -0.015681490302085876, -0.08369144797325134, 0.010282346978783607, -0.04473024234175682, -0.004806789103895426, 0.017971642315387726, -0.006528592202812433, -0.015160013921558857, 0.04873548075556755, -0.02743375301361084, 0.011196700856089592, -0.07398908585309982, -0.011588092893362045, -0.023755289614200592, 0.0411926731467247, 0.010338228195905685, -0.022300440818071365, -0.008331803604960442, -0.027904991060495377, -0.04093782976269722, -0.015326832421123981, 0.03808017820119858, -0.051318373531103134, -0.024300789460539818, 0.04562228545546532, -0.061880841851234436, 0.03077036142349243, 0.021159285679459572, 0.022214969620108604, 0.060705386102199554, 0.01134374551475048, -0.014696194790303707, -0.028919031843543053, 0.02079354226589203, 0.043745964765548706, -0.014964657835662365, -0.005705541465431452, -0.031220342963933945, -0.019084418192505836, 0.04197575896978378, -0.00844008568674326, -0.017657846212387085, 0.006111616268754005, 2.774087022316962e-07, 0.016666021198034286, 0.07850082218647003, 0.007772988174110651, -0.024054063484072685, 0.005036022514104843, 0.011189142242074013, -0.015222545713186264, 0.032519347965717316, -0.04201823100447655, 0.03580072894692421, 0.03257973492145538, -0.03095581941306591, -0.009571617469191551, 0.022772008553147316, -0.09797953814268112, -0.029009627178311348, -0.08226217329502106, -0.06691991537809372, -0.08138250559568405, -0.0003222164523322135, 0.06035661697387695, -0.020899774506688118, -0.00947913620620966, 0.005484322085976601, -0.03521907329559326, -0.010244359262287617, 0.005734174977988005, -0.0008886537398211658, -0.0015459350543096662, 0.05454367771744728, 0.04079185426235199, 0.023241350427269936, -0.05205601453781128, 0.005425676703453064, -0.01987694390118122, -0.01107178907841444, 0.03297165036201477, 0.014338457025587559, 0.021194109693169594, 0.021702300757169724, 0.01526171900331974, -0.001134830410592258, 0.014611344784498215, -0.04583092778921127, 0.04404640197753906, -0.01642959751188755, -0.015643293038010597, -0.06041302531957626, -0.048554494976997375, -0.018060356378555298, 0.012388757430016994, -0.05480235069990158, -0.014113960787653923, 0.010465756990015507, -0.0360306017100811, -0.0274804774671793, 0.0008093419601209462, -0.06011344864964485, 0.06484778970479965, 0.02822742611169815, 0.009919705800712109, -0.016710476949810982, -0.006088848225772381, -0.019324278458952904, 0.01393621601164341, -0.020510878413915634, 0.018534287810325623, 2.8298451517287462e-34, 0.03905955329537392, -0.03433135151863098, -0.03822503983974457, -0.003227669047191739, -0.024831537157297134, -0.019663596525788307, -0.021244939416646957, 0.04772743210196495, -0.04490964859724045, -0.030794473364949226, 0.0176496971398592]

['Uri Kartoun']

1306.0541v1

The paper presents a time-series-based classification approach to identify similarities in pairs of simulated human-generated patterns. An example for a pattern is a time-series representing a heart rate during a specific time-range, wherein the time-series is a sequence of data points that represent the changes in the heart rate values. A bio-medical simulator system was developed to acquire a collection of 7,871 price patterns of financial instruments. The financial instruments traded in real-time on three American stock exchanges, NASDAQ, NYSE, and AMEX, simulate bio-medical measurements. The system simulates a human in which each price pattern represents one bio-medical sensor. Data provided during trading hours from the stock exchanges allowed real-time classification. Classification is based on new machine learning techniques: self-labeling, which allows the application of supervised learning methods on unlabeled time-series and similarity ranking, which applied on a decision tree learning algorithm to classify time-series regardless of type and quantity.

Identifying Pairs in Simulated Bio-Medical Time-Series

http://arxiv.org/pdf/1306.0541v1

Title Identifying Pairs Simulated BioMedical TimeSeries Summary paper present timeseriesbased classification approach identify similarity pair simulated humangenerated pattern example pattern timeseries representing heart rate specific timerange wherein timeseries sequence data point represent change heart rate value biomedical simulator system developed acquire collection 7871 price pattern financial instrument financial instrument traded realtime three American stock exchange NASDAQ NYSE AMEX simulate biomedical measurement system simulates human price pattern represents one biomedical sensor Data provided trading hour stock exchange allowed realtime classification Classification based new machine learning technique selflabeling allows application supervised learning method unlabeled timeseries similarity ranking applied decision tree learning algorithm classify timeseries regardless type quantity Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.033926818519830704, 0.01321318931877613, -0.04818198084831238, -0.040026113390922546, -0.0336187370121479, 0.008227603510022163, 0.030654489994049072, 0.05741054192185402, -0.0037763018626719713, 0.021910427138209343, 0.033914338797330856, -0.0056370096281170845, 0.02820969931781292, 0.056458353996276855, -0.013969501480460167, -0.03916510194540024, 0.040343981236219406, 0.021099945530295372, -0.01477501168847084, 0.02092045545578003, 0.016880782321095467, -0.030306853353977203, 0.015544305555522442, 0.03306683897972107, 0.03575419262051582, 0.012575454078614712, 0.001343343872576952, -0.05724978819489479, 0.04443572834134102, -0.08860775828361511, 0.026642989367246628, -0.005189255811274052, -0.008043350651860237, 0.04051782563328743, 1.7464873280914617e-06, -0.04039643704891205, -0.004282322246581316, -6.58894277876243e-05, 0.01437087170779705, -0.04012425243854523, -0.015266361646354198, -0.002697231248021126, 0.06942356377840042, -0.008445375598967075, -0.0502052903175354, -0.011342136189341545, 0.01270997803658247, 0.01894410327076912, 0.029835112392902374, 0.03044421598315239, -0.02256201207637787, 0.04731298238039017, 0.001397973159328103, -0.05004857853055, 0.057681165635585785, 0.011099005118012428, 0.028065776452422142, 0.01809602975845337, 0.07259020209312439, -0.016068054363131523, 0.03066970780491829, 0.023112555965781212, -0.006353770848363638, 0.04871272295713425, 0.07353652268648148, 0.03452101722359657, -0.007448543794453144, 0.006429621949791908, -0.02993502840399742, 0.04505157470703125, -0.016206098720431328, -0.03174184635281563, 0.07512347400188446, 0.024587424471974373, -0.052030034363269806, 0.017477666959166527, -0.006030120421200991, -0.03017270565032959, -0.05243948474526405, 0.00035435453173704445, -0.0013051364803686738, 0.08704838901758194, -0.025797726586461067, -0.019100390374660492, -0.001357142347842455, -0.04582907259464264, -0.013427787460386753, -0.01788971945643425, 0.0004294032114557922, -0.036701593548059464, 0.013745510950684547, -0.046111006289720535, 0.026721054688096046, 0.004093254916369915, -0.03484857454895973, -0.038656555116176605, 0.007615937851369381, -0.00782841257750988, 0.029484935104846954, -0.050170205533504486, 0.0169967208057642, -0.0125066377222538, 0.02597026154398918, -0.005509478971362114, -0.061236683279275894, -0.0010010814294219017, -0.04163403809070587, 0.008249477483332157, -0.010202096775174141, 0.0807279720902443, -0.07100648432970047, 0.029763078317046165, 0.02382046915590763, 0.04322309419512749, 0.041952986270189285, -0.001827905885875225, -0.08541479706764221, -0.011316061019897461, -0.030509112402796745, 0.020853541791439056, 0.003517263336107135, 0.01647942326962948, 0.04343858361244202, 0.037794049829244614, -0.02455703541636467, -0.0351218655705452, -0.025919076055288315, 0.033520035445690155, -0.027955254539847374, -0.016233360394835472, 0.03992082178592682, -0.01847420632839203, 0.007562926039099693, 0.012054839171469212, -0.02068774774670601, 0.02906656637787819, 0.04053524509072304, 0.03710442781448364, -0.05511033162474632, -0.04957542195916176, 0.016443563625216484, 0.04717515781521797, -0.0445607528090477, -0.006880119442939758, -0.007538623176515102, -0.02946878969669342, -0.022283118218183517, 0.06545805931091309, 0.017840072512626648, -0.020843565464019775, -0.002761635696515441, 0.09560646116733551, 0.004256682936102152, 0.025983406230807304, 0.04590953513979912, -0.009863484650850296, 0.019926341250538826, -0.024520905688405037, 0.027277737855911255, -0.04618474096059799, 0.018735256046056747, -0.04012003913521767, 0.00773854972794652, -0.025999730452895164, -0.030499083921313286, -0.105014368891716, -0.04471368342638016, -0.0032069620210677385, 0.017258713021874428, 0.05820200592279434, 0.00846385769546032, -0.005222539883106947, 0.009025584906339645, -0.018621083348989487, 0.040107354521751404, 0.0407528355717659, 0.04214495047926903, 0.013181271962821484, 0.015115431509912014, -0.004736041184514761, 0.00275626964867115, -0.04266899451613426, 0.04891337454319, 0.017651263624429703, -0.00617566704750061, -0.0052864691242575645, -0.07584697008132935, -0.023458093404769897, -0.028680915012955666, -0.04271246865391731, -0.0036195951979607344, -0.0514889657497406, -0.009303051978349686, -0.04983343929052353, -0.006643325090408325, -0.03448248282074928, -0.004724368918687105, -0.013494609855115414, 0.02379290573298931, 0.06027722358703613, -0.06662905961275101, -0.02883734367787838, 0.01860973611474037, 0.008219704031944275, -0.01523522287607193, -0.019903896376490593, 0.05102183297276497, -0.043229296803474426, -0.04355976730585098, -0.060843952000141144, 0.016086488962173462, 0.008267591707408428, -0.04098581150174141, -0.03701617941260338, -0.009431696496903896, 0.057777825742959976, -0.02122914232313633, -0.0033328821882605553, -0.05912018194794655, 0.062151290476322174, 0.0002530563797336072, 0.044347044080495834, 0.021629713475704193, -0.031184043735265732, -0.05447683483362198, -0.003028611419722438, 0.04189743846654892, 0.021416587755084038, 0.03159388527274132, 0.006522535812109709, 0.03826495632529259, 0.0006333671626634896, 0.011899520643055439, -0.050439417362213135, -0.04223087802529335, 0.05428002402186394, -0.021137751638889313, 0.008193674497306347, -0.015268984250724316, 0.0409204438328743, -0.002487179124727845, -0.013121872209012508, -0.03153694421052933, -0.03806227445602417, -0.01068418100476265, -0.05422215163707733, 0.029316745698451996, -0.017761440947651863, 0.0021367298904806376, 0.007944422774016857, 0.01211776677519083, -0.01886477880179882, 0.01603522151708603, 0.037977710366249084, 0.028430640697479248, -0.03889157623052597, -0.050216883420944214, 0.036541856825351715, -0.039695631712675095, 0.058802783489227295, -0.013051575049757957, -0.053495656698942184, -0.01922164298593998, -0.008117354474961758, -0.017226872965693474, 0.013982851058244705, 0.047286875545978546, 0.0009139876929111779, -0.029353439807891846, 0.07398289442062378, 0.028898416087031364, -0.02755848318338394, -0.014309900812804699, 0.011990681290626526, -0.026682917028665543, 0.006836595479398966, 0.00844433531165123, -0.016936680302023888, -0.05905831605195999, 0.07565448433160782, 0.0016144926194101572, -0.03387025371193886, 0.006316349375993013, 0.028511077165603638, -0.0403897650539875, 0.038458649069070816, 0.052034005522727966, -0.012353627011179924, 0.01186473947018385, -0.03184863552451134, 0.007662967778742313, -0.007401871494948864, 0.032504111528396606, -0.0006021329900249839, -0.03016275353729725, 0.023257272318005562, -0.022943835705518723, 0.028034940361976624, 0.0675232782959938, -0.0015969208907335997, -0.021895375102758408, 0.05513475090265274, 0.022867342457175255, 0.019696202129125595, -0.018009398132562637, 0.08223447948694229, 0.05077612027525902, 0.0014409152790904045, -0.005898013710975647, 0.062200043350458145, 0.04017854481935501, -0.015343342907726765, 0.017243171110749245, 0.021969780325889587, 0.021981874480843544, 0.002489452948793769, -0.06387388706207275, 0.012495450675487518, -0.018666615709662437, 0.001506995060481131, 0.0021193474531173706, -0.046072814613580704, 0.037243157625198364, 0.044254694133996964, 0.02803995832800865, -0.013177554123103619, -0.06331087648868561, -0.016778718680143356, -0.037849560379981995, -0.027753204107284546, 0.003924529533833265, -0.023802287876605988, -0.013149308040738106, 0.028396202251315117, -0.01076414529234171, 0.015028532594442368, -0.054226893931627274, 0.004251100122928619, -0.03311906009912491, 0.015897974371910095, 0.030442215502262115, -0.0014679493615403771, -0.0366797111928463, 0.03802269697189331, 0.011971169151365757, -0.028046589344739914, -0.02659514732658863, -0.0016867310041561723, 0.009888054803013802, 0.07357104867696762, -0.029574664309620857, 0.019669178873300552, 0.011306646279990673, -0.046162914484739304, 0.024854891002178192, 0.08003583550453186, 0.02438984625041485, -0.034712519496679306, -0.03150028735399246, 0.010993512347340584, 0.05846947804093361, -0.01781374402344227, 0.03076304867863655, 0.07733487337827682, -0.0736709013581276, 0.028978576883673668, -0.054225046187639236, -0.050932981073856354, -0.011512956582009792, 0.00121431821025908, -0.06804630160331726, -0.010267462581396103, 0.024633163586258888, 0.056906722486019135, 0.01754690892994404, -0.05794662982225418, -0.015895379707217216, 0.023311404511332512, -0.06546954065561295, -0.029352402314543724, -0.01806887611746788, -0.01368383876979351, 0.024888211861252785, -0.018727561458945274, 0.01655871421098709, -0.047578226774930954, -0.0428539477288723, -0.011131088249385357, -0.03474119305610657, 0.01707581616938114, 0.00812222994863987, -0.04903186857700348, -0.007803572341799736, -0.12566149234771729, -0.009783749468624592, -0.05506616085767746, -0.009814092889428139, -0.04094976559281349, -0.022868214175105095, 0.0050112283788621426, 0.039460163563489914, -0.11110024899244308, -0.00422245217487216, 0.01147976703941822, 0.012019733898341656, -0.009862976148724556, -0.00011126098252134398, 0.04733790457248688, -0.018011728301644325, -0.04653911292552948, -0.04437146708369255, 0.0011783742811530828, 0.03014412708580494, -0.04951595515012741, 0.03397546336054802, 0.06404995173215866, -0.02544526383280754, -0.020429925993084908, 0.07182532548904419, 0.003992059268057346, 0.05570268630981445, 0.009906303137540817, 0.05022866651415825, -0.013317463919520378, -0.03041006624698639, -0.049386218190193176, -0.0008650794043205678, 0.027881084010004997, 0.029035545885562897, 0.016651909798383713, -0.009077122434973717, -0.03342489153146744, 0.05463096499443054, 0.062019046396017075, -0.026731695979833603, -0.02908695861697197, -0.024012994021177292, -0.00649326853454113, -0.010973221622407436, -0.043772757053375244, 0.008887706324458122, -0.06577228009700775, 0.036326900124549866, 0.0034569797571748495, 0.06288910657167435, 0.07152950018644333, -0.018385300412774086, -0.05396365746855736, -0.02638089284300804, 0.07124627381563187, 0.053557928651571274, -0.05352003127336502, 0.011480379849672318, 0.021929845213890076, -0.0014958868268877268, -0.06337438523769379, -0.04503392055630684, -0.03509191423654556, 0.01168132945895195, 0.007525554392486811, 0.020645806565880775, 0.01371685042977333, -0.009269127622246742, -0.010563415475189686, 0.06428647041320801, -0.002653153147548437, 0.03845767676830292, 0.015012133866548538, -0.05085569992661476, -0.049634359776973724, 0.013659307733178139, -0.03677694872021675, -0.017024541273713112, 0.02953113429248333, 0.08684039115905762, -0.029843680560588837, -0.06261967867612839, -0.026111267507076263, -0.0005619394942186773, -0.013898950070142746, 0.04583285376429558, 0.05718504637479782, 0.06311853975057602, -0.02050413005053997, 0.0005072085186839104, 0.005570487584918737, -0.006069696042686701, 0.024686500430107117, -0.022809946909546852, -0.036017630249261856, 0.0459509901702404, 0.030856940895318985, -0.021618662402033806, -0.02362741157412529, 0.045201219618320465, -0.11054083704948425, -0.030125556513667107, 0.046341244131326675, -0.021679867058992386, 0.10320575535297394, -0.061597615480422974, 0.015432870015501976, 0.029833124950528145, -0.006875514052808285, 0.03602275624871254, 0.03340664505958557, -0.002331499243155122, 0.03088401071727276, -0.009006712585687637, 0.02210880070924759, 0.0039741117507219315, -0.010928552597761154, 0.002403469057753682, 0.028101956471800804, 0.03549964353442192, -0.033857859671115875, -0.03411853313446045, -0.051173459738492966, -0.001034530345350504, 0.014233848080039024, 0.023900402709841728, -0.013564086519181728, 0.06542201340198517, -0.07134859263896942, 0.088836170732975, 0.010238589718937874, -0.00014003914839122444, -0.05386864021420479, -0.0023787051904946566, 0.05244322121143341, 0.008843465708196163, -0.010273910127580166, -0.012663280591368675, -0.08489174395799637, -0.013539082370698452, 0.07230919599533081, 0.04783157631754875, -0.08091728389263153, 0.002444376004859805, -0.014787856489419937, -0.026023613288998604, 0.02374456636607647, 0.06271260976791382, 0.011486097238957882, 0.039411772042512894, 0.022475894540548325, 0.026192305609583855, -0.014971877448260784, -0.03693480044603348, 0.04641260579228401, 0.03930388391017914, -1.1557281140994746e-06, -0.030224837362766266, -0.03647011145949364, -0.05006137490272522, -4.953174668588119e-33, 0.024707866832613945, -0.042758435010910034, -0.010299711488187313, -0.0038198628462851048, -0.02467423677444458, 0.0518847331404686, -0.03330329433083534, -0.013073979876935482, 0.04602121189236641, -0.037661612033843994, 0.011378402821719646, -0.0215079877525568, 0.010901914909482002, -0.025945240631699562, 0.07054200023412704, -0.005261184647679329, 0.017992068082094193, 0.014930912293493748, 0.045202650129795074, -0.00654272036626935, 0.026306532323360443, 0.022873925045132637, -0.02374527044594288, -0.022649548947811127, -0.06858251988887787, 0.04264748468995094, 0.006816839799284935, -0.024291278794407845, 0.003502779407426715, 0.031210284680128098, -0.014895323663949966, 0.027601419016718864, -0.01341167651116848, -0.0035713824909180403, -0.005684859585016966, 0.009103784337639809, -0.06163377687335014, -0.027216356247663498, -0.05286305397748947, -0.027098525315523148, 0.035798486322164536, 0.0004815574502572417, 0.06512869149446487, -0.014416725374758244, -0.046821802854537964, 0.01186955813318491, 0.053670160472393036, -0.008418478071689606, -0.02312409318983555, -0.03206536918878555, 0.028456972911953926, 0.027786970138549805, -0.010284698568284512, 0.030445994809269905, 0.034092050045728683, 0.03979383036494255, -0.03331983834505081, 0.0037200050428509712, -0.0296028982847929, 0.0463455393910408, -0.000571368495002389, 0.008771632798016071, -0.04757528752088547, 0.003307698294520378, 0.06920331716537476, 0.0023419035132974386, 0.01409473828971386, -0.02003532648086548, 0.04275774955749512, 0.05003538727760315, -0.046160321682691574, 0.037473831325769424, 0.01137693040072918, -0.0036266865208745003, 0.054058320820331573, -0.09029503911733627, -0.033655744045972824, 0.08152274787425995, 0.013956132344901562, -0.03858853876590729, -0.058647431433200836, -0.010916566476225853, -0.00645776791498065, 0.03703920915722847, 0.06636073440313339, 0.01880135014653206, -0.02173253335058689, -0.022768206894397736, 0.017124155536293983, 0.006623637396842241, 0.040960583835840225, 0.061121441423892975, -0.04305059462785721, -0.056095484644174576, 0.0017460616072639823, -0.06585031747817993, 0.05394788086414337, 0.003913417458534241, 0.039691291749477386, -0.0801825225353241, 0.011495428159832954, -0.04065871611237526, 0.010932761244475842, -0.014623465947806835, 0.04224799945950508, -0.06917835026979446, -0.0016055235173553228, -0.01888713426887989, -0.01888827048242092, -0.0026536521036177874, 0.057481247931718826, -0.04090067744255066, -0.022082002833485603, -0.049589842557907104, 0.009645793586969376, -0.03232875093817711, -0.004232754930853844, 0.05195782333612442, -0.01996654085814953, -0.01740623265504837, -0.04399004951119423, -0.026997089385986328, -0.017489267513155937, 0.05023255944252014, -0.0009020650177262723, -0.014253751374781132, -0.041634269058704376, 0.05547690764069557, -0.04279493913054466, -0.027001770213246346, -0.012924275361001492, -0.0012520221062004566, 2.5860344976536e-07, -0.019960617646574974, 0.04815131425857544, 0.02526802569627762, -0.01803339086472988, 0.030186686664819717, -0.011073262430727482, -0.026705292984843254, -0.013320562429726124, -0.0571928545832634, -0.0003539547324180603, 0.09292083978652954, -0.044438835233449936, 0.06689660251140594, -0.0009581267950125039, 0.017013298347592354, -0.06357574462890625, -0.03843965753912926, 0.025372641161084175, -0.047718312591314316, -0.012433841824531555, 0.020678123459219933, -0.015919793397188187, 0.02195516973733902, -0.013069936074316502, 0.045183178037405014, -0.016001204028725624, 0.014228589832782745, -0.02475932240486145, 0.0012768314918503165, -0.0053705754689872265, -0.005098491907119751, -0.011203611269593239, 0.0036075373645871878, -0.00499897263944149, -0.0029695015400648117, 0.004135563969612122, 0.01072064507752657, -0.01878330111503601, -0.01501708198338747, 0.04461750388145447, 0.024098306894302368, 0.03933863341808319, 0.03919835388660431, -0.03761030361056328, 0.016750484704971313, -0.029808809980750084, -0.016610197722911835, -0.02646205574274063, -0.016534563153982162, 0.03726588189601898, 0.0680609866976738, 0.05658360570669174, -0.026182353496551514, 0.027513127774000168, 0.010118349455296993, 0.009148436598479748, 0.03403552621603012, 0.013438244350254536, -0.0007472311262972653, 0.06878022104501724, -0.028486885130405426, 0.031024301424622536, -0.03157138079404831, 0.020064078271389008, 0.054671380668878555, -0.022490430623292923, -0.03607970476150513, 2.37920056606431e-34, 0.010405574925243855, -0.0036641540937125683, -0.03650059178471565, 0.009546286426484585, -0.020381104201078415, -0.006037610583007336, 0.025170696899294853, 0.011999865062534809, -0.0003775122750084847, 0.007801399100571871, -0.022089453414082527]

['Munther Abualkibash', 'Ahmed ElSayed', 'Ausif Mahmood']

1306.1467v1

AdaBoost is an important algorithm in machine learning and is being widely used in object detection. AdaBoost works by iteratively selecting the best amongst weak classifiers, and then combines several weak classifiers to obtain a strong classifier. Even though AdaBoost has proven to be very effective, its learning execution time can be quite large depending upon the application e.g., in face detection, the learning time can be several days. Due to its increasing use in computer vision applications, the learning time needs to be drastically reduced so that an adaptive near real time object detection system can be incorporated. In this paper, we develop a hybrid parallel and distributed AdaBoost algorithm that exploits the multiple cores in a CPU via light weight threads, and also uses multiple machines via a web service software architecture to achieve high scalability. We present a novel hierarchical web services based distributed architecture and achieve nearly linear speedup up to the number of processors available to us. In comparison with the previously published work, which used a single level master-slave parallel and distributed implementation [1] and only achieved a speedup of 2.66 on four nodes, we achieve a speedup of 95.1 on 31 workstations each having a quad-core processor, resulting in a learning time of only 4.8 seconds per feature.

Highly Scalable, Parallel and Distributed AdaBoost Algorithm using Light Weight Threads and Web Services on a Network of Multi-Core Machines

http://arxiv.org/pdf/1306.1467v1

Title Highly Scalable Parallel Distributed AdaBoost Algorithm using Light Weight Threads Web Services Network MultiCore Machines Summary AdaBoost important algorithm machine learning widely used object detection AdaBoost work iteratively selecting best amongst weak classifier combine several weak classifier obtain strong classifier Even though AdaBoost proven effective learning execution time quite large depending upon application eg face detection learning time several day Due increasing use computer vision application learning time need drastically reduced adaptive near real time object detection system incorporated paper develop hybrid parallel distributed AdaBoost algorithm exploit multiple core CPU via light weight thread also us multiple machine via web service software architecture achieve high scalability present novel hierarchical web service based distributed architecture achieve nearly linear speedup number processor available u comparison previously published work used single level masterslave parallel distributed implementation 1 achieved speedup 266 four node achieve speedup 951 31 workstation quadcore processor resulting learning time 48 second per feature Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.020577240735292435, -0.01793212629854679, -0.017669038847088814, 0.02355971746146679, 0.0009952974505722523, 0.03504246473312378, 0.04536261782050133, 0.027165869250893593, 0.03911958262324333, -0.04637344181537628, 0.008026575669646263, -0.008088751696050167, -0.001224119565449655, 0.026093121618032455, -0.016757788136601448, -0.002395668299868703, -0.023033497855067253, 0.013181502930819988, -0.003085338743403554, -0.03555651381611824, 0.039232492446899414, -0.017118513584136963, 7.448170890711481e-06, 0.0021584960632026196, -0.04347909241914749, -0.022388387471437454, -0.014862081035971642, -0.02798793464899063, 0.030409585684537888, -0.036091677844524384, 0.008540618233382702, -0.0174484234303236, 0.02332177758216858, 0.022340118885040283, 2.3012710244074697e-06, -0.02876460738480091, 0.005329727195203304, -0.013194743543863297, 0.016802607104182243, -0.023324711248278618, -0.01859375089406967, 0.017986422404646873, 0.008160412311553955, 0.039554379880428314, 0.00020399056666065007, -0.013614273630082607, 0.04948994144797325, 0.050837673246860504, 0.019951775670051575, 0.025912147015333176, -0.00503773707896471, -0.04561224207282066, 0.01249312236905098, 0.0016011623665690422, -0.08646071702241898, -0.04557902365922928, 0.020929371938109398, 0.0016484332736581564, -0.008914968930184841, -0.0063054501079022884, -0.00523178419098258, 0.0003446006739977747, -0.005735029000788927, -0.0008212675456888974, 0.007288689725100994, 0.008399791084229946, -0.033663537353277206, 0.006376981735229492, -0.03463953733444214, -0.014853962697088718, -0.04113130643963814, 0.0237457025796175, -0.024988330900669098, 0.03203639015555382, -0.02192748337984085, 0.011842391453683376, -0.006122757215052843, 0.049468860030174255, -0.038481712341308594, 0.004744338802993298, -0.009373127482831478, -0.008837858214974403, -0.017103200778365135, 0.00990142859518528, 0.030230451375246048, 0.025738298892974854, -0.020114196464419365, 0.035625308752059937, -0.019343383610248566, 0.03919808939099312, -0.04267933964729309, -0.015230461955070496, 0.055746421217918396, 0.009735990315675735, -0.039960719645023346, -0.016310526058077812, -0.025697626173496246, -0.029853519052267075, 0.019685443490743637, -0.07885638624429703, 0.0622742585837841, -0.043066225945949554, -0.042673077434301376, 0.052450086921453476, -0.019698886200785637, 0.030426621437072754, -0.02385491505265236, -0.1007784828543663, 0.001616538967937231, 0.04734340310096741, -0.019855862483382225, -0.013346508145332336, -0.0011511693010106683, 0.06713937222957611, 0.01523542869836092, -0.03425471857190132, -0.04559479281306267, 0.05058811977505684, 0.008769523352384567, -0.06594125181436539, -0.026974640786647797, -0.03401860594749451, 0.025975078344345093, -0.008437439799308777, 0.042685963213443756, 0.014310500584542751, 0.008357538841664791, -0.005280281417071819, -0.055565763264894485, -0.015445264987647533, 0.03081374615430832, 0.015239966101944447, 0.04164255037903786, 0.03620901703834534, 0.035601094365119934, 0.009713543578982353, 0.01095183938741684, 0.027131110429763794, -0.05864815413951874, 0.010979927144944668, 0.009828992187976837, 0.017384447157382965, -0.03808334097266197, -0.036175232380628586, -0.019104283303022385, -0.013616061769425869, 0.03489040583372116, 0.042062532156705856, -0.008918414823710918, 0.008094243705272675, -0.022255010902881622, 0.03867252543568611, -0.04821918532252312, -0.028357457369565964, 0.05290622636675835, -0.023380722850561142, 0.005447384435683489, 0.050378527492284775, -0.021313875913619995, 0.08303482085466385, 0.0084232734516263, -0.010699245147407055, -0.01758440025150776, 0.015047135762870312, -0.04637029394507408, -0.01097702793776989, 0.006331062410026789, -0.0034996983595192432, -0.005777754820883274, -0.003701174631714821, 0.01529761217534542, 0.0062815286219120026, 0.007493630982935429, -0.022848090156912804, 0.03855188935995102, 0.006714006420224905, -0.045987505465745926, -0.02144358679652214, -0.014870062470436096, 0.03444511443376541, -0.006830220576375723, -0.014890759252011776, 0.03463416174054146, 0.041355736553668976, -0.0937286987900734, -0.07321619242429733, -0.07554314285516739, 0.06577686965465546, -0.03426975756883621, 0.0017572983633726835, -0.009344840422272682, -0.03651629760861397, -0.05928832292556763, 0.04265955835580826, 0.06741219013929367, -0.024554992094635963, -0.022099977359175682, -0.05867061764001846, 0.03702970966696739, 0.03374205902218819, -0.03132307529449463, -0.06230660155415535, -0.024040618911385536, -0.045773476362228394, 0.012169340625405312, 0.004279979504644871, -0.00456641661003232, -0.0138748399913311, 0.05742443725466728, -0.027830690145492554, -0.009742011316120625, -0.007990933954715729, -0.021086890250444412, 0.007911150343716145, -0.01866837963461876, 0.045815274119377136, 0.00167272484395653, -0.007131206337362528, -0.015020499005913734, 0.02314474992454052, -0.032030731439590454, 0.0550832524895668, 0.025314485654234886, 0.05754536762833595, 0.09612489491701126, 0.06911564618349075, 0.02801154926419258, 0.029552262276411057, 0.03743813559412956, -0.027696426957845688, 0.024911968037486076, -0.04501328244805336, 0.021092800423502922, -0.04316280409693718, -0.034001674503088, 0.014518394134938717, 0.02330314740538597, -0.03049953281879425, 0.08148394525051117, 0.005662576761096716, 0.0249332208186388, 0.05491676926612854, 0.006533951964229345, -0.021668976172804832, 0.009522784501314163, -0.07151690870523453, -0.05090964213013649, -0.005698485765606165, 0.06845444440841675, -0.032175153493881226, 0.07506721466779709, -0.04980761185288429, 0.0569831058382988, 0.04939635470509529, -0.031038299202919006, -0.06649145483970642, 0.014896527864038944, 0.06408583372831345, -0.008310184814035892, -0.0047996509820222855, 2.98724935419159e-05, -0.019156677648425102, -0.023292165249586105, 0.0177609920501709, -0.026463942602276802, 0.03091057762503624, 0.04306834936141968, -0.051049843430519104, 0.005278983153402805, 0.0010328938951715827, -0.031108541414141655, -0.0022009084932506084, 0.015493473969399929, 0.07185818254947662, -0.052989594638347626, 0.0025559754576534033, 0.13016758859157562, -0.03428371250629425, -0.004618487320840359, 0.005788429640233517, -0.014551091007888317, -0.03684186562895775, 0.06353922188282013, -0.02945644035935402, 0.016609996557235718, 0.025020455941557884, 0.08298265188932419, -0.014828345738351345, -0.034479036927223206, -0.018924560397863388, -0.009003189392387867, 0.012696060352027416, 0.005736032500863075, -0.0006890587392263114, -0.021255921572446823, -0.004196325317025185, 0.003578740172088146, 0.10060969740152359, 0.05011695250868797, 0.015504693612456322, 0.0006575502338819206, 0.08163722604513168, 0.01519730407744646, -0.009089802391827106, 0.00654611736536026, 0.05117883160710335, -0.013192488811910152, 0.04851873219013214, 0.00510373804718256, -0.001327488454990089, 0.001324963173829019, 0.0014649460790678859, 0.021552592515945435, -0.019062252715229988, 0.001875667367130518, 0.02597312442958355, -0.10245893150568008, 0.010764000937342644, -0.02300039492547512, -0.04902629926800728, 0.010978521779179573, -0.06124439835548401, 0.028931694105267525, 0.02799287438392639, -0.009174715727567673, 0.005323757417500019, -0.04143071919679642, 0.016448598355054855, 0.004597069229930639, 0.03860410302877426, 0.05952788516879082, -0.12244715541601181, 0.0030566377099603415, 0.048565931618213654, 0.08434750139713287, 0.00035356570151634514, -0.02920381911098957, -0.0021232792641967535, 0.029163707047700882, 0.001761816325597465, -0.05837323144078255, -0.07414987683296204, -0.024698100984096527, 0.04388319328427315, -0.05380413681268692, 0.003683412680402398, -0.01400037296116352, -0.019730979576706886, -0.05499892681837082, 0.062255505472421646, 0.019731365144252777, 0.05310240015387535, -0.020230650901794434, -0.013386625796556473, 0.035717837512493134, -0.002756106434389949, 0.028390983119606972, -0.0749567374587059, -0.020514218136668205, 0.02868146449327469, 0.06300774216651917, 0.06707566231489182, 0.04009179025888443, -0.0013386316131800413, -0.11760789155960083, 0.019904058426618576, 0.04068797826766968, -0.0008914265199564397, -0.02571740560233593, -0.037804849445819855, -0.027259893715381622, -0.002636100398376584, 0.04009714722633362, 0.033119913190603256, -0.017915232107043266, -0.03615209832787514, -0.02139391377568245, -0.01657993346452713, -0.045315537601709366, 0.04967894405126572, -0.0027054317761212587, 0.010307126678526402, -0.030450327321887016, 0.008477402850985527, -0.0042152623645961285, -0.010180585086345673, -0.04622800275683403, 0.02422725223004818, -0.02435346506536007, 0.03945567458868027, -0.005934673361480236, -0.028966384008526802, 0.0260637104511261, -0.057036835700273514, 0.04587027058005333, -0.030756529420614243, -0.03491934388875961, 0.032235488295555115, 0.021464765071868896, -0.0226579699665308, 0.0007840042235329747, -0.036506287753582, 0.056704454123973846, -0.011554444208741188, -0.06092619523406029, -0.03252403065562248, 0.005015998147428036, 0.03784675896167755, 0.01617717742919922, -0.0465393029153347, 0.012798681855201721, 0.011186609975993633, 0.00640029227361083, -0.07260368019342422, -0.007307376712560654, -0.01329492311924696, -0.03710855171084404, 0.007266800384968519, 0.012220690958201885, -0.008917493745684624, 0.03219907358288765, 0.0400189571082592, 0.032106757164001465, -0.04858337715268135, 0.02254614047706127, -0.04840501397848129, -0.026355145499110222, -0.023258652538061142, -0.0017544528236612678, -0.025592533871531487, -0.048964206129312515, -0.005396523047238588, 0.02938210777938366, -0.033894676715135574, 0.004819765221327543, 0.03878428786993027, 0.020245376974344254, -0.06536642462015152, -0.0006020254222676158, -0.07313386350870132, 0.04061121493577957, 0.0005137007683515549, 0.04549386724829674, 0.01640954427421093, 0.015721894800662994, -0.02686000056564808, 0.04658689722418785, -0.05094842240214348, -0.01230709720402956, -0.00010139241931028664, 0.008921955712139606, -0.02258516661822796, 0.016101760789752007, 0.05926048383116722, -0.07178089767694473, -0.03749457001686096, 0.007069517858326435, 0.0348990261554718, 0.007872352376580238, 0.025199590250849724, 0.0008366608526557684, -0.006999454461038113, -0.05467810109257698, -0.017244167625904083, -0.04398410767316818, -0.0396232008934021, 0.012612286023795605, 0.05872679501771927, 0.03014099784195423, 0.0002047394373221323, -0.052034758031368256, -0.001396161736920476, 0.022765619680285454, 0.01739923283457756, 0.05373435467481613, 0.019980493932962418, -0.09930410981178284, -0.014775224961340427, 0.002717213472351432, -0.01857629045844078, 0.06806876510381699, 0.026168355718255043, -0.009123347699642181, -0.0065430523827672005, 0.0034333323128521442, 0.016027990728616714, 0.03165033459663391, -0.0029513807967305183, -0.05816810950636864, -0.0014062932459637523, 0.040864601731300354, 0.008193292655050755, 0.01900029554963112, 0.01357140764594078, 0.10607068240642548, -0.0724157840013504, 0.021779322996735573, 0.010649812407791615, 0.0189889594912529, 0.041793350130319595, -0.026446733623743057, -0.004389225505292416, 0.013895884156227112, -0.06129439175128937, 0.0835588127374649, 0.028925331309437752, -0.024750791490077972, 0.03436710685491562, 0.007303173188120127, -0.011960268020629883, -0.028081992641091347, 0.03467242047190666, 0.018046177923679352, 0.02372857742011547, -0.02804715186357498, 0.05653643235564232, 0.03359051048755646, 0.012285996228456497, 0.017290478572249413, -0.03256906941533089, -0.005377238616347313, -0.058385949581861496, 0.0008862229879014194, -0.01863948442041874, 0.002035990823060274, 0.030432285740971565, 0.03702808916568756, -0.015589259564876556, 0.050695765763521194, 0.010545540601015091, 0.008409591391682625, -0.006017991807311773, 0.009637387469410896, -0.04486485943198204, -0.05585675686597824, 0.035124361515045166, 0.03782353177666664, 0.03282646834850311, 0.007680030073970556, 0.0046861181035637856, 0.03835511580109596, 0.018248436972498894, -0.010576662607491016, -0.07474304735660553, 0.06600145250558853, 0.015322357416152954, 0.0059612891636788845, 0.02487662062048912, 0.019688967615365982, -0.026476798579096794, -0.03581637516617775, 0.018058283254504204, -0.019538013264536858, 0.05418723076581955, 0.011704713106155396, -5.914141300385339e-33, 0.003180391388013959, -0.011346574872732162, -0.07979854941368103, -0.022091664373874664, -0.007417341694235802, 0.026326987892389297, 0.07887142151594162, 0.011350166983902454, 0.007401089183986187, -0.03480514511466026, -0.011857579462230206, 0.004398229066282511, 0.014037450775504112, 0.01028792466968298, -0.008195322006940842, 0.04821721836924553, 0.023994233459234238, -0.018216153606772423, -0.008623018860816956, -0.0193889569491148, 0.015569477342069149, 0.01772429049015045, 0.018238285556435585, -0.05011067911982536, -0.07883704453706741, -0.016015097498893738, -0.03763940930366516, -0.004319059196859598, -0.00039727622061036527, -0.028250109404325485, -0.0210115909576416, 0.004106172360479832, 0.007727596443146467, -0.018861068412661552, 0.018033143132925034, -0.002205882454290986, -0.0451849102973938, 0.04345693439245224, -0.02468188852071762, 0.07371050119400024, -0.0013951162109151483, 0.04063666984438896, 0.03498454391956329, -0.03824527934193611, -0.006591717712581158, 0.0006134742288850248, 0.020476017147302628, -0.10212504863739014, -0.022604001685976982, 0.012396655976772308, -0.0057900939136743546, 0.007181860506534576, 0.017088819295167923, 0.03248604014515877, 0.03888971731066704, -0.08472588658332825, -0.0030888936016708612, -0.0012541849864646792, 0.004114505834877491, 0.02484380453824997, -0.059198495000600815, 0.004286940209567547, -0.02819882147014141, 0.06796250492334366, 0.04218559339642525, 0.02903151698410511, 0.06551909446716309, -0.043902650475502014, 0.03721664845943451, 0.008931545540690422, -0.007675334345549345, 0.04670264571905136, 0.05464176833629608, 0.015422048047184944, 0.06381788104772568, -0.06301692128181458, -0.057215917855501175, 0.004757891874760389, 0.034114912152290344, -0.013528821989893913, -0.0038883222732692957, -0.015245060436427593, -0.04560147225856781, -0.006198300048708916, 0.05473072826862335, 0.030720889568328857, -0.009732337668538094, -0.011437201872467995, 0.00987387727946043, 0.032800111919641495, -0.06638798862695694, 0.08777766674757004, -0.029193662106990814, -0.0497625432908535, 0.014191395603120327, -0.0022107879631221294, 0.03529823571443558, -0.011981344781816006, 0.03471245989203453, -0.04861829802393913, -0.018031872808933258, -0.043784525245428085, -0.03942307457327843, 0.019477976486086845, -0.03417869284749031, -0.005289575085043907, 0.05999661609530449, 0.007541794329881668, -0.009871198795735836, 0.00956190936267376, 0.004886933136731386, -0.014769340865314007, 0.04633244127035141, 0.06599467247724533, 0.025166718289256096, -0.07039051502943039, 0.012017384171485901, 0.013445249758660793, 0.007077323272824287, -0.04735228791832924, -0.027465565130114555, -0.0485600084066391, -0.007717732805758715, -0.011367817409336567, -0.0416543073952198, 0.0018127401126548648, -0.017297938466072083, -0.03529917076230049, -0.004801541566848755, -0.0906556248664856, -0.012694837525486946, -0.0447656512260437, 2.895872910357866e-07, -0.06502846628427505, 0.019568098708987236, -0.054364245384931564, -0.0691467896103859, -0.0016900261398404837, -0.010851810686290264, -0.012966878712177277, 0.0016956913750618696, 0.028639785945415497, 0.029689520597457886, -0.014778939075767994, -0.03185180947184563, 0.027250858023762703, -0.007928530685603619, -0.02620990201830864, -0.02394128032028675, 0.032053835690021515, 0.02584727481007576, -0.02223106101155281, 0.03533734381198883, -0.047291502356529236, 0.040058933198451996, 0.04664336144924164, -0.062304891645908356, 0.0752471536397934, -0.03585628792643547, -0.031239353120326996, 0.028053952381014824, 0.022467447444796562, -0.05857536569237709, 0.00047295764670707285, 0.069728784263134, 0.0006327113951556385, 0.03189515322446823, -0.013559459708631039, 0.03660065308213234, 0.02304612286388874, 0.009686167351901531, -0.05028644949197769, 0.07598677277565002, 0.04929332435131073, 0.0031064911745488644, 0.002948008943349123, 0.02675662934780121, 0.046053819358348846, 0.028384918347001076, -0.043847933411598206, -0.05555272474884987, 0.021968789398670197, -0.058648958802223206, -0.010997907258570194, 0.01104151364415884, 0.04682750999927521, -0.016277140006422997, -0.025286268442869186, -0.07873202115297318, -0.014508290216326714, 0.006441863253712654, -0.007878067903220654, -0.01745636761188507, -0.027207879349589348, -0.03645723685622215, 0.022287264466285706, 0.03145652636885643, 0.047543153166770935, 0.008383354172110558, -0.0337759293615818, 2.4520892514212056e-34, 0.02812778204679489, -0.0004790069651789963, 0.018954405561089516, 0.029185747727751732, -0.03786991536617279, -0.004324589390307665, -0.017668969929218292, -0.031690310686826706, -0.015114348381757736, 0.007920367643237114, 0.020739544183015823]

['Kiyana Zolfaghar', 'Nele Verbiest', 'Jayshree Agarwal', 'Naren Meadem', 'Si-Chi Chin', 'Senjuti Basu Roy', 'Ankur Teredesai', 'David Hazel', 'Paul Amoroso', 'Lester Reed']

1306.2094v1

Mitigating risk-of-readmission of Congestive Heart Failure (CHF) patients within 30 days of discharge is important because such readmissions are not only expensive but also critical indicator of provider care and quality of treatment. Accurately predicting the risk-of-readmission may allow hospitals to identify high-risk patients and eventually improve quality of care by identifying factors that contribute to such readmissions in many scenarios. In this paper, we investigate the problem of predicting risk-of-readmission as a supervised learning problem, using a multi-layer classification approach. Earlier contributions inadequately attempted to assess a risk value for 30 day readmission by building a direct predictive model as opposed to our approach. We first split the problem into various stages, (a) at risk in general (b) risk within 60 days (c) risk within 30 days, and then build suitable classifiers for each stage, thereby increasing the ability to accurately predict the risk using multiple layers of decision. The advantage of our approach is that we can use different classification models for the subtasks that are more suited for the respective problems. Moreover, each of the subtasks can be solved using different features and training data leading to a highly confident diagnosis or risk compared to a one-shot single layer approach. An experimental evaluation on actual hospital patient record data from Multicare Health Systems shows that our model is significantly better at predicting risk-of-readmission of CHF patients within 30 days after discharge compared to prior attempts.

Predicting Risk-of-Readmission for Congestive Heart Failure Patients: A Multi-Layer Approach

http://arxiv.org/pdf/1306.2094v1

Title Predicting RiskofReadmission Congestive Heart Failure Patients MultiLayer Approach Summary Mitigating riskofreadmission Congestive Heart Failure CHF patient within 30 day discharge important readmission expensive also critical indicator provider care quality treatment Accurately predicting riskofreadmission may allow hospital identify highrisk patient eventually improve quality care identifying factor contribute readmission many scenario paper investigate problem predicting riskofreadmission supervised learning problem using multilayer classification approach Earlier contribution inadequately attempted ass risk value 30 day readmission building direct predictive model opposed approach first split problem various stage risk general b risk within 60 day c risk within 30 day build suitable classifier stage thereby increasing ability accurately predict risk using multiple layer decision advantage approach use different classification model subtasks suited respective problem Moreover subtasks solved using different feature training data leading highly confident diagnosis risk compared oneshot single layer approach experimental evaluation actual hospital patient record data Multicare Health Systems show model significantly better predicting riskofreadmission CHF patient within 30 day discharge compared prior attempt Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.007240136153995991, 0.005292464047670364, -0.023636823520064354, -0.057679470628499985, 0.015010968782007694, 0.009371825493872166, 0.03836749494075775, 0.002671446418389678, 0.02266484871506691, 0.027414459735155106, 0.06402693688869476, -0.024306105449795723, 0.025660984218120575, 0.0320698618888855, -0.006447419989854097, -0.01060478761792183, 0.04867752641439438, -0.011477398686110973, 0.009649609215557575, 0.00547307264059782, 0.009572524577379227, -0.02329435385763645, 0.02718709409236908, 0.07030683010816574, 0.009269583970308304, -0.01056760735809803, 0.005072739906609058, -0.058367639780044556, 0.002393406117334962, -0.07106462121009827, 0.032109636813402176, -0.01726112700998783, -0.016142116859555244, -0.0495859831571579, 2.2235242340684636e-06, -0.047987811267375946, -0.0528445802628994, -0.0056787231005728245, 0.0041945013217628, -0.07623200863599777, -0.051187220960855484, -0.06433742493391037, 0.0493495799601078, 0.00674310140311718, -0.03267158940434456, -0.010346234776079655, 0.0013409032253548503, 0.09965509176254272, 0.021883489564061165, -0.0033226818777620792, -0.0008333394071087241, 0.007534450851380825, -0.016371101140975952, -0.006660851184278727, -0.009403510950505733, -0.07458687573671341, 0.01367209292948246, 0.02635912224650383, -0.0023699889425188303, -0.0838242843747139, -0.02403229847550392, 0.05307980254292488, 0.03614964336156845, 0.053000763058662415, 0.04515007883310318, 0.016681140288710594, 0.032610032707452774, -0.019489813596010208, -0.027090314775705338, 0.027184439823031425, -0.06139831244945526, 0.03859713673591614, -0.030634863302111626, -0.007951260544359684, 0.03981802612543106, 0.010402072221040726, -0.013036137446761131, -0.004398885648697615, -0.03747706115245819, 0.01412112545222044, -7.295470277313143e-05, 0.043285250663757324, -0.001183440675958991, -0.02138957753777504, 0.024169843643903732, -0.023178089410066605, -0.020943932235240936, -0.006495467387139797, 0.02537222020328045, 0.006438590120524168, 0.011034194380044937, 0.010982191190123558, 0.02381078526377678, -0.003211959498003125, -0.059713251888751984, -0.000584536581300199, 0.0455150306224823, -0.00041454905294813216, 0.09638907760381699, -0.08306582272052765, 0.039257463067770004, -0.011396469548344612, 0.013891107402741909, -0.005562539678066969, 0.0033151304814964533, -0.031416404992341995, -0.02630387619137764, 0.009099242277443409, -0.024246269837021828, 0.053697630763053894, -0.021811898797750473, 0.027015933766961098, 0.010542791336774826, 0.07411886006593704, 0.0648367628455162, 0.024154065176844597, -0.11097779870033264, -0.03545013442635536, -0.01307578757405281, -0.0351136215031147, 0.06345973908901215, 0.047796960920095444, 0.024042675271630287, 0.04362662881612778, -0.002508661476895213, 0.0016405228525400162, 0.010604086332023144, 0.028939668089151382, -0.02771543338894844, 0.006144896615296602, 0.05242766812443733, 0.01741359941661358, -0.007848650217056274, 0.011797857470810413, -0.012875145301222801, 0.034389838576316833, -0.0034916666336357594, -0.009248392656445503, -0.07507342845201492, -0.007962249219417572, -0.02031892165541649, 0.03276882693171501, -0.029125886037945747, -0.004760118667036295, -0.01901238225400448, -0.011635541915893555, 0.003449486568570137, 0.025392362847924232, 0.004936892073601484, -0.03893207013607025, -0.0037160548381507397, 0.022599907591938972, -0.04568219184875488, 0.015268158167600632, 0.07740678638219833, 0.045923735946416855, -0.042154815047979355, -0.0026871885638684034, 0.014504708349704742, -0.010717214085161686, -0.02672005072236061, -0.032952066510915756, 0.04422854259610176, 0.002478164853528142, -0.024364739656448364, -0.0838303491473198, 0.04115370288491249, 0.0030267906840890646, -0.041831158101558685, 0.03430192545056343, -0.03396140784025192, 0.0015772873302921653, 0.008053258061408997, -0.003761133411899209, 0.015875017270445824, -0.050767287611961365, 0.08182477951049805, -0.016292044892907143, -0.012577751651406288, 0.011403275653719902, -0.026441024616360664, -0.0517943799495697, 0.03905056044459343, 0.015973476693034172, -0.008607651107013226, -0.022301577031612396, -0.05812901258468628, -0.028663402423262596, -0.02178891934454441, -0.06946558505296707, -0.005298176314681768, -0.024441612884402275, -0.022319583222270012, -0.017891068011522293, 0.022864356637001038, -0.014695779420435429, -0.008363370783627033, 0.020404750481247902, 0.045830655843019485, 0.030468305572867393, -0.05491268262267113, -0.1058119609951973, -0.010419218800961971, 0.010447676293551922, -0.026721490547060966, -0.03069370426237583, 0.017918359488248825, -0.025379488244652748, -0.006370256654918194, -0.10387608408927917, 0.014075358398258686, -0.004730249289423227, 0.03259221091866493, -0.0066146282479166985, 0.02038109302520752, 0.06030251085758209, 0.014675642363727093, 0.024242304265499115, -0.04240941256284714, -0.006421492900699377, -0.028079800307750702, 0.008131073787808418, -0.028278574347496033, 0.031615741550922394, -0.0220948439091444, 0.016503948718309402, 0.017898034304380417, 0.038709606975317, 0.025073518976569176, -0.023838916793465614, 0.04495517909526825, 0.018839487805962563, 0.008068736642599106, 0.01727328635752201, -0.10720506310462952, -0.010414755903184414, -0.03437028080224991, -0.0398012138903141, -0.011089388281106949, 0.020369792357087135, 0.011026180349290371, -0.030950812622904778, -0.007109809201210737, -0.01710430346429348, -0.01163727417588234, -0.020216941833496094, -0.02143244631588459, -0.013775374740362167, 0.022889453917741776, 0.020257947966456413, -0.00826321542263031, -0.029401134699583054, 0.018147816881537437, -0.02514932118356228, -0.023877672851085663, -0.02992417849600315, -0.04866988956928253, 0.034805357456207275, 0.023517288267612457, 0.015931053087115288, -0.022921260446310043, -0.07129178941249847, 0.0340290442109108, -0.023382065817713737, 0.016807226464152336, -0.023212837055325508, 0.0166782233864069, -0.04760647565126419, -0.032738588750362396, -0.0012126666260883212, -0.0417390801012516, -0.06401289254426956, 0.000825709430500865, -0.002369936555624008, -0.03967970609664917, -0.003424181370064616, -0.007407438009977341, 0.0020508323796093464, -0.012061189860105515, 0.04121130704879761, 0.05607610568404198, -0.004128012806177139, 0.009679744020104408, 0.02444515749812126, -0.023948999121785164, 0.04118109866976738, 0.04129979759454727, -0.022508876398205757, 0.01331299263983965, -0.03082888014614582, 0.03446514531970024, -0.0468042753636837, 0.014278948307037354, -0.016148898750543594, -0.05644640326499939, -0.020118296146392822, -0.06113054230809212, 0.006476858165115118, -0.026146400719881058, 0.04867766052484512, 0.045175958424806595, 0.06021636724472046, -0.015212520025670528, 0.03179454803466797, -0.06097754091024399, -0.012990065850317478, 0.03650334104895592, -0.0048787216655910015, -0.05850769951939583, 0.010290391743183136, 0.06373725831508636, -0.010254861786961555, -0.003975407686084509, 0.006211817730218172, 0.014129097573459148, -0.0007244270527735353, -0.04847705736756325, -0.014798196963965893, 0.002054952783510089, 0.023714572191238403, 0.02926682122051716, -0.02577996253967285, 0.01824129745364189, 0.043813835829496384, 0.04453444108366966, -0.051895011216402054, -0.08718696236610413, -0.013172516599297523, -0.018638554960489273, -0.057698022574186325, 0.011202397756278515, 0.019738856703042984, -0.0054863328114151955, 0.026896458119153976, 0.020961055532097816, -0.000695601396728307, 0.0019185746787115932, 0.02717418223619461, -0.04646311327815056, 0.022739781066775322, 0.02541222982108593, -0.04543038830161095, -0.028557561337947845, 0.04311315342783928, -0.0030965732876211405, -0.00033825586433522403, -0.048707153648138046, 0.04985424503684044, -0.015509312972426414, 0.00936664454638958, -0.05973384901881218, 0.03346891701221466, -0.022537067532539368, -0.039202094078063965, 0.030493780970573425, 0.016717776656150818, -0.002969918539747596, -0.0363757461309433, -0.019148562103509903, -0.013333630748093128, 0.08518916368484497, 0.01772652566432953, -0.024522220715880394, 0.03635023534297943, -0.04775431752204895, 0.04307312145829201, -0.020402658730745316, -0.019613657146692276, 0.0010755066759884357, 0.003612704575061798, 0.005775544326752424, -0.03913865610957146, 0.03856241703033447, 0.040767014026641846, 0.02438855543732643, -0.04068029299378395, 0.022603053599596024, -0.055018872022628784, -0.04876040294766426, -0.018567169085144997, -0.025657128542661667, 0.032231565564870834, -0.00877339206635952, -0.0025751590728759766, 0.006548818666487932, -0.009225267916917801, -0.040048256516456604, 0.019310079514980316, 0.023942802101373672, 0.03271881863474846, -0.020732520148158073, -0.03227905556559563, -0.036452069878578186, -0.04966718703508377, -0.014818037860095501, -0.03599487990140915, -0.03402687981724739, -0.035495880991220474, 0.010984702035784721, -0.0015641897916793823, 0.017263047397136688, -0.11310306936502457, -0.0030882626306265593, 0.07316486537456512, -0.0034410555381327868, 0.006830162834376097, 0.014051856473088264, 0.015760978683829308, -0.023226501420140266, 0.03223302215337753, 0.01375263649970293, 0.0014250139938667417, 0.07562095671892166, -0.03656582906842232, 0.08600910007953644, 0.04944637790322304, 0.02810528315603733, -0.027200577780604362, 0.02110583893954754, 0.017105288803577423, 0.018459279090166092, 0.054752275347709656, 0.053146567195653915, -0.06301197409629822, -0.06924465298652649, -0.05231071263551712, 0.04077017679810524, 0.04538354277610779, -0.016451137140393257, -0.004210128448903561, -0.02564738504588604, -0.019990306347608566, 0.04455917328596115, 0.027828913182020187, -0.007700964342802763, 0.057203259319067, 0.04420934244990349, -0.03562656417489052, -0.03704999014735222, 0.000322342588333413, -0.006477032322436571, -0.0016576466150581837, 0.031242895871400833, 0.027058947831392288, 0.05238410457968712, 0.041821859776973724, 0.053527992218732834, -0.02626185119152069, -0.013292745687067509, 0.08245985209941864, 0.036626994609832764, -0.007621829863637686, 0.029163574799895287, 0.020725730806589127, -0.011201351881027222, -0.03042810782790184, -0.09055789560079575, 0.03387163206934929, 0.01538865827023983, -0.010076379403471947, 0.09008199721574783, 0.02246846631169319, -0.020828712731599808, -0.00164295663125813, -0.01824556104838848, 0.06235016509890556, -0.0637662261724472, -0.010644570924341679, -0.06808499991893768, 0.02369740605354309, -0.05659443512558937, -0.03765525296330452, 0.015783922746777534, 0.022710522636771202, 0.07193104177713394, 0.006116234231740236, -0.03400972858071327, -0.019174037501215935, 0.044754114001989365, -0.028515685349702835, 0.007502574939280748, 0.041649192571640015, -0.01975869946181774, -0.03158855065703392, -0.022755056619644165, 0.01405919250100851, 0.007573006208986044, 0.02901756577193737, 0.0007421699119731784, 0.046857528388500214, 0.0349712111055851, 0.008551432751119137, 0.019019518047571182, -0.06260467320680618, 0.021909214556217194, -0.08745017647743225, 9.294338087784126e-05, 0.10185489058494568, 0.04206402599811554, 0.030025595799088478, 0.025068700313568115, 0.02059406042098999, 0.013200454413890839, -0.02458157390356064, 0.050218358635902405, -0.014511565677821636, 0.028327394276857376, 0.053016360849142075, -0.032104335725307465, 0.005084664560854435, -0.03860481455922127, 0.015269238501787186, 0.01367791835218668, -0.009840678423643112, -0.0015367690939456224, -0.0062419637106359005, -0.00881389994174242, 0.006269924342632294, -0.016215501353144646, -0.00030318237259052694, 0.024931935593485832, -0.023955445736646652, 0.05958424508571625, -0.043910734355449677, 0.01667557656764984, 0.06438545882701874, -0.01591666042804718, -0.04102043807506561, -0.017190460115671158, 0.09679065644741058, 0.05348886922001839, -0.02188868075609207, -0.06756880134344101, -0.05527711287140846, -0.04846940562129021, 0.016622699797153473, 0.08564168214797974, 0.03768768161535263, -0.061893004924058914, 0.008453773334622383, -0.05716108903288841, -0.0022507840767502785, 0.07175636291503906, -0.03724654018878937, 0.052051566541194916, 0.005730998702347279, -0.0027364706620573997, 0.009902525693178177, -0.010422763414680958, 0.0118469949811697, -0.0444963276386261, -0.031559765338897705, -0.007556125987321138, 0.020264752209186554, 0.009802297689020634, -4.917987714564192e-33, 0.02438126690685749, -0.03543972223997116, -0.0035162155982106924, -0.03419307991862297, -0.003704649396240711, 0.04346347227692604, -0.002668128814548254, -0.006145029794424772, 0.007474071811884642, -0.016560524702072144, 0.009883069433271885, -0.011963584460318089, 0.005914796609431505, 0.015191452577710152, 0.07654641568660736, -0.055207833647727966, -0.017339857295155525, 0.029716353863477707, 0.011508971452713013, -0.002973397960886359, -0.04426518455147743, 0.07190485298633575, -0.020641392096877098, -0.04335338622331619, -0.026317045092582703, 0.04622908681631088, -0.017010822892189026, -0.023362547159194946, -0.026589326560497284, 0.02520863339304924, 0.004760983400046825, 0.04582909122109413, 0.02890315093100071, -0.06540875881910324, 0.021976761519908905, 0.03463272377848625, 0.00568479485809803, -0.025049351155757904, -0.0235297828912735, -0.02056354098021984, 0.03570256754755974, 0.008339093066751957, 0.007154789753258228, 0.022463234141469002, -0.007797647267580032, -0.015141764655709267, 0.03188690170645714, -0.03620065003633499, 0.0011872559553012252, -0.061242714524269104, 0.0032127329614013433, 0.04266186058521271, -0.009393665008246899, 0.026798317208886147, -0.020772267132997513, 0.04128047823905945, -0.024766448885202408, 0.03191404044628143, -0.04043618217110634, -0.015652915462851524, -0.020634250715374947, -0.022360440343618393, -0.0075957500375807285, -0.0010076658800244331, -0.044215161353349686, 0.04174415022134781, 0.010172146372497082, -0.016118744388222694, -0.015697812661528587, 0.0295903068035841, -0.08606114983558655, 0.04530924931168556, 0.040696531534194946, 0.020344648510217667, 0.012853153049945831, -0.09202384948730469, -0.09686601161956787, 0.056902576237916946, -0.014613045379519463, -0.021998805925250053, -0.014053735882043839, -0.0236087366938591, -0.02225262112915516, -0.015486770309507847, -0.010283409617841244, 0.014079350046813488, 0.006133563816547394, -0.005980722140520811, 0.030842969194054604, 0.011398802511394024, 0.04859006404876709, 0.032940976321697235, -0.005711250938475132, -0.04185645654797554, 0.022226817905902863, -0.016220996156334877, 0.06168680638074875, 0.004245773423463106, 0.0018812631024047732, 0.007260382175445557, 0.028613310307264328, 0.001325582037679851, -0.014407741837203503, -0.019398784264922142, 0.032489195466041565, -0.012612102553248405, 0.06981656700372696, -0.018926646560430527, -0.010001096874475479, -0.02454357221722603, 0.08619363605976105, -0.07202127575874329, -0.011564290151000023, 0.07705197483301163, -0.01491735689342022, -0.0064026773907244205, -0.017321815714240074, 0.05681057646870613, 0.016478464007377625, 0.03768175095319748, -0.056128136813640594, -0.029345190152525902, -0.028305446729063988, -0.03804478049278259, -0.03931567072868347, -0.013340133242309093, -0.04079035669565201, 0.013349496759474277, 0.022136598825454712, -0.0752209946513176, -0.005665554199367762, -0.013295182026922703, 2.751700947101199e-07, 0.03558472916483879, 0.016482127830386162, -0.05808389559388161, -0.08035041391849518, -0.004303520545363426, 0.032146379351615906, -0.03660561889410019, -0.0072505963034927845, -0.011903250589966774, 0.03542536869645119, 0.07247062027454376, -0.06501615792512894, 0.014816087670624256, 0.019253982231020927, -0.04011862352490425, -0.08976289629936218, -0.003716428065672517, 0.01662866212427616, -0.027178190648555756, 0.024215448647737503, 0.060483645647764206, 0.050230614840984344, -0.032916080206632614, -0.04628031328320503, 0.005545982625335455, 0.04565926268696785, -0.010337689891457558, 0.01129088643938303, -0.011872982606291771, -0.014161817729473114, 0.04448572173714638, 0.044905003160238266, 0.008267824538052082, 0.03879597783088684, -0.039346929639577866, -0.005209367256611586, 0.029055388644337654, 0.06167956441640854, -0.024299293756484985, 0.021029070019721985, 0.051528580486774445, 0.010960737243294716, 0.06932617723941803, -0.016286460682749748, 0.056339945644140244, -0.020985594019293785, -0.026582302525639534, -0.032990001142024994, 0.014392560347914696, 0.02697511576116085, 0.09475545585155487, -0.0038092895410954952, 0.002612868556752801, 0.011307133361697197, -0.018485141918063164, -0.0028015184216201305, 0.00968059804290533, -0.021714892238378525, -0.048938389867544174, 0.04657682031393051, -0.0023307015653699636, -0.025812778621912003, 0.05763902887701988, -0.005631755571812391, 0.06398091465234756, -0.0733635425567627, -0.020293235778808594, 2.407244601114816e-34, 0.0188604686409235, -0.016917185857892036, -0.02637721598148346, -0.0014418408973142505, 0.004489582497626543, -0.024017345160245895, 0.042926155030727386, 0.01437393855303526, -0.03474283218383789, -0.004728795029222965, -0.026454905048012733]

['E. N. Sathishkumar', 'K. Thangavel', 'T. Chandrasekhar']

1306.2118v1

We extend the standard rough set-based approach to deal with huge amounts of numeric attributes versus small amount of available objects. Here, a novel approach of clustering along with dimensionality reduction; Hybrid Fuzzy C Means-Quick Reduct (FCMQR) algorithm is proposed for single gene selection. Gene selection is a process to select genes which are more informative. It is one of the important steps in knowledge discovery. The problem is that all genes are not important in gene expression data. Some of the genes may be redundant, and others may be irrelevant and noisy. In this study, the entire dataset is divided in proper grouping of similar genes by applying Fuzzy C Means (FCM) algorithm. A high class discriminated genes has been selected based on their degree of dependence by applying Quick Reduct algorithm based on Rough Set Theory to all the resultant clusters. Average Correlation Value (ACV) is calculated for the high class discriminated genes. The clusters which have the ACV value a s 1 is determined as significant clusters, whose classification accuracy will be equal or high when comparing to the accuracy of the entire dataset. The proposed algorithm is evaluated using WEKA classifiers and compared. Finally, experimental results related to the leukemia cancer data confirm that our approach is quite promising, though it surely requires further research.

A Novel Approach for Single Gene Selection Using Clustering and Dimensionality Reduction

http://arxiv.org/pdf/1306.2118v1

Title Novel Approach Single Gene Selection Using Clustering Dimensionality Reduction Summary extend standard rough setbased approach deal huge amount numeric attribute versus small amount available object novel approach clustering along dimensionality reduction Hybrid Fuzzy C MeansQuick Reduct FCMQR algorithm proposed single gene selection Gene selection process select gene informative one important step knowledge discovery problem gene important gene expression data gene may redundant others may irrelevant noisy study entire dataset divided proper grouping similar gene applying Fuzzy C Means FCM algorithm high class discriminated gene selected based degree dependence applying Quick Reduct algorithm based Rough Set Theory resultant cluster Average Correlation Value ACV calculated high class discriminated gene cluster ACV value 1 determined significant cluster whose classification accuracy equal high comparing accuracy entire dataset proposed algorithm evaluated using WEKA classifier compared Finally experimental result related leukemia cancer data confirm approach quite promising though surely requires research Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.015683623030781746, 0.037801798433065414, -0.06341832131147385, -0.015194571577012539, -0.017401203513145447, 0.032554078847169876, 0.08914054930210114, 0.0571579709649086, 0.04462077468633652, 0.01577116921544075, 0.0735616460442543, 0.028621861711144447, 0.015277151949703693, -0.0050374181009829044, 0.006994462106376886, 0.013557885773479939, -0.004969063214957714, 0.015742039307951927, 0.030004635453224182, -0.011211913079023361, -0.01628737710416317, 0.01292685978114605, 0.043378885835409164, 0.02143840864300728, -0.03272624686360359, 0.022133851423859596, 0.06195250526070595, -0.05556238442659378, -0.0034871597308665514, -0.005137613508850336, 0.03731050714850426, 0.02707851678133011, -0.02175443060696125, -0.0215208288282156, 2.1094413114042254e-06, -0.081711545586586, -0.02759341150522232, -0.00432629743590951, 0.018690072000026703, -0.025277651846408844, 0.005074917804449797, 0.039599791169166565, 0.026755815371870995, -0.030149856582283974, 0.0010810812236741185, -0.01303636934608221, 0.016299787908792496, 0.049640923738479614, -0.01872362568974495, 0.005788900889456272, 0.003377023618668318, -0.06362080574035645, -0.0023146290332078934, -0.0064790695905685425, 0.07757381349802017, 0.0006277068168856204, 0.047182369977235794, 0.021532362326979637, 0.025217054411768913, -0.04298289492726326, 0.01679677702486515, 0.03236530348658562, -0.028760593384504318, -0.0035371119156479836, -0.0030835233628749847, 0.044746026396751404, -0.019504547119140625, -0.041423045098781586, 0.06847742199897766, 0.014350980520248413, -0.05530169978737831, -0.04564756527543068, 0.07503596693277359, 0.020766250789165497, 0.03900913521647453, -0.008817200548946857, 0.0017415909096598625, -0.02856786549091339, -0.07060619443655014, 0.016742806881666183, 0.0031641898676753044, 0.03978237137198448, -0.018666360527276993, -0.0015802272828295827, 0.04581465944647789, -0.002091445028781891, -0.03458205610513687, 0.012035650201141834, 0.0009556430159136653, -0.008066483773291111, -0.03638673573732376, 0.0462472103536129, 0.017382629215717316, -0.010807846672832966, -0.005320385098457336, -0.0800616666674614, 0.06199441850185394, -0.02924443408846855, 0.1078183576464653, -0.03949568420648575, -0.03996684029698372, -0.019529826939105988, 0.030818665400147438, 0.0175692830234766, -0.01583750545978546, -0.04782503843307495, 0.013331099413335323, 0.06415488570928574, 0.016395719721913338, 0.03255394101142883, -0.05429431051015854, 0.047925401479005814, -0.021599406376481056, 0.06933407485485077, 0.04955286160111427, 0.03621366620063782, -0.0782380998134613, -0.04825674742460251, -0.012973456643521786, 0.006545680575072765, 0.03547981008887291, 0.014703438617289066, 0.051271822303533554, 0.06731211394071579, 0.05357981473207474, -0.023302488029003143, -0.059679724276065826, -0.006164667196571827, -0.04701308161020279, -0.045655716210603714, 0.015772897750139236, -0.0007535257609561086, 0.048391856253147125, 0.005578017793595791, -0.0350399874150753, -0.002396476687863469, -0.006935467943549156, -0.030618535354733467, -0.009673322550952435, -0.0006729179294779897, -0.04691590368747711, -0.012771211564540863, -0.06712048500776291, 0.0032587337773293257, -0.031572550535202026, 0.03689491003751755, -0.02552913688123226, 0.015487788245081902, -0.010471227578818798, -0.048066895455121994, -0.014011110179126263, 0.0258520245552063, -0.031563758850097656, 0.012204409576952457, 0.06944139301776886, -0.02639913745224476, 0.0008297818712890148, -0.07292115688323975, -0.009506171569228172, 0.011830064468085766, 0.035647645592689514, -0.03455240651965141, 0.01481853798031807, -0.025250088423490524, -0.0270495917648077, -0.05225491151213646, 0.02197274938225746, 0.010809504427015781, 0.027172861620783806, -0.01434597373008728, -0.025140002369880676, -0.03945435583591461, -0.007952016778290272, -0.015580530278384686, 0.014052954502403736, 0.0355667769908905, 0.08591291308403015, 0.05445915833115578, -0.048163849860429764, 0.062459055334329605, -0.021837912499904633, -0.033021848648786545, 0.02599845640361309, 0.07174914330244064, -0.06087096035480499, 0.025493698194622993, 0.004220125265419483, 0.008948947302997112, 0.001842579455114901, -0.005879272241145372, 0.005045418627560139, 0.02384963259100914, -0.004805444274097681, -0.07175535708665848, 0.017495376989245415, -0.010810930281877518, 0.008759734220802784, -0.0801277682185173, 0.041661448776721954, 0.00773236621171236, -0.019209174439311028, -0.005181425716727972, 0.03913849592208862, -0.07517586648464203, 0.006886348128318787, -0.06851053237915039, -0.004688577726483345, -0.037782683968544006, -0.035146940499544144, -0.06537283211946487, -0.04825027659535408, -0.012967581860721111, -0.006519532762467861, -0.00932901632040739, 0.0401497483253479, 0.04719085991382599, 0.01829667016863823, -0.009905938059091568, -0.0502842478454113, 0.03446757420897484, -0.009762486442923546, -0.0008180793956853449, -0.032554347068071365, 0.0014023862313479185, 0.048994895070791245, -0.00015562193584628403, 0.01646740548312664, 0.0018624658696353436, 0.05569947883486748, -0.04659351706504822, -0.015753956511616707, -0.014827706851065159, 0.018603382632136345, -0.046021148562431335, -0.03435255587100983, -0.005347668658941984, 0.009080952033400536, -0.05572593957185745, -0.04979643598198891, 0.008127524517476559, -0.032863814383745193, -0.03583337366580963, -0.04522261396050453, 0.01889830082654953, 0.007802151143550873, -0.040250014513731, -0.02690071426331997, -0.004764182027429342, 0.0012223483063280582, -0.028140274807810783, -0.012629860080778599, 0.004374000243842602, 0.06970702856779099, 0.023184671998023987, -0.004662690218538046, -0.010204022750258446, -0.06172608956694603, 0.015088561922311783, -0.008506901562213898, 0.042315416038036346, -0.03741903603076935, -0.010563175193965435, -0.00159791752230376, 0.008157460018992424, 0.007177009712904692, -0.012748263776302338, 0.013232034631073475, 0.04602331668138504, -0.05966637656092644, 0.0152540672570467, 0.02179480716586113, -0.07287731766700745, -0.021575041115283966, 0.0346079058945179, -0.010127583518624306, -0.02764003351330757, 0.034520223736763, -0.011122629046440125, -0.03364827483892441, 0.040608663111925125, -0.027297712862491608, -0.007683959323912859, -0.02853045053780079, 0.012732197530567646, 0.0033457642421126366, 0.049875658005476, 0.08889158070087433, -0.04192464053630829, 0.07169786840677261, 0.0559425912797451, -0.012366381473839283, -0.020120037719607353, 0.0096665658056736, -0.013548477552831173, -0.029493464156985283, -4.258668559486978e-05, -0.0674659013748169, 0.0033960966393351555, 0.03370526060461998, -0.05946435406804085, -0.0011621353914961219, 0.01932641863822937, 0.029211733490228653, 0.01651884987950325, 0.004948173183947802, 0.049430735409259796, 0.04761304333806038, 0.03605329990386963, 0.00370821263641119, -0.034557491540908813, 0.0551651306450367, -0.0349997915327549, -0.05108398199081421, -0.007874459028244019, 0.03179250657558441, 0.040533941239118576, -0.06975824385881424, 0.0192885585129261, -0.017879823222756386, 0.006015645805746317, 0.02116319164633751, -0.020159726962447166, 0.06785894930362701, 0.02569943107664585, -0.011338305659592152, -0.024142034351825714, 0.03602417930960655, 0.05776611343026161, -0.06012172996997833, -0.019609125331044197, 0.02114717848598957, -0.05861542001366615, 0.01710919849574566, 0.04856792464852333, 0.021537629887461662, 0.029885323718190193, -0.03103187307715416, 0.045598458498716354, -0.007550342474132776, 0.012643002904951572, 0.028238633647561073, 0.0034136136528104544, -0.0002871121105272323, 0.0676683858036995, 0.03874184191226959, -0.011072695255279541, 0.05483243241906166, 0.008962408639490604, -0.05576279014348984, 0.028432538732886314, -0.0007357995491474867, 0.03161665052175522, -0.03264215961098671, 0.025085361674427986, 0.002230264013633132, -0.010037276893854141, -0.016471493989229202, -0.057635270059108734, -0.06420286744832993, -0.01614561304450035, 0.05324918404221535, 0.0031593404710292816, -0.03336464613676071, -0.032701969146728516, 0.030603481456637383, 0.010946349240839481, -0.028438813984394073, -0.03499886393547058, -0.008540629409253597, -0.04948306828737259, 0.016196340322494507, -0.00808821339160204, 0.00500756548717618, 0.06540672481060028, 0.03299030661582947, -0.0883956179022789, 0.012237225659191608, -0.025569414719939232, -0.0489349365234375, -0.014400267042219639, 0.054273899644613266, 0.034423623234033585, -0.0023777098394930363, -0.04619433358311653, -0.047187689691782, -0.032580919563770294, -0.0808500424027443, 0.04366480931639671, 0.01775282807648182, -0.014821279793977737, 0.02066812850534916, -0.052810512483119965, -0.02986050955951214, -0.05608044192194939, -0.016009831801056862, -0.05485733225941658, -0.06792110949754715, -0.013248111121356487, 0.03144414350390434, -0.029775768518447876, -0.03245991840958595, -0.030602751299738884, 0.008402973413467407, 0.04178620129823685, -0.0012199553893879056, 0.0004751771339215338, -0.031397126615047455, 0.024425547569990158, -0.015130571089684963, 0.015559416264295578, -0.03828653320670128, -0.03969580680131912, -0.0018015630776062608, -0.08443494141101837, 0.10291925817728043, 0.06904631108045578, -0.005714142229408026, -0.04731592535972595, 0.008906587958335876, 0.012986251153051853, 0.0006132674170657992, 0.00414774427190423, 0.004943179432302713, -0.007093335501849651, -0.08265767991542816, 0.011350576765835285, 0.028673453256487846, -0.051853686571121216, -0.007530517876148224, 0.02509259432554245, -0.028369398787617683, 0.021546075120568275, 0.00601222226396203, 0.03333517909049988, 0.02476906217634678, -0.012266065925359726, 0.02862265706062317, -0.05062457174062729, -0.014615901745855808, -0.04144926741719246, 0.031707391142845154, 0.025122759863734245, 0.062391459941864014, 0.001535824965685606, 0.06431448459625244, -0.004725262988358736, -0.07454238831996918, -0.0053784954361617565, 0.00422772578895092, 0.09456416219472885, -0.009246744215488434, -0.02592286840081215, -0.056149713695049286, 0.055728133767843246, -0.014161973260343075, -0.00658033974468708, -0.007527976296842098, 0.02228245884180069, -0.004633117932826281, -0.051510609686374664, 0.020420268177986145, -0.005754718091338873, -0.07832573354244232, -0.010619665496051311, -0.05088586360216141, 0.06120305135846138, -0.0005771145224571228, -0.014561237767338753, -0.009109735488891602, -0.04932883381843567, -0.05523085594177246, 0.005628284066915512, 0.01279059424996376, 0.003153648227453232, 0.06737503409385681, 0.037291958928108215, -0.05031825229525566, -0.04731585085391998, -0.002893730066716671, 0.010426823981106281, 0.06559637188911438, 0.07354268431663513, 0.03498982638120651, -0.015814336016774178, -0.015741528943181038, 0.0208211038261652, 0.033490072935819626, 0.018082723021507263, 0.028193000704050064, 0.0010628426680341363, -0.034714266657829285, 0.03845108300447464, -0.047977786511182785, -0.0009590709232725203, 0.016776174306869507, -0.06150945648550987, -0.011871837079524994, -0.008481326512992382, -0.006140867248177528, 0.04681878536939621, 0.029425444081425667, -0.01617739349603653, -0.016331955790519714, -0.019328249618411064, 0.0041070436127483845, 0.01882825419306755, -0.004873697180300951, -0.013142267242074013, 0.008373456075787544, 0.07671527564525604, -0.054087236523628235, -0.0038838074542582035, 0.040568459779024124, 0.06825616955757141, 0.0187394879758358, 0.0055830394849181175, 0.0035906664561480284, -0.04343673959374428, 0.05112401023507118, 0.027890676632523537, 0.009507517330348492, -0.08136576414108276, 0.05303513631224632, -0.015545840375125408, 0.01167961023747921, -0.03545701876282692, 0.010365250520408154, -0.037427447736263275, -0.03328113630414009, 0.021877693012356758, -0.016402313485741615, -0.0460825189948082, -0.05574517324566841, -0.03403518348932266, -0.05584362894296646, 0.06527698785066605, 0.0614023432135582, 0.008097250014543533, 0.002370776142925024, 0.02882438339293003, -0.02648324705660343, 0.018028324469923973, 0.023374302312731743, -0.010882343165576458, 0.02767179347574711, 0.06484853476285934, 0.007526860572397709, -0.02937939763069153, 0.021741094067692757, -0.06663621962070465, -0.013428129255771637, -0.06185375899076462, 0.028811348602175713, -0.02728353999555111, 0.02668757550418377, -5.800621239532538e-33, 0.04483466222882271, -0.062275759875774384, -0.043092887848615646, 0.007236565463244915, 0.033516302704811096, 0.00016965878603514284, -0.027040334418416023, -0.01470567099750042, 0.01941812038421631, 0.03653978183865547, 0.008814912289381027, -0.028020890429615974, -0.0348593071103096, -0.01765383780002594, 0.04907047748565674, 0.019997239112854004, 0.013327142223715782, 0.05327758193016052, 0.015723858028650284, 0.02919566072523594, 0.04484189301729202, 0.035840410739183426, -0.022434480488300323, -0.00030239304760470986, -0.04409361630678177, 0.06189708411693573, -0.014740883372724056, -0.011550734750926495, -0.07147229462862015, 0.005319059826433659, 0.06485488265752792, 0.017675328999757767, 0.011866273358464241, 0.011696310713887215, 0.012717559933662415, -0.07261323183774948, 0.009919842705130577, -0.0028079375624656677, -0.01859906315803528, 0.000476431188872084, 0.03345168009400368, -0.023674074560403824, 0.06623276323080063, -0.011298703961074352, -0.02607969008386135, 0.013547364622354507, 0.09346144646406174, -0.03149921074509621, -0.0607980452477932, -0.023373037576675415, 0.014941737055778503, 0.02409481629729271, -0.03543669357895851, 0.053176674991846085, 0.006450703367590904, -0.027058754116296768, -0.06422057002782822, 0.011422715149819851, -0.018830575048923492, 0.027377597987651825, -0.00026758460444398224, 0.024905046448111534, 0.008612575009465218, -0.020552201196551323, 0.04065488278865814, 0.026833873242139816, -0.0075422730296850204, -0.05698825418949127, -0.0036921321880072355, 0.014370134100317955, -0.03364096209406853, 0.02259107679128647, -0.02056066133081913, 0.028016742318868637, 0.0013562145177274942, -0.06349346041679382, -0.05842093378305435, 0.0755692794919014, 0.0017191714141517878, 0.0034622224047780037, -0.019532129168510437, 0.00966460071504116, 0.0017072550253942609, 0.02412058785557747, 0.00810283049941063, 0.015229792334139347, -0.0032959480304270983, -3.837907934212126e-05, -0.021222231909632683, -0.05067144334316254, -0.05058089271187782, 0.013095246627926826, -0.010139611549675465, 0.0020473424810916185, 0.011434534564614296, -0.028953585773706436, -0.01621885597705841, -0.006675904616713524, 0.019124727696180344, -0.024221936240792274, -0.0026711157988756895, -0.006277590058743954, 0.02761281095445156, -0.07347597181797028, -0.00230881804600358, 0.005607398692518473, 0.013326186686754227, -0.022273220121860504, -0.04039333388209343, 0.00026393216103315353, 0.049867670983076096, -0.0512024462223053, 0.023987874388694763, -0.007806341163814068, -0.0419735461473465, -0.02592407539486885, 0.015201043337583542, 0.06712616980075836, 0.044453900307416916, -0.00014132038631942123, 0.017066558822989464, 0.0019368714420124888, 0.012229450978338718, -0.021170007064938545, -0.0460476353764534, -0.007080956362187862, -0.03526182845234871, -0.01035225111991167, -0.0005007212748751044, -0.005187449511140585, -0.008567477576434612, 0.018426040187478065, 2.8359045245451853e-07, 0.037703435868024826, 0.01740911789238453, -0.0568886436522007, -0.06804598867893219, 0.00011548426846275106, 0.0118859289214015, -0.0374181903898716, 0.0048642950132489204, -0.08659142255783081, 0.05162317678332329, 0.08239881694316864, -0.020881980657577515, 0.033279743045568466, 0.0006164602236822248, -0.005943397060036659, 0.0042500486597418785, -0.005981240887194872, 0.013225248083472252, -0.003937941510230303, 0.013782422058284283, 0.017170066013932228, 0.0719883143901825, 0.041067466139793396, 0.013749117963016033, 0.06040390953421593, 0.007033110596239567, -0.036465417593717575, 0.005668542347848415, 0.011267334222793579, 0.02466386929154396, -0.0027565353084355593, -0.053585704416036606, 0.0001749654475133866, 0.060951560735702515, -0.020338473841547966, -0.042248424142599106, -0.032787423580884933, 0.000897534831892699, 0.01679733209311962, 0.05706925690174103, 0.05223701894283295, 0.04889126867055893, 0.07105637341737747, -0.054586779326200485, 0.00996597670018673, -0.01381708588451147, -0.08097178488969803, 0.02716243453323841, 0.07112222909927368, -0.020048340782523155, 0.011902175843715668, 0.05318712070584297, -0.008032426238059998, 0.06546954810619354, -0.004976915195584297, -0.013479751534759998, -0.026441222056746483, 0.02667221799492836, 0.04973188042640686, 0.0012384048895910382, -0.04430628940463066, -0.011089193634688854, 0.015687519684433937, 0.026543065905570984, 0.05048270523548126, 0.03527548164129257, 0.021006235852837563, 2.7446691065746517e-34, 0.008523033931851387, -0.008593236096203327, -0.019977569580078125, -0.008854522369801998, -0.014325335621833801, -0.004961605183780193, -0.00012092083488823846, -0.0021504233591258526, -0.0229053795337677, -0.03241327777504921, -0.007786798756569624]

['Guoqiang Zhong', 'Mohamed Cheriet']

1306.2663v1

Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent these tensor perceptions in a "manifold" way, and how can they be recognized on the "manifold"? In this paper, we present a supervised model to learn the intrinsic structure of the tensors embedded in a high dimensional Euclidean space. With the fixed point continuation procedures, our model automatically and jointly discovers the optimal dimensionality and the representations of the low dimensional embeddings. This makes it an effective simulation of the cognitive process of human brain. Furthermore, the generalization of our model based on similarity between the learned low dimensional embeddings can be viewed as counterpart of recognition of human brain. Experiments on applications for object recognition and face recognition demonstrate the superiority of our proposed model over state-of-the-art approaches.

Large Margin Low Rank Tensor Analysis

http://arxiv.org/pdf/1306.2663v1

Title Large Margin Low Rank Tensor Analysis Summary vector representation direct object human cognition generally highorder tensor 2D image 3D texture fact two interesting question naturally arise human brain represent tensor perception manifold way recognized manifold paper present supervised model learn intrinsic structure tensor embedded high dimensional Euclidean space fixed point continuation procedure model automatically jointly discovers optimal dimensionality representation low dimensional embeddings make effective simulation cognitive process human brain Furthermore generalization model based similarity learned low dimensional embeddings viewed counterpart recognition human brain Experiments application object recognition face recognition demonstrate superiority proposed model stateoftheart approach Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.01312856376171112, 0.008436097763478756, -0.026101181283593178, 0.04572521895170212, -0.004310741554945707, 0.06184489652514458, 0.04025770351290703, 0.03099670633673668, 0.03631086274981499, -0.0003798453835770488, -0.030281830579042435, -0.023829851299524307, 0.016241878271102905, -0.002555807586759329, 0.06294073164463043, -0.07651175558567047, -0.06344529241323471, -0.01731361262500286, 0.0028413976542651653, -0.0338037945330143, -0.040976669639348984, -0.04004884883761406, -0.0028489890974014997, -0.0007395233842544258, -0.010287833400070667, 0.021778520196676254, -0.012286762706935406, -0.03181080520153046, 0.0008282366907224059, -0.015323092229664326, -0.012333452701568604, 0.04104238748550415, 0.06128071993589401, 0.002802537754178047, 2.273839982080972e-06, 0.01979382336139679, 0.009695877321064472, -0.0030324377585202456, 0.059941891580820084, -0.03643441200256348, 0.007200510706752539, -0.014590754173696041, -0.01891498453915119, -0.0407395213842392, -0.020649606361985207, -0.020133433863520622, 0.02980007976293564, 0.09860169887542725, 0.03384316712617874, 0.023504072800278664, -0.02812052331864834, -0.043185487389564514, 0.008114594034850597, 0.007416365202516317, 0.00878352951258421, 0.021931763738393784, 0.00817622896283865, 0.01761733926832676, -0.03317691385746002, -0.003148994641378522, -0.012038636952638626, -0.0023175582755357027, -0.005715337116271257, 0.046125829219818115, 0.055260319262742996, 0.09107766300439835, -0.00892374012619257, 0.005352852400392294, -0.010105622932314873, 0.07579392194747925, -0.017425905913114548, -0.014739440754055977, 0.01834387518465519, 0.03254114091396332, -0.004856118466705084, 0.008826768025755882, -0.045981746166944504, -0.011306281201541424, 0.007898458279669285, 0.03586946055293083, -0.023745032027363777, -0.008696337230503559, -0.041196249425411224, -0.018184321001172066, -0.011440441943705082, -0.008118781261146069, 0.04788179695606232, -0.0089319609105587, -0.020815031602978706, -0.01875588856637478, 0.00985826924443245, 0.03878609836101532, -0.010404231026768684, -0.027464553713798523, 0.00534747913479805, -0.06956730782985687, 0.0074883257038891315, -0.11485737562179565, 0.012923005037009716, -0.10950085520744324, 0.09774114936590195, 0.031159324571490288, -0.05447500944137573, 0.04901083558797836, -0.08289854973554611, 0.08773161470890045, -0.071573905646801, 0.05589323863387108, -0.03115067444741726, 0.021109633147716522, 0.0034296936355531216, 0.011533468961715698, 0.004978502169251442, 0.028604192659258842, 0.018148647621273994, -0.040804795920848846, -0.04279911145567894, 0.026755357161164284, -0.022924156859517097, -0.0021588820964097977, -0.021326944231987, 0.04626019671559334, 0.057097580283880234, -0.0007441525813192129, -0.05701865628361702, -0.040195267647504807, 0.014590855687856674, 0.03602742403745651, -0.080037422478199, 0.04092187061905861, 0.02021716721355915, 0.047054264694452286, 0.0030439754482358694, -0.00804304052144289, 0.03645198047161102, 0.0568731464445591, -0.014049875549972057, -0.004338817670941353, -0.000830522330943495, 0.04117149859666824, 0.030714021995663643, -0.01586049422621727, 0.061915911734104156, -0.02650703303515911, 0.012760546058416367, -0.02532569319009781, -0.020373042672872543, -0.01764477603137493, -0.045607056468725204, -0.018906177952885628, -0.08637137711048126, 0.05756133422255516, 0.037920888513326645, -0.02198892831802368, 0.10641611367464066, -0.01037451159209013, 0.029863862320780754, -0.04806920140981674, 0.005696150474250317, 0.028549276292324066, -0.03599809482693672, -0.044053297489881516, -0.010149727575480938, -0.011190964840352535, -0.016224749386310577, -0.0343838669359684, -0.05578126013278961, -0.04142969474196434, 0.031159471720457077, 0.07402792572975159, 0.015512853860855103, 0.052477799355983734, -0.029651252552866936, -0.01745096780359745, 0.010459627956151962, 0.08024442195892334, 0.027857176959514618, 0.03298557922244072, 0.013003972359001637, -0.008715495467185974, -0.02021990343928337, 0.01985812932252884, -0.018174897879362106, 0.0896311029791832, 0.003944037016481161, -0.01761615090072155, 0.034324441105127335, -0.00671483064070344, -0.0217143502086401, 0.015626609325408936, 0.0299071054905653, -0.03871419280767441, 0.010723328217864037, -0.036141738295555115, 0.05718936398625374, -0.06710907816886902, -0.002979736542329192, -0.006694074720144272, -0.00630446569994092, 0.02907681092619896, -0.028571417555212975, 0.011769485659897327, 0.02556605637073517, -0.04556477442383766, -0.021960485726594925, -0.016922665759921074, 0.02013436146080494, 0.006539854686707258, 0.0005564774037338793, -0.04200008511543274, 0.01161260437220335, 0.011083920486271381, 0.014859158545732498, -0.023267095908522606, -0.04769415408372879, 0.006345435045659542, 0.0043515102006495, 0.009151973761618137, -0.050603389739990234, -0.011508048512041569, 0.006551417522132397, 0.0014363519148901105, 0.05472799018025398, 0.015195713378489017, -0.02303597889840603, -0.012350688688457012, 0.0207949411123991, 0.052592985332012177, 0.024146486073732376, 0.00665944954380393, 0.022350488230586052, -0.03037269599735737, 0.028994018211960793, -0.05030619725584984, -0.039794065058231354, -0.030108369886875153, -0.01716764084994793, 0.029209556058049202, 0.026261791586875916, -0.025812944397330284, 0.007502601481974125, -0.009611167013645172, -0.006218408700078726, -0.05102819576859474, 0.049186062067747116, 0.00787315797060728, -0.03665231168270111, -0.04272841662168503, 0.0004142384568694979, -0.009183443151414394, 0.015336249023675919, -0.028140095993876457, 0.0683923065662384, -0.010518176481127739, 0.024417854845523834, 0.010580434463918209, -0.06830195337533951, 0.05036003515124321, -0.039990682154893875, -0.023115035146474838, 0.061459191143512726, 0.018986180424690247, -0.00231384439393878, -0.00014966695744078606, 0.02802315168082714, 0.006087869871407747, -0.026551954448223114, -0.05547311156988144, -0.025570346042513847, 0.03832096979022026, -0.015324335545301437, 0.0011817582417279482, -0.044169727712869644, 0.01910969987511635, -0.010963167995214462, -0.006588013842701912, 0.03209678456187248, -0.006289574783295393, -0.035605836659669876, 0.050088778138160706, 0.013927141204476357, 0.004430167842656374, 0.01812536083161831, -0.013805234804749489, -0.017068983986973763, 0.04553481191396713, -0.006309720687568188, 0.001169670489616692, -0.013398068957030773, -0.025776639580726624, -0.02106620743870735, 0.0559336394071579, -0.00031039604800753295, -0.023742906749248505, 0.018403291702270508, -0.02640843577682972, 0.07214439660310745, 0.055589739233255386, 0.026432093232870102, -0.004242333117872477, 0.021020475775003433, 0.07633918523788452, 0.004309553187340498, -0.018180638551712036, -0.00977613776922226, 0.024882981553673744, 0.021588189527392387, 0.011082174256443977, -0.015534946694970131, 0.03401371091604233, 0.046329814940690994, 0.02613525465130806, -0.025707043707370758, 0.019261889159679413, 0.013653726316988468, 0.015050027519464493, -0.08029021322727203, 0.008777475915849209, -0.03569839522242546, -0.016191581264138222, 0.01599719189107418, 0.02269856072962284, 0.0637301430106163, -0.0023895567283034325, 0.020571473985910416, 0.009744714945554733, -0.009449537843465805, 0.0014418887440115213, -0.01194456871598959, 0.017578337341547012, 0.04785339534282684, -0.06745673716068268, -0.006489809602499008, -0.028063621371984482, 0.04605961963534355, 0.032660096883773804, -0.009138906374573708, -0.07004942744970322, -0.02806750498712063, -0.040667466819286346, -0.030926166102290154, -0.010778728872537613, -0.02526271902024746, 0.011625903658568859, 0.0025558711495250463, -0.007767342962324619, -0.06409814953804016, 0.02130984142422676, 0.00010034340084530413, -0.005005555227398872, 0.034675680100917816, 0.03765103965997696, -0.033288661390542984, -0.011711698025465012, 0.012096581980586052, 0.11736154556274414, 0.027461431920528412, 0.011131462641060352, -0.029288623481988907, 0.013723500072956085, 0.010105469264090061, 0.04756419360637665, -0.008404172956943512, 0.012065977789461613, -0.09644688665866852, 0.031242961063981056, 0.010439114645123482, 0.06655213981866837, -0.013075119815766811, 0.019208673387765884, -0.04455755650997162, 0.05015372112393379, 0.040556300431489944, 0.0493772029876709, -0.02141922526061535, -0.06953675299882889, -0.024237383157014847, 0.007394873537123203, -0.03278660401701927, 0.021367965266108513, -0.007512026000767946, 0.009134150110185146, 0.027829015627503395, -0.026846809312701225, -0.026368891820311546, 0.008866584859788418, -0.045448560267686844, 0.06832025200128555, 0.014432383701205254, 0.014828956685960293, -0.009242497384548187, -0.019475441426038742, -0.029546206817030907, -0.038324784487485886, -0.003076227381825447, 0.029066048562526703, -0.012901647947728634, -0.03662850335240364, 0.006575232837349176, -0.02148263156414032, 0.02300345152616501, 0.03695541247725487, -0.010424413718283176, 0.03143050894141197, -0.010799937881529331, -0.002661966485902667, -0.05639498680830002, 0.06932863593101501, -0.04211931303143501, -0.06398341059684753, -0.031067969277501106, 0.026639003306627274, 0.030045010149478912, -0.025765547528862953, -0.004315008409321308, 0.023137353360652924, 0.0038147764280438423, -0.021877581253647804, 0.08966859430074692, 0.00509899714961648, 0.035905491560697556, -0.07194267958402634, 0.08546964079141617, -0.02580789104104042, -0.0024668739642947912, -0.0518626905977726, -0.0451725535094738, -0.011961594223976135, 0.002474019071087241, 0.021679501980543137, -0.04941091313958168, -0.013403680175542831, 0.057091739028692245, 0.08165789395570755, 0.05424335226416588, -0.03241066634654999, -0.00012402469292283058, -0.008333219215273857, 0.013417081907391548, -0.048252981156110764, 0.08443920314311981, -0.04486287757754326, 0.045160990208387375, -0.007949083112180233, -0.017609624192118645, -0.008305978961288929, -0.05309128388762474, -0.0400175005197525, 0.04668015241622925, 0.029131894931197166, -0.01246800646185875, -0.013480977155268192, -0.006261986680328846, 0.014839084818959236, -0.04623624309897423, -0.0408487543463707, -0.056371841579675674, -0.042444389313459396, -0.014251268468797207, -0.0197158120572567, 0.03513534739613533, -0.009088404476642609, -0.017565716058015823, 0.011839039623737335, -0.0634697824716568, 0.08308883011341095, -0.02323625050485134, -0.0380384661257267, 0.05073487013578415, -0.009922067634761333, -0.04121893644332886, -0.019651832059025764, -0.00936733279377222, 0.002968746703118086, 0.032889578491449356, 0.013333488255739212, -0.09930233657360077, 0.028971107676625252, 0.012782108969986439, -0.015385063365101814, 0.012342743575572968, 0.09722752869129181, -0.019823605194687843, 0.04627080261707306, -0.04237766191363335, -0.003669450059533119, 0.012944662012159824, 0.009083005599677563, 0.0031039861496537924, -0.039816178381443024, 0.021080726757645607, 0.03882903233170509, -0.047257691621780396, -0.0830560252070427, 0.033399663865566254, 0.0261328537017107, -0.002505347365513444, -0.010847936384379864, 0.011024837382137775, -0.0036735753528773785, -0.02988816797733307, 0.032561078667640686, -0.016263986006379128, -0.010690489783883095, -0.07411158084869385, 0.030896950513124466, -0.02348504215478897, 0.029124099761247635, -0.004790014587342739, 0.006506095640361309, -0.054408103227615356, 0.0486641526222229, 0.00694955512881279, -0.061579179018735886, -0.012593015097081661, -0.0006950091337785125, 0.03590524569153786, -0.014923217706382275, -0.02785310335457325, -0.03938468545675278, 0.00771832512691617, 0.0005091754719614983, 0.0369417741894722, -0.02745278924703598, 0.007071263622492552, 0.08138520270586014, -0.010101174004375935, 0.02037283219397068, 0.010978039354085922, 0.023467011749744415, 0.025035932660102844, -0.04753492772579193, -0.051589615643024445, -0.006018209271132946, -0.04315639287233353, 0.04591653496026993, 0.024317536503076553, 0.07202794402837753, -0.02100892923772335, 0.027277396991848946, 0.003211099188774824, -0.008910518139600754, -0.02874166890978813, -0.018301866948604584, -0.013233852572739124, -0.0022292379289865494, 0.00691962568089366, 0.01912631280720234, -0.0070421649143099785, -0.007797456346452236, 0.009262528270483017, 0.008050601929426193, 0.00651074294000864, -0.04772161692380905, -0.05157218128442764, -6.0054603137129375e-33, 0.016334446147084236, 0.013043626211583614, -0.016660697758197784, -0.02613876760005951, -0.00443451339378953, 0.019064951688051224, -0.028740068897604942, 0.004167416598647833, -0.005639553535729647, -0.0018268557032570243, -0.008640753105282784, -0.052746690809726715, -0.011956043541431427, 0.005765623413026333, 0.05638129636645317, 0.04727121815085411, -0.031926270574331284, -0.033242031931877136, 0.008874285034835339, 0.036219522356987, 0.04140360653400421, 0.008920316584408283, 0.07153113931417465, -0.12677064538002014, -0.05588525906205177, 0.022767528891563416, 0.005516009870916605, -0.0008917004452086985, 0.006154458969831467, 0.0007960338843986392, -0.09506790339946747, -0.05038914084434509, -0.0014097290113568306, -0.03186297416687012, 0.0054467469453811646, -0.005445600021630526, -0.04123394563794136, -0.002042436972260475, -0.0432126447558403, -0.017436496913433075, -0.027370797470211983, 0.005105894990265369, 0.03190669044852257, -0.03283179923892021, -0.0249381884932518, 0.005971051752567291, 0.06649570912122726, -0.028256261721253395, -0.005203064065426588, 0.017866965383291245, -0.030210718512535095, -0.013465526513755322, -0.01359388418495655, 0.032397713512182236, 0.07500952482223511, -0.014839348383247852, -0.04468471556901932, 0.05046728253364563, -0.04484723508358002, 0.057512909173965454, -0.0882992222905159, -0.04278070852160454, -0.008460601791739464, -0.0118233822286129, 0.06113235652446747, 0.05158960819244385, 0.02922113426029682, -0.031206628307700157, -0.02405272051692009, -0.04617888480424881, 0.03677883744239807, 0.04278331622481346, 0.011798446998000145, 0.024569593369960785, 0.008810751140117645, -0.03165871649980545, -0.025164689868688583, 0.031357552856206894, -0.03125301003456116, 0.0142179811373353, 0.019551029428839684, 0.020978549495339394, -0.041399337351322174, -0.01810106635093689, 0.0343342088162899, -0.006233919877558947, -0.022454729303717613, 0.005615083035081625, -0.004122787620872259, -0.039107970893383026, -0.006352087017148733, -0.07427018135786057, 0.022408034652471542, -0.015215683728456497, 0.06041482463479042, -0.02526385337114334, 0.010367436334490776, 0.047271568328142166, 0.04754103347659111, -0.036817457526922226, -0.04429398849606514, -0.06301997601985931, 0.012827129103243351, -0.053720198571681976, 0.05443250760436058, -0.01127917505800724, 0.0063045141287148, 0.02916625887155533, 0.011505192145705223, -0.022016433998942375, 0.002089602639898658, -0.08631469309329987, 0.043736886233091354, 0.047035351395606995, -0.01813375949859619, -0.05047106742858887, 0.017832381650805473, 0.015604794025421143, -0.0069275302812457085, 0.014763320796191692, -0.003312020329758525, -0.03740832582116127, 0.02546839788556099, 0.022177407518029213, -0.011477051302790642, 0.012291667982935905, -0.040773529559373856, -0.07170848548412323, 0.0666516125202179, -0.04572666063904762, -0.0027243688236922026, -0.01152673177421093, 3.001711661454465e-07, -0.07103919237852097, 0.032712362706661224, -0.019584672525525093, -0.06549110263586044, 0.024640696123242378, 0.05538500100374222, 0.008831635117530823, 0.057072099298238754, -0.012509573251008987, -0.010980021208524704, 0.039873454719781876, -0.0025004956405609846, -0.029734158888459206, -0.03643084317445755, -0.02834698185324669, 0.002830851124599576, -0.01752764731645584, 0.03241000697016716, -0.00799943320453167, 0.017126988619565964, 0.025666935369372368, 0.01434099767357111, 0.03109893761575222, -0.023200586438179016, 0.029920147731900215, 0.027370696887373924, 0.05391398072242737, -0.031760599464178085, 0.07428578287363052, -0.04731340333819389, 0.01994791254401207, 0.024807583540678024, 0.017633358016610146, 0.019511986523866653, -0.005497706588357687, 0.02149607054889202, 0.0373995341360569, -0.01444655004888773, -0.007609413471072912, 0.031277015805244446, 0.013056298717856407, 0.02551940083503723, 0.007724144030362368, -0.07681970298290253, 0.02194947376847267, -0.021166184917092323, -0.05636608973145485, -0.062485601752996445, -0.005739686544984579, -0.00023340436746366322, 0.03411996364593506, 0.014393405057489872, 0.012907239608466625, 0.0014698789454996586, 0.02982187643647194, -0.03066101111471653, 0.07944147288799286, -0.033803727477788925, 0.03267085924744606, 0.05730852857232094, -0.05461450293660164, 0.029436683282256126, 0.0063653928227722645, -0.011846841312944889, 0.08857071399688721, 0.01256631687283516, -0.024061432108283043, 2.1747247012712154e-34, -0.05417180433869362, 0.027845019474625587, 0.028252890333533287, 0.006116341333836317, -0.011971802450716496, -0.0203928854316473, 0.022566430270671844, 0.002097424352541566, 0.00984548032283783, -0.047863371670246124, -0.018842360004782677]

['B. Mishra', 'R. Sepulchre']

1306.2672v2

We exploit the versatile framework of Riemannian optimization on quotient manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank matrix completion. The underlying search space of fixed-rank matrices is endowed with a novel Riemannian metric that is tailored to the least-squares cost. Numerical comparisons suggest that R3MC robustly outperforms state-of-the-art algorithms across different problem instances, especially those that combine scarcely sampled and ill-conditioned data.

R3MC: A Riemannian three-factor algorithm for low-rank matrix completion

http://arxiv.org/pdf/1306.2672v2

Title R3MC Riemannian threefactor algorithm lowrank matrix completion Summary exploit versatile framework Riemannian optimization quotient manifold develop R3MC nonlinear conjugategradient method lowrank matrix completion underlying search space fixedrank matrix endowed novel Riemannian metric tailored leastsquares cost Numerical comparison suggest R3MC robustly outperforms stateoftheart algorithm across different problem instance especially combine scarcely sampled illconditioned data Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03727960214018822, 0.03324487805366516, 0.031223371624946594, 0.018054598942399025, 0.029332399368286133, -0.004496040288358927, -0.05504288896918297, 0.028129201382398605, 0.051877569407224655, 0.027102960273623466, -0.014630625955760479, -0.00028477521846070886, 0.056117668747901917, -0.021774988621473312, -0.004376030992716551, -0.039393458515405655, -0.03951718285679817, -0.021217478439211845, -0.01946299895644188, -0.04190666228532791, -0.02065083011984825, 0.029322050511837006, 0.020705752074718475, -0.011159603483974934, -0.042157161980867386, 0.009756513871252537, -0.004444642923772335, -0.02229578234255314, -0.02953992411494255, -0.013377061113715172, 0.02689470537006855, 0.05290067195892334, 6.932294490979984e-05, -0.017286833375692368, 2.1364789972722065e-06, 0.0008552949875593185, 0.0008489753818139434, -0.019086360931396484, 0.08961956202983856, -0.0010347607312723994, 0.025032950565218925, 0.032980915158987045, 0.03929321467876434, -0.02765391394495964, -0.0342615470290184, 0.005425809882581234, -0.03605206683278084, 0.036318883299827576, 0.016401447355747223, -0.05520397052168846, -0.0077882991172373295, -0.011553634889423847, -0.03756026178598404, -0.040589652955532074, -0.020093979313969612, -0.07531872391700745, 0.030134126543998718, 0.024699537083506584, 0.08204593509435654, 0.004050564020872116, -0.026990870013833046, 0.05646658316254616, -0.04153727367520332, 0.028854576870799065, 0.09065425395965576, 0.015089417807757854, 0.011758272536098957, -0.0036973366513848305, -0.0073878769762814045, 0.06775537133216858, -0.01626281440258026, 0.040506511926651, 0.01819685660302639, 0.026314930990338326, -0.011166653595864773, -0.016769252717494965, 0.0030512362718582153, -0.04317362606525421, -0.024301808327436447, -0.013465769588947296, -0.09796014428138733, -0.03133830800652504, -0.008498513139784336, -0.00840833317488432, -0.02647371031343937, 0.11158876866102219, 0.03142321854829788, 0.014185703359544277, -0.013935314491391182, -0.019746262580156326, -0.04245550557971001, -0.018579276278614998, 0.01283977460116148, -0.03220086544752121, -0.06239597126841545, -0.03299308195710182, -0.0140262795612216, -0.07387173175811768, -0.0009297620272263885, 0.01888856664299965, -0.005228502210229635, -0.0016081449575722218, 0.05513967201113701, 0.024132009595632553, -0.011974736116826534, -0.033567048609256744, -0.04660608991980553, 0.04080447554588318, -0.07532455027103424, -0.03875426948070526, 0.04121389240026474, -0.005814076401293278, 0.018134087324142456, 0.07681261003017426, 0.007153803948312998, -0.002151300897821784, -0.032152410596609116, 0.002275947481393814, -0.014881003648042679, -0.01828835904598236, 0.008678481914103031, 0.07771551609039307, 0.02532653510570526, -0.014673884958028793, -0.06152765452861786, -0.019389238208532333, 0.040432579815387726, 0.04256661981344223, -0.039427872747182846, 0.09549019485712051, 0.01172198448330164, -0.026039190590381622, -0.0015119045274332166, -0.028521928936243057, 0.023242909461259842, -0.001082838629372418, -0.05217989161610603, -0.003722011810168624, 0.018816908821463585, 0.006507315672934055, -0.002233311999589205, -0.06732134521007538, 0.00010506579565117136, -0.011721234768629074, 0.03710000962018967, -0.001806741813197732, 0.022926131263375282, -0.00533384969457984, 0.011926594190299511, -0.046511951833963394, -0.09576615691184998, 0.0653715431690216, 0.0023782686330378056, -0.0009421134018339217, 0.053528618067502975, -0.02402333915233612, 0.03836492449045181, 0.024336930364370346, -0.04418851435184479, 0.028189435601234436, -0.038722213357686996, 0.008110204711556435, -0.012411750853061676, -0.0038788628298789263, 0.010768500156700611, 0.011548923328518867, 0.011867301538586617, -0.03674587979912758, 0.006088722962886095, 0.007054169662296772, 0.019977135583758354, 0.04572960361838341, 0.02900599129498005, -0.01983519271016121, -0.011646819300949574, 0.03808791935443878, 0.008227184414863586, -0.020436005666851997, -0.023662831634283066, -0.010410003364086151, 0.0008968125912360847, 0.017220988869667053, 0.01132911816239357, 0.05787532031536102, -0.020774099975824356, -0.040403831750154495, 0.056629590690135956, 0.04029947146773338, -0.01900136098265648, -0.02665092423558235, 0.012673531658947468, -0.07140444964170456, -0.03211170434951782, 0.0036181393079459667, 0.10591479390859604, -0.02733372151851654, -0.05359263718128204, -0.09687449038028717, 0.00012809601321350783, -0.04404222592711449, 0.014182407408952713, 0.03253129497170448, 0.04221554845571518, -0.0408187210559845, 0.009004035033285618, -0.058274220675230026, -0.018460169434547424, -0.005388707388192415, 0.005385333206504583, -0.05572449043393135, -0.038987670093774796, 0.028408238664269447, 0.03970641642808914, 0.018744194880127907, -0.072980597615242, 0.0750652551651001, 0.02378803677856922, -0.0021882641594856977, -0.015416983515024185, -0.06204115226864815, -0.030240347608923912, -0.010374363511800766, 0.0783865824341774, -0.001965615898370743, -0.004326554015278816, 0.037740159779787064, 0.07731915265321732, 0.04780101776123047, 0.05637342110276222, 0.016760319471359253, 0.05893997102975845, -0.045901063829660416, 0.029534153640270233, -0.020038874819874763, -0.05965909734368324, -0.02407468482851982, 0.045386649668216705, -0.011646182276308537, 0.041654255241155624, -0.0356731191277504, -0.042503733187913895, 0.08114554733037949, -0.010114730335772038, -0.06925897300243378, 0.029215391725301743, -0.02138420380651951, -0.005685578566044569, -0.05197795107960701, 0.006359143182635307, -0.001968499505892396, 0.026937361806631088, -0.02626441791653633, 0.0023856067564338446, -0.06267014145851135, 0.020531196147203445, 0.014588823541998863, 0.0044930120930075645, 0.0030162346083670855, 0.02039041370153427, -0.03301357477903366, 0.047680195420980453, 0.025133345276117325, -0.019575197249650955, 0.03148062527179718, 0.0016941187204793096, 0.04159286245703697, -0.01280982606112957, 0.029548976570367813, -0.0020006855484098196, 0.035955559462308884, -0.03738948702812195, -0.007558306213468313, 0.0057375761680305, 0.04935111105442047, 0.015094863250851631, 0.060858529061079025, 0.02718764916062355, 0.028301142156124115, -0.03528735414147377, 0.014638413675129414, 0.01915230043232441, -0.02290196903049946, -0.006268259137868881, -0.01602322794497013, 0.01835714280605316, 0.01794714480638504, -0.0062482631765306, -0.021585991606116295, 0.013233709149062634, -0.003939976450055838, -0.07051612436771393, 0.01248056348413229, -0.02041538432240486, -0.03156373277306557, -0.07653623074293137, -0.014471175149083138, 0.04652736335992813, 0.04186888039112091, -0.020605439320206642, -0.07402171194553375, 0.01131732203066349, 0.06079995632171631, 0.014164174906909466, -0.006881836801767349, -0.04208533465862274, -0.016772886738181114, 0.08513522148132324, -0.0370047427713871, 0.02136295475065708, -0.01472688652575016, 0.0457778126001358, -0.007846340537071228, -0.01628073863685131, -0.019008100032806396, 0.012803918682038784, -0.024114934727549553, -0.046654701232910156, 0.01269978005439043, -0.008777578361332417, -0.002265580464154482, -0.007121959701180458, 0.0004949287394993007, 0.0720931813120842, 0.0008874871418811381, -0.021796811372041702, -0.01668618619441986, -0.009779640473425388, 0.0029494259506464005, -0.09583146870136261, 0.007306069601327181, 0.010393916629254818, -0.051687613129615784, -0.01336357556283474, 0.019498186185956, -0.0043615419417619705, 0.01343338843435049, -0.013499291613698006, -0.02561975084245205, 0.019156327471137047, 0.02786397747695446, 0.07055174559354782, -0.037189826369285583, -0.013886525295674801, 0.02446501888334751, -0.003996218554675579, -0.021579040214419365, -0.03709157183766365, 0.00441755959764123, -0.004503374453634024, 0.00016496455646120012, 0.002811989514157176, 0.0004483806842472404, -0.024324750527739525, -0.03227764740586281, 0.009400038979947567, 0.034438177943229675, -0.001658242312259972, -0.00556610943749547, -0.028909267857670784, -0.03181708976626396, 0.03203572705388069, 0.060548000037670135, 0.06535366922616959, 0.01522912923246622, -0.03635191544890404, 0.022910572588443756, 0.04805563762784004, 0.07323148101568222, -0.035334330052137375, -0.0341544970870018, -0.03780769184231758, 0.03584565967321396, 0.053028181195259094, 0.03084421344101429, 0.012235274538397789, -0.06844323128461838, -0.035218317061662674, 0.011232682503759861, 0.07522598654031754, 0.06458431482315063, -0.014113500714302063, 0.041038524359464645, 0.021801065653562546, 0.02314387634396553, 0.051817964762449265, 0.00457413075491786, -0.02476363815367222, 0.022647038102149963, -0.02484988048672676, 0.0478212833404541, 0.00597931444644928, -0.041193317621946335, -0.01746678166091442, -0.08763343095779419, 0.030938653275370598, 0.011635085567831993, -0.058828938752412796, 0.016730694100260735, -0.005678696557879448, -0.055181629955768585, -0.03778146952390671, -0.031066492199897766, -0.011481285095214844, -0.017908865585923195, -0.014770706184208393, -0.015030693262815475, -0.034682851284742355, 0.04372565448284149, -0.029902465641498566, -0.04405089467763901, 0.019865794107317924, 0.05317668244242668, -0.03595729172229767, -0.08483909070491791, 0.02781715616583824, 0.03874289244413376, 0.023303309455513954, -0.024873675778508186, 0.059247903525829315, -0.03769401088356972, 0.027017313987016678, -0.03957346826791763, 0.10824045538902283, 0.0006549847312271595, 0.062045495957136154, -0.009663180448114872, -0.009634319692850113, 0.020865393802523613, -0.0010538377100601792, -0.034950342029333115, -0.03660788759589195, 0.026197973638772964, 0.01736755110323429, 0.066200390458107, 0.0065644485875964165, 0.044565845280885696, 0.019428716972470284, -0.04201323166489601, -0.007405481766909361, -0.03365498036146164, 0.07840102165937424, 0.019777968525886536, 0.023687338456511497, 0.012543800286948681, -0.0031790772918611765, -0.0035923977848142385, -0.008259359747171402, -0.028038471937179565, -0.000495457265060395, 0.008954392746090889, 0.029007935896515846, -0.009814305230975151, 0.009014448150992393, 0.026094431057572365, -0.03966391086578369, -0.016259828582406044, -0.05149272456765175, -0.041480835527181625, 0.0038296638522297144, -0.051090288907289505, 0.05947175249457359, -0.005757930688560009, 0.01772424578666687, -0.03428449481725693, -0.031809091567993164, -0.018359556794166565, -0.005379601381719112, 0.030049560591578484, 0.10585934668779373, 0.014792735688388348, -0.03529420867562294, -0.0025785367470234632, 0.010323130525648594, -0.048583731055259705, 0.008155588060617447, 0.014607120305299759, -0.0434710867702961, 0.026159171015024185, 0.018214048817753792, 0.011605953797698021, 0.05519402027130127, 0.03550075367093086, -0.0035247839987277985, -0.003946263808757067, -0.04986799508333206, -0.007578330580145121, -0.03324252367019653, 0.01674744300544262, -0.025858178734779358, 0.006051618605852127, -0.004907248541712761, 0.03134610131382942, -0.04418734461069107, -0.03986137732863426, 0.0006339563988149166, 0.021001523360610008, 0.002333050826564431, -0.011926350183784962, -0.024323299527168274, -0.04368702694773674, 0.00030292142764665186, 0.01634245552122593, 0.019876817241311073, -0.017479723319411278, 0.012678193859755993, 0.025395043194293976, 0.02648678980767727, -0.02680853195488453, -0.012589415535330772, 0.02990313246846199, -0.029108496382832527, 3.897168789990246e-05, -0.021730739623308182, 0.0021193469874560833, -0.04211706668138504, -0.014347166754305363, 0.08961254358291626, 0.00225256965495646, 0.038250964134931564, 0.010150197893381119, 0.0025152284651994705, -0.006168750114738941, 0.027918430045247078, -0.01956607960164547, 0.006308825686573982, 0.052896030247211456, -0.047578468918800354, 0.0045028855092823505, 0.11091315001249313, 0.03231189772486687, -0.03422228619456291, 0.013062679208815098, -0.032003846019506454, -0.0009254261385649443, -0.052041321992874146, 0.0014762863283976912, 0.007425129879266024, 0.045064881443977356, -0.030592089518904686, 0.008768057450652122, 0.026550550013780594, -0.02355567365884781, 0.0385698638856411, -0.020866181701421738, -0.09002742171287537, -0.019936667755246162, 0.0016500871861353517, 0.019897328689694405, -0.05410471186041832, -0.003466289723291993, -0.027196217328310013, -0.0770750418305397, -0.012056092731654644, -0.05890047550201416, 0.03312452509999275, -5.911050117584661e-33, -0.026587102562189102, -0.07211335748434067, -0.11334637552499771, 0.011549270711839199, -0.05319151282310486, -0.005376429762691259, 0.014276521280407906, -0.02225050888955593, 0.04345798119902611, -0.024252047762274742, -0.052463214844465256, -0.0045343260280787945, -0.018782280385494232, 4.8764526582090184e-05, -0.012647920288145542, 0.03596023470163345, 0.008360913023352623, 0.007360727526247501, 0.010308969765901566, 0.04123086854815483, 0.008386963047087193, 0.06748972088098526, -0.022257329896092415, -0.04130040854215622, -0.08400365710258484, 0.023675356060266495, -0.05360715463757515, 0.033207621425390244, -0.025738341733813286, -0.005285362713038921, -0.01594541408121586, 2.3749886167934164e-05, -0.014919782057404518, 0.022926587611436844, -0.0051641929894685745, -0.02876061573624611, -0.03633945807814598, 0.02774995006620884, 0.013921445235610008, 0.021552763879299164, -0.002180936513468623, 0.025449832901358604, 0.009469508193433285, 0.012041740119457245, -0.014784296043217182, -0.031046461313962936, 0.0553959459066391, -0.02480686828494072, -0.06108929216861725, -0.04366460070014, 0.04259007051587105, -0.006198127754032612, -0.01289263367652893, 0.003175219986587763, 0.050931647419929504, 0.06162339448928833, -0.006924130488187075, 0.045879945158958435, 0.03190811350941658, 0.006670639384537935, -0.07825233787298203, 0.01877855695784092, 0.004823263268917799, 0.052149999886751175, 0.01689070649445057, 0.023142797872424126, 0.009405812248587608, 0.0012197806499898434, 0.0017938850214704871, -0.009235798381268978, -0.0053951130248606205, 0.0068564387038350105, -0.012062952853739262, -5.066020094091073e-05, -0.049503788352012634, -0.049445852637290955, -0.02889424003660679, 0.04054489731788635, -0.11185098439455032, -0.01332971639931202, -0.03459809720516205, 0.015324601903557777, 0.00834160577505827, -0.010254690423607826, -0.029095586389303207, 0.007592606823891401, -0.014466624706983566, 0.038795217871665955, -0.019995588809251785, 0.009912670589983463, -0.04477991908788681, -0.0374390073120594, -0.013193260878324509, 0.000830749049782753, 0.030309805646538734, -0.03503674268722534, 0.01498524472117424, 0.0354035459458828, 0.034600209444761276, -0.012662367895245552, 0.006026634480804205, 0.0005230824463069439, -0.02784334309399128, -0.006291685160249472, -0.01167244091629982, -0.007397257722914219, -0.043457381427288055, -0.02142505720257759, -0.011693167500197887, -0.00123309635091573, -0.010523648001253605, -0.020389756187796593, -0.0007151669124141335, 0.017410852015018463, 0.02789461985230446, -0.029738696292042732, 0.02807742916047573, 0.09675406664609909, 0.001885495614260435, 0.06865358352661133, -0.043049588799476624, -0.028396187350153923, -0.014134908095002174, -0.017923293635249138, -0.016016323119401932, -0.01164466142654419, -0.02774120308458805, -0.02160952240228653, 0.06150754541158676, -0.03324903920292854, -0.008234533481299877, -0.0461418516933918, 2.6838628741643333e-07, -0.015141399577260017, 0.05270097404718399, -0.04837116599082947, -0.06227807700634003, -0.07676432281732559, -0.001816816977225244, 0.005422371905297041, 0.0010017233435064554, -0.006035263650119305, 0.004763565491884947, 0.03329518437385559, -0.03674449026584625, 0.04436521604657173, -0.02146545983850956, -0.05196395143866539, 0.06371039152145386, -0.010296180844306946, 0.017589297145605087, -0.03836125507950783, -0.042460791766643524, -0.006872826721519232, 0.04143509268760681, 0.0501236766576767, -0.04604364559054375, -0.02082507684826851, 0.01915997639298439, 0.0336899496614933, -0.021343694999814034, 0.0017000684747472405, 0.02823353186249733, 0.07681084424257278, -0.026641299948096275, 0.02635924704372883, 0.004263053648173809, 0.00345064839348197, 0.029647761955857277, 0.04830382019281387, 0.014703777618706226, 0.019735731184482574, -0.03972212225198746, 0.019549647346138954, 0.09021580964326859, 0.0032621552236378193, -0.0045508723706007, 0.03471316769719124, 0.006332620978355408, 0.016775118187069893, 0.018678849563002586, -0.014769379049539566, 0.0327756404876709, 0.09558341652154922, -0.004852602258324623, 0.026893967762589455, 0.02825494483113289, -0.013966944999992847, -0.006102160084992647, 0.06890086084604263, 0.010291172191500664, 0.08890384435653687, 0.04941511154174805, -0.07962564378976822, -0.02879202924668789, 0.056829605251550674, 0.009590660221874714, 0.03496147692203522, 0.0014361764770001173, -0.008803587406873703, 2.452969035474399e-34, 0.02115439809858799, -0.019549082964658737, 0.037248093634843826, 0.04122938588261604, -0.04879923537373543, -0.028570905327796936, 0.009828672744333744, -0.009340076707303524, -0.010832905769348145, -0.053812023252248764, 0.016103193163871765]

['Sudipto Guha', 'Kamesh Munagala']

1306.3525v2

In this paper, we consider several finite-horizon Bayesian multi-armed bandit problems with side constraints which are computationally intractable (NP-Hard) and for which no optimal (or near optimal) algorithms are known to exist with sub-exponential running time. All of these problems violate the standard exchange property, which assumes that the reward from the play of an arm is not contingent upon when the arm is played. Not only are index policies suboptimal in these contexts, there has been little analysis of such policies in these problem settings. We show that if we consider near-optimal policies, in the sense of approximation algorithms, then there exists (near) index policies. Conceptually, if we can find policies that satisfy an approximate version of the exchange property, namely, that the reward from the play of an arm depends on when the arm is played to within a constant factor, then we have an avenue towards solving these problems. However such an approximate version of the idling bandit property does not hold on a per-play basis and are shown to hold in a global sense. Clearly, such a property is not necessarily true of arbitrary single arm policies and finding such single arm policies is nontrivial. We show that by restricting the state spaces of arms we can find single arm policies and that these single arm policies can be combined into global (near) index policies where the approximate version of the exchange property is true in expectation. The number of different bandit problems that can be addressed by this technique already demonstrate its wide applicability.

Approximation Algorithms for Bayesian Multi-Armed Bandit Problems

http://arxiv.org/pdf/1306.3525v2

Title Approximation Algorithms Bayesian MultiArmed Bandit Problems Summary paper consider several finitehorizon Bayesian multiarmed bandit problem side constraint computationally intractable NPHard optimal near optimal algorithm known exist subexponential running time problem violate standard exchange property assumes reward play arm contingent upon arm played index policy suboptimal context little analysis policy problem setting show consider nearoptimal policy sense approximation algorithm exists near index policy Conceptually find policy satisfy approximate version exchange property namely reward play arm depends arm played within constant factor avenue towards solving problem However approximate version idling bandit property hold perplay basis shown hold global sense Clearly property necessarily true arbitrary single arm policy finding single arm policy nontrivial show restricting state space arm find single arm policy single arm policy combined global near index policy approximate version exchange property true expectation number different bandit problem addressed technique already demonstrate wide applicability Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.001519938581623137, 0.024292510002851486, -0.004495494067668915, -0.03787628933787346, -0.025138648226857185, -0.013913615606725216, -0.00709216995164752, 0.03406977280974388, -0.013726779259741306, 0.0014902115799486637, -0.038477085530757904, 0.01106543280184269, -0.04127714782953262, 0.00657456973567605, 0.007808813825249672, -0.021929306909441948, 0.026955220848321915, -0.04724058508872986, 0.03963997960090637, -0.03577704355120659, 0.026492970064282417, -0.05455982685089111, -0.0437793955206871, 0.012121522799134254, 0.05869745835661888, 0.023314818739891052, -0.032534513622522354, -0.016870930790901184, 0.03447490930557251, -0.09267143905162811, 0.03815937787294388, -0.054342418909072876, 0.0005792419542558491, 0.047803305089473724, 2.349928308831295e-06, -0.058412764221429825, -0.05305258184671402, -0.050228219479322433, 0.030433595180511475, -0.037302013486623764, 0.08291524648666382, 0.027610788121819496, 0.04934486001729965, 0.040269635617733, -0.015069838613271713, -0.033460136502981186, 0.021896515041589737, 0.10091320425271988, 0.006442478857934475, -0.007470171898603439, 0.02271144464612007, 0.0313262939453125, -0.021720366552472115, -0.04656586796045303, 0.011489889584481716, -0.10741155594587326, 0.02891325019299984, -0.0015975185669958591, 0.05462753027677536, -0.04223720356822014, 0.003716332372277975, -0.015012785792350769, -0.029631396755576134, 0.019163822755217552, 0.003835113951936364, 0.01121013518422842, 0.023797638714313507, 0.029872603714466095, -0.0031460020691156387, -0.023457825183868408, -0.038501106202602386, 0.005930140148848295, 0.02259773015975952, -0.0472513772547245, 0.012041903100907803, 0.026833366602659225, -0.01745530776679516, 0.04747634381055832, -0.06221820041537285, 0.007650492712855339, 0.03198298439383507, 0.028560824692249298, 0.004389168228954077, 0.02488609217107296, 0.00217853719368577, 0.060623638331890106, -0.035979922860860825, -0.061468157917261124, 0.052121635526418686, 0.0253862664103508, -0.016670765355229378, -0.011411385610699654, 0.009174410253763199, -0.020907118916511536, -0.05634047091007233, -0.005767647176980972, 0.0006471647066064179, 0.02056220918893814, 0.028191735967993736, -0.0034359924029558897, 0.04143284261226654, -0.01499411091208458, 0.0204547718167305, 0.04033510386943817, 0.02061205916106701, -0.018798375502228737, -0.07572919875383377, -0.010506928898394108, 0.009538793936371803, 0.03732805326581001, -0.03346201032400131, 0.02243840880692005, -0.025335244834423065, 0.0567697249352932, 0.03779526427388191, -0.031393375247716904, -0.016741154715418816, 0.007385388482362032, -0.02603636309504509, -0.02300628460943699, 0.02849533036351204, 0.039242420345544815, -0.017681902274489403, 0.029107220470905304, -0.03147559612989426, -0.04135971888899803, -0.08594127744436264, 0.04772324115037918, 0.01503915898501873, 0.08936797827482224, 0.0019689216278493404, 0.021267535164952278, -0.02705763652920723, -0.06247018650174141, -0.00204919814132154, 0.0621633343398571, 0.026659231632947922, 0.016763929277658463, -0.06910405308008194, -0.020554136484861374, -0.020008129999041557, 0.006052979733794928, -0.050365712493658066, -0.02721402235329151, 0.007191827986389399, -0.07598980516195297, -0.026281775906682014, 0.03409609943628311, -0.007321433164179325, -0.03402069956064224, -0.04752778634428978, 0.04897840693593025, 0.06084644794464111, -0.026800919324159622, 0.05057898908853531, -0.004232746083289385, -0.040482714772224426, 0.02742808870971203, 0.018774427473545074, 0.05552056431770325, -0.008822926320135593, 0.017198802903294563, -0.025862259790301323, 0.005631936248391867, 0.008411737158894539, 0.008412715047597885, 0.0498141311109066, -0.04415738210082054, 0.0686829537153244, 0.09764961898326874, 0.01702842116355896, -0.040545232594013214, -0.073345847427845, -0.014890327118337154, 0.02058691531419754, -0.032803766429424286, 0.05661920830607414, -0.05971600115299225, 0.012807940132915974, -0.012587441131472588, -0.04762164503335953, -0.02037874050438404, -0.006025669164955616, 0.020413868129253387, -0.03825370594859123, -0.002789108781144023, 0.027157433331012726, 0.009157073684036732, 0.012056260369718075, -0.0009200064232572913, 0.03444409370422363, -0.008709283545613289, -0.06149277836084366, 0.028970738872885704, 0.031281884759664536, -0.042699117213487625, -0.05327172577381134, -0.08336100727319717, 0.041804686188697815, 0.08659464865922928, -0.03915588930249214, -0.024782348424196243, 0.010377966798841953, -0.04520559683442116, 0.0090609947219491, -0.0497736856341362, -0.0059282188303768635, -0.014716855250298977, -0.025995710864663124, -0.07300055027008057, 0.017339473590254784, -0.011772001162171364, 0.04378611966967583, -0.006313637364655733, -0.027188707143068314, -0.026252109557390213, -0.0007897714385762811, 0.06630053371191025, -0.02129027247428894, -0.0072126127779483795, -0.053385358303785324, 0.027583587914705276, 0.0505368709564209, -0.008637377992272377, -0.03250563144683838, -0.054688263684511185, 0.06462977826595306, -0.008532421663403511, 0.0505601167678833, -0.04720446094870567, -0.010835256427526474, 0.0024306036066263914, 0.0020064618438482285, 0.0018478756537660956, -0.0271621011197567, -0.026389747858047485, 0.03733043745160103, -0.03998223692178726, 0.02405855618417263, -0.027422696352005005, 0.08953607827425003, 0.013776698149740696, -0.0012595414882525802, -0.038084838539361954, 0.005538077559322119, 0.013501856476068497, 0.007599379867315292, 0.013281736522912979, 0.018941162154078484, 0.02339576743543148, 0.02928813174366951, -0.03775950148701668, 0.0291448887437582, -0.011962831020355225, 0.007573726121336222, -0.03848140314221382, -0.03950120881199837, 0.0005950401537120342, -0.11415812373161316, 0.04037777706980705, -0.008910083211958408, 0.015141809359192848, -0.050997328013181686, 0.04551687836647034, 0.032252829521894455, 0.024671243503689766, -0.01879570633172989, -0.037385307252407074, 0.03414405882358551, 0.0033656873274594545, -0.01757187955081463, -0.0212472602725029, -0.009366045705974102, -0.008522996678948402, -0.025652211159467697, 0.01578441634774208, -0.007087410427629948, 0.0047372994013130665, 0.0012130426475778222, 0.013758144341409206, 0.05683189257979393, 0.032068416476249695, -0.006332924589514732, -0.03175380825996399, -0.011518648825585842, -0.005114956758916378, 0.00905314926058054, 0.021072525531053543, -0.01876869425177574, -0.04799767956137657, -0.011618310585618019, 0.04138124734163284, -0.004415621981024742, 0.04320259392261505, -0.007925842888653278, -0.02016366273164749, -0.04442717134952545, 0.04785076156258583, 0.0009578006574884057, 0.020726457238197327, 0.05445508286356926, 0.028067268431186676, -0.0308702252805233, 0.03326971083879471, -0.015278827399015427, -0.026563338935375214, 0.002993794623762369, -0.028373733162879944, 0.04030170664191246, 0.0637555867433548, 0.03042622283101082, 0.020564531907439232, -0.0007222814601846039, 0.03724128007888794, 0.038336124271154404, -0.045276232063770294, -0.023051954805850983, 0.026904122903943062, -0.03554898500442505, -0.027841195464134216, -0.022728582844138145, 0.012521516531705856, 0.09542468935251236, 0.023363828659057617, 0.014760584570467472, 0.016178470104932785, -0.03108363226056099, -0.00022223619453143328, -0.02336111105978489, 0.026133393868803978, 0.045857153832912445, -0.0033042626455426216, 0.02046034298837185, -0.02169600874185562, 0.00432951794937253, 0.05341843515634537, -0.0006703362450934947, -0.04896922782063484, 0.01967592164874077, 0.025442559272050858, -0.010673437267541885, -0.044397298246622086, 0.026410328224301338, -0.03944439813494682, 0.02523217536509037, -0.0302287470549345, 0.003095942549407482, -0.014254942536354065, -0.023441240191459656, -0.04629391059279442, 0.03119674324989319, 0.039627041667699814, -0.015080203302204609, -0.03623295947909355, 0.003945150878280401, 0.02925177663564682, 0.05595166236162186, -0.06764405965805054, 0.018545283004641533, -0.038026683032512665, 0.04302866756916046, 0.002843037713319063, 0.07088544219732285, -0.018034648150205612, -0.0006168390391394496, 0.04259983450174332, 0.02916628308594227, -0.0771709755063057, -0.042095307260751724, 0.050269998610019684, -0.025160420686006546, 0.0013529437128454447, -0.013217714615166187, 0.01205996423959732, 0.016150804236531258, -0.031882382929325104, 0.014713946729898453, -0.07056483626365662, 0.06239989772439003, -0.0035760956816375256, 0.05816586688160896, -0.06101011112332344, -0.024328486993908882, -0.023833051323890686, 0.09618933498859406, -0.03846846520900726, -0.08805426955223083, 0.020845972001552582, -0.07168524712324142, 0.005560143850743771, -0.0004944531247019768, -0.03090514801442623, 0.023388247936964035, -0.050389256328344345, -0.03037690743803978, -0.10381776094436646, -0.046033021062612534, 0.0470709465444088, 0.014875459484755993, 0.012928294017910957, 0.016650201752781868, 0.035343870520591736, 0.0717931017279625, 0.022057069465517998, -0.029893366619944572, 0.029554609209299088, -0.004484947305172682, -0.04795412719249725, -0.0022457775194197893, -0.014295179396867752, -0.04583626985549927, 0.018490325659513474, -0.005276557989418507, 0.0006357879028655589, -0.006109800189733505, -0.015186147764325142, 0.04620571807026863, 0.041891466826200485, 0.031723108142614365, 0.02689327299594879, 0.00393871683627367, 0.06024264916777611, 0.04270327463746071, -0.043310269713401794, -0.001017749891616404, -0.006904705427587032, -0.010918764397501945, 0.05961345508694649, 0.006094253621995449, -0.048256766051054, -0.024364355951547623, -0.018383240327239037, 0.004597506485879421, -0.036126818507909775, -0.04846717789769173, 0.07131163775920868, -0.004377484321594238, -0.01562895067036152, 0.01348259299993515, -0.06981357932090759, -0.021731290966272354, -0.03175828978419304, 0.09347060322761536, -0.03673936426639557, 0.02021792158484459, -0.06460963934659958, 0.033971477299928665, -0.017291197553277016, -0.04106658697128296, -0.004355133511126041, -0.02111048996448517, -0.01863725855946541, 0.04193393141031265, 0.010301409289240837, -0.05206828564405441, -0.04391930252313614, -0.030479686334729195, -0.029665062204003334, -0.03824884071946144, 0.021044636145234108, 0.08948773145675659, 0.005453857127577066, 0.011193622834980488, -0.014311100356280804, -0.030986879020929337, -0.020434388890862465, -0.044082142412662506, 0.050690051168203354, 0.029009731486439705, 0.03223307803273201, 0.01050845067948103, -0.009677385911345482, 0.0020090173929929733, -0.041287828236818314, -0.0031688299495726824, -0.017044782638549805, 0.011530084535479546, -0.015486614778637886, 0.027707640081644058, 0.012797747738659382, -0.007868416607379913, 0.03139645606279373, -0.023475276306271553, -0.019285641610622406, -0.009665071964263916, -0.002189191523939371, 0.02537827007472515, -0.02127847447991371, -0.02129330486059189, 0.021535463631153107, 0.018400654196739197, 0.0022897052112966776, 0.04253094270825386, -0.01106995064765215, 0.02971896342933178, -0.022730141878128052, 0.0005274704308249056, -0.006258348003029823, 0.04894507676362991, 0.0830594077706337, -0.003015828086063266, 0.007806300651282072, 0.0418214313685894, 0.03136078268289566, 0.04548990726470947, 0.049949467182159424, 0.017173290252685547, 0.0372437983751297, 0.04374818876385689, 0.002213110215961933, -0.014072027057409286, -0.0579695999622345, -0.013091513887047768, -0.045138221234083176, -0.028672801330685616, 0.03534914180636406, 0.05396725609898567, -0.008718741126358509, -0.028202977031469345, -0.015257819555699825, -0.0036681771744042635, 0.013851497322320938, -0.02383396402001381, -0.031063111498951912, -0.025476980954408646, 0.0377473458647728, 0.047869905829429626, 0.011693264357745647, 0.05713527277112007, 0.05770974978804588, 0.05525566264986992, 0.08517108112573624, -0.03022731840610504, -0.004218112677335739, -0.026695512235164642, -0.027386179193854332, 0.08010237663984299, 0.1121772900223732, -0.031269822269678116, -0.02388661354780197, -0.003016280010342598, 0.04535363242030144, 0.0009892989182844758, 0.025523358955979347, 0.04700971394777298, -0.01113554835319519, 0.013750302605330944, -0.056177131831645966, -0.027793804183602333, 0.051469311118125916, -0.05887432023882866, -0.04376767575740814, 0.0007544085383415222, -0.01963263563811779, -0.03279340639710426, -6.440759096133877e-33, 0.003967483527958393, -0.03919948637485504, 0.016891155391931534, -0.12149154394865036, -0.03306181728839874, -0.06996997445821762, 0.011832291260361671, 0.02509244717657566, 0.03976484760642052, -0.029867442324757576, -0.0032765616197139025, -0.032481610774993896, 0.015049275010824203, -0.007330244407057762, 0.04893142357468605, 0.001502337516285479, -0.022515127435326576, -0.003190886927768588, -0.046174488961696625, 0.003430668730288744, 0.03222925588488579, 0.04604315012693405, -0.0034586405381560326, 0.03372013196349144, 0.01951143518090248, 0.034157030284404755, -0.04662634804844856, 0.007740572094917297, -0.02808922715485096, 0.03415847197175026, 0.005627555772662163, -0.03506842255592346, -0.017845606431365013, -0.05452654883265495, 0.021086106076836586, -0.05848044529557228, 0.029044153168797493, -0.04592552036046982, -0.03075573407113552, 0.0037367308977991343, 0.01621374860405922, -0.005900762975215912, 0.011355854570865631, 0.009778894484043121, -0.0042528980411589146, 0.01634843647480011, 0.035032887011766434, -0.007700123358517885, -0.037717174738645554, -0.012980828061699867, 0.04624470695853233, 0.0029767872765660286, -0.015521135181188583, 0.030456459149718285, 0.008468015119433403, 0.03440506383776665, -0.031315699219703674, 0.01805475540459156, 0.02884732373058796, 0.017855742946267128, 0.03653592988848686, 0.015087872743606567, 0.00913980882614851, 0.023357916623353958, 0.06751231104135513, 0.009174883365631104, -0.004103152081370354, -0.05175875127315521, 0.018032874912023544, -0.05704700946807861, -0.03465154767036438, -0.00784786231815815, -0.011298330500721931, 0.03903118520975113, 0.05955691263079643, 0.02848351188004017, 0.0005883254343643785, 0.030186906456947327, 0.017760153859853745, 0.009407687932252884, -0.03089570626616478, 0.04407761991024017, -0.028697406873106956, 0.027555182576179504, -0.023248521611094475, -0.022414550185203552, 0.0017148677725344896, -0.01171216182410717, 0.017741410061717033, 0.004016208462417126, 0.011133173480629921, -0.008334058336913586, 0.007895248010754585, -0.007940184324979782, 0.007510486990213394, -0.053996045142412186, 0.03601812198758125, 0.04409889131784439, -0.0365631990134716, -0.009378410875797272, -0.0353681780397892, -0.06010109931230545, -0.03160412237048149, -0.05256834626197815, 0.010734647512435913, 0.01140314619988203, -0.009540327824652195, -0.027192387729883194, -0.025408001616597176, 0.030034177005290985, 0.027686379849910736, -0.00254963431507349, 0.022924913093447685, -0.018962739035487175, 0.05085194110870361, -0.0717722699046135, -0.005843367427587509, 0.06201149523258209, 0.04152911528944969, -0.09083421528339386, 0.008000168949365616, 0.01041574589908123, -0.032285600900650024, -0.0007920694188214839, -0.020575864240527153, 0.05434688553214073, -0.007967984303832054, -0.005396230611950159, -0.06428859382867813, -0.048506028950214386, -0.014660898596048355, -0.003151471260935068, 2.918222890002653e-07, -0.03584655746817589, 0.010974637232720852, -0.019044304266572, -0.034843526780605316, -0.020644931122660637, 0.03776710107922554, -0.01397249847650528, 0.009264787659049034, -0.0763024240732193, 0.029498709365725517, 0.0643238052725792, 0.00019073118164669722, -0.014538913033902645, -0.021381722763180733, -0.010520034469664097, -0.00865897722542286, 0.0017191757215186954, 0.08230594545602798, -0.030282098799943924, -0.03413010016083717, -0.04879846051335335, 0.021864797919988632, 0.030832258984446526, -0.010120774619281292, 0.03235629200935364, -0.010846245102584362, 0.020375149324536324, 0.018694639205932617, 0.015768062323331833, 0.0006536183645948768, 0.0013832250842824578, -0.0006006478797644377, -0.042370591312646866, -0.024526428431272507, -0.006201059557497501, 0.03672396391630173, -0.01032045017927885, 0.03563816845417023, 0.023943617939949036, -0.02149876393377781, -0.006867682095617056, 0.023247448727488518, 0.021171148866415024, -0.016254307702183723, 0.011669119819998741, -0.03473467379808426, -0.014948400668799877, -0.0436202809214592, -0.014160034246742725, -0.03070405311882496, 0.0012896702392026782, -0.0023879518266767263, 0.007759496103972197, -0.01781858131289482, -0.028618289157748222, 0.03441344574093819, 0.014550790190696716, -0.007501218467950821, 0.025673378258943558, 0.10084499418735504, 0.006069110240787268, -0.00019014535064343363, 0.03752061724662781, 0.051602452993392944, 0.037402860820293427, -0.14542683959007263, -0.037808336317539215, 2.7100507979429354e-34, 0.04584609344601631, -0.048367761075496674, -0.005380559712648392, 0.009816943667829037, 0.005619185045361519, -0.009283781982958317, -0.01097190286964178, -0.013325376436114311, 0.07489445060491562, 0.005764777306467295, -0.005848320666700602]

['Huahua Wang', 'Arindam Banerjee']

1306.3721v2

Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization under linear constraints where the objective could be non-smooth. We introduce new proof techniques for ADM in the batch setting, which yields a O(1/T) convergence rate for ADM and forms the basis for regret anal- ysis in the online setting. We consider two scenarios in the online setting, based on whether an additional Bregman divergence is needed or not. In both settings, we establish regret bounds for both the objective function as well as constraints violation for general and strongly convex functions. We also consider inexact ADM updates where certain terms are linearized to yield efficient updates and show the stochastic convergence rates. In addition, we briefly discuss that online ADM can be used as projection- free online learning algorithm in some scenarios. Preliminary results are presented to illustrate the performance of the proposed algorithms.

Online Alternating Direction Method (longer version)

http://arxiv.org/pdf/1306.3721v2

Title Online Alternating Direction Method longer version Summary Online optimization emerged powerful tool large scale optimization pa per introduce efficient online optimization algorithm based alternating direction method ADM solve online convex optimization linear constraint objective could nonsmooth introduce new proof technique ADM batch setting yield O1T convergence rate ADM form basis regret anal ysis online setting consider two scenario online setting based whether additional Bregman divergence needed setting establish regret bound objective function well constraint violation general strongly convex function also consider inexact ADM update certain term linearized yield efficient update show stochastic convergence rate addition briefly discus online ADM used projection free online learning algorithm scenario Preliminary result presented illustrate performance proposed algorithm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.02695453353226185, 0.051341354846954346, -0.004009578842669725, -0.02091202139854431, -0.015904469415545464, -0.0342288464307785, 0.006778797600418329, -0.023130815476179123, -0.010411330498754978, 0.005700125824660063, 0.0034026051871478558, -0.02853068709373474, -0.003528041299432516, 0.05744919180870056, 0.004856412764638662, 0.04032865911722183, -0.02263515070080757, -0.010536566376686096, -0.015753159299492836, -0.0379105806350708, 0.04296014457941055, -0.048160016536712646, 0.008313563652336597, -0.023619266226887703, -0.026469584554433823, -0.015248450450599194, -0.04364820942282677, -0.009253199212253094, 0.02953817881643772, -0.04720836877822876, 0.0653248280286789, -0.05470677837729454, 0.00856214202940464, 0.018176410347223282, 2.3074769615050172e-06, -0.036493293941020966, -0.036648187786340714, 0.006842539645731449, 0.0018943034810945392, 0.04336651787161827, 0.02868395671248436, -0.010474120266735554, 0.02076670713722706, 0.014284109696745872, -0.019030889496207237, -0.011423767544329166, 0.025783812627196312, 0.0594569556415081, 0.03666796535253525, 0.030003683641552925, 0.016788743436336517, -0.023916523903608322, 0.038585271686315536, -0.01618623360991478, -0.06114418804645538, -0.04333587735891342, 0.013843701221048832, -0.05377392843365669, -0.07880285382270813, -0.017282407730817795, 0.014900699257850647, 0.040326204150915146, 0.01934603787958622, 0.014302094466984272, 0.047141194343566895, -0.009424114599823952, -0.022778255864977837, -0.0017587136244401336, 0.005484817083925009, 0.04328720271587372, -0.02874569036066532, -0.0020399915520101786, 0.01444569043815136, -0.008227002806961536, -0.04282545670866966, -0.028943760320544243, -0.023656733334064484, 0.04243376851081848, -0.048049140721559525, 0.029966291040182114, -0.03765567019581795, -0.018343806266784668, -0.007863305509090424, 0.03347039967775345, -0.013173563405871391, 0.0860358402132988, -0.036775555461645126, -0.0359344519674778, 0.056773629039525986, -0.016480624675750732, -0.09276054799556732, 0.025628957897424698, 0.05938234180212021, 0.018855348229408264, -0.11660689860582352, -0.01730954833328724, 0.055090710520744324, -0.04483873397111893, 0.009868531487882137, -0.009762095287442207, 0.11073130369186401, -0.03662094101309776, 0.018108699470758438, 0.00836978293955326, -0.01571425050497055, 0.01668655313551426, -0.016135329380631447, -0.02753630466759205, 0.02227059006690979, 0.039792172610759735, -0.02889268845319748, 0.0006195493042469025, -0.008435885421931744, 0.07050716876983643, 0.014822378754615784, 0.004537979606539011, -0.0472242496907711, 0.004956887103617191, -0.04484992101788521, -0.023014014586806297, 0.06599578261375427, 0.053955260664224625, -0.0062207127921283245, -0.0018587703816592693, -0.013001536019146442, 0.0018605956574901938, -0.041503023356199265, 0.0368996299803257, -0.0502600371837616, 0.0246700681746006, 0.006717201322317123, 0.04130949079990387, -0.01963595114648342, 0.02462570182979107, -0.0021508075296878815, 0.07809258997440338, -0.02851121313869953, 0.038923315703868866, 0.015005066059529781, -0.009873513132333755, -0.007869403809309006, -0.019352266564965248, -0.012083293870091438, -0.01735646463930607, -0.013645773753523827, -0.044829048216342926, -0.02903655730187893, 0.047870997339487076, 0.03916379064321518, -0.06769641488790512, 0.009382220916450024, 0.015062839724123478, -0.018286000937223434, 0.016492832452058792, 0.059833988547325134, 0.004927829373627901, -0.05893218517303467, 0.05061887949705124, -0.02970956452190876, 0.02661721035838127, -0.010096379555761814, 0.02571290358901024, -0.015120766125619411, -0.004792333580553532, 0.062205083668231964, -0.004987765569239855, -0.032283518463373184, -0.03599344566464424, -0.02404676005244255, 0.06100063398480415, -0.003180201631039381, 0.013458123430609703, -0.03622293472290039, -0.020906658843159676, 0.05156522989273071, -0.057368677109479904, 0.04055383801460266, 0.023742979392409325, -0.04173242300748825, 0.060934510082006454, -0.0167428907006979, -0.06486896425485611, 0.03587283939123154, 0.02291594073176384, -0.07535197585821152, -0.011295073665678501, 0.0049714380875229836, -0.007093127816915512, -0.027195189148187637, 0.007150671444833279, 0.013804652728140354, -0.03602176159620285, -0.05674945190548897, 0.0029734172858297825, -0.0032740780152380466, -0.027362268418073654, -0.0344698540866375, -0.0393378920853138, 0.06268976628780365, 0.019392557442188263, -0.06300637871026993, -0.011505217291414738, -0.004959840327501297, -0.05327034369111061, 0.00880191195756197, -0.020985469222068787, -0.08610053360462189, -0.027796929702162743, 0.005312300752848387, -0.004087314009666443, -0.04076593741774559, 0.013343465514481068, 0.032981839030981064, 0.01577802002429962, -0.007715503219515085, 0.05033152177929878, -0.019035952165722847, 0.0014957692474126816, 0.030197186395525932, 0.008841813541948795, -0.025584591552615166, 0.0258126612752676, 0.001418641651980579, 0.02185199409723282, -0.055732790380716324, -0.010592508129775524, 0.07400891184806824, 0.025921080261468887, 0.03850150853395462, -0.029005322605371475, 0.028948141261935234, -0.06062712520360947, 0.04996630176901817, -0.04005201533436775, -0.0987502858042717, -0.025444267317652702, -0.01627225987613201, -0.023377874866127968, 0.05478280037641525, -0.0633406937122345, 0.0378885455429554, 0.013912596739828587, -0.012126983143389225, -0.029525604099035263, -0.009605255909264088, -0.030908308923244476, -0.0016070010606199503, -0.03977951407432556, 0.02384711243212223, 0.010580380447208881, 0.033398352563381195, -0.01282108761370182, 0.036489978432655334, -0.01108595635741949, 0.06176153942942619, -0.006939851678907871, -0.011856692843139172, 0.006823370698839426, -0.03610837087035179, -0.0007272220682352781, -0.020429575815796852, -0.030907534062862396, -0.006131560076028109, 0.013748480938374996, 0.03235951438546181, 0.040885135531425476, 0.0211293026804924, -0.03740780055522919, 0.0017335652373731136, -0.018593715503811836, -0.016795547679066658, 0.03028804622590542, -0.06065160408616066, 0.02082429639995098, -4.831548721995205e-05, -0.0021749024745076895, 0.07695724070072174, -0.07739653438329697, -0.019136831164360046, 0.01842094212770462, 0.00993525143712759, 0.024856828153133392, -0.01031405944377184, -0.03346842899918556, 0.003736934857442975, 0.0006630074931308627, -0.019807375967502594, 3.051151907129679e-05, -0.04017779231071472, 0.02748141810297966, -0.03384291008114815, 0.0040852962993085384, -0.018689820542931557, -0.005533231887966394, -0.03185431286692619, -0.03697957098484039, -0.02624444104731083, 0.0004999052034690976, 0.036721497774124146, -0.047069765627384186, -0.012925676070153713, 0.048276450484991074, -0.0406678132712841, -0.000795947213191539, -0.010607089847326279, 0.023422550410032272, 0.06314564496278763, 0.004357272293418646, 0.0016582965617999434, 0.03205735608935356, 0.004768163897097111, 0.012236077338457108, 0.03238832578063011, 0.0012447074986994267, 0.0007131960592232645, -0.01781338080763817, -0.07459060847759247, 0.03032740391790867, 0.0015295273624360561, -0.024358732625842094, 0.019710969179868698, -0.019037166610360146, 0.06319088488817215, 0.04864270240068436, -0.016072526574134827, -0.00254459329880774, -0.030096810311079025, -0.005943836644291878, -0.05094298720359802, 0.002741160336881876, 0.04289764538407326, -0.059322696179151535, -0.017621610313653946, 0.004984415601938963, 0.03222597762942314, 0.07122176885604858, -0.02434356138110161, -0.04130267724394798, 0.09860607981681824, 0.007910119369626045, -0.008993733674287796, -0.035310737788677216, -0.044613067060709, -0.015865955501794815, 0.05396809056401253, -0.006694206967949867, -0.0035158293321728706, -0.003686909331008792, -0.0192590169608593, 0.03229299560189247, -0.0096210278570652, 0.018269838765263557, -0.06316237151622772, -0.01491670310497284, 0.011751937679946423, 0.029650837182998657, 0.052503157407045364, -0.029004547744989395, -0.04734904319047928, 0.020380116999149323, 0.07311263680458069, -0.006330596283078194, 0.01665433868765831, -0.014244955964386463, -0.025303775444626808, -0.00286396243609488, 0.007245904766023159, -0.021338023245334625, -0.011317990720272064, 0.014198647812008858, -0.02969539351761341, -0.014703519642353058, -0.013141912408173084, 0.021670682355761528, 0.019249146804213524, -0.07131614536046982, -0.02990828827023506, -0.038396142423152924, 0.04066471755504608, 0.008244065567851067, -0.02525479346513748, -0.01615988276898861, -0.021044569090008736, -0.019472220912575722, 0.0723060667514801, 0.01352553442120552, -0.052223969250917435, 0.0025903815403580666, -0.06851695477962494, 0.0017453458858653903, -0.030194532126188278, -0.02744552679359913, -0.0068342844024300575, -0.07457458227872849, 0.003670947626233101, -0.09134279936552048, 0.0028873078990727663, 0.06808001548051834, 0.006864097900688648, 0.0011642399476841092, -0.018875448033213615, -0.03479558974504471, 0.027178732678294182, -0.016912449151277542, -0.09528089314699173, -0.01997210457921028, 0.049168843775987625, 0.014913258142769337, -0.017321374267339706, -0.02089112438261509, 0.03666941076517105, 0.02732909470796585, 0.01616796851158142, -0.025018416345119476, -0.01157977432012558, 0.04128618165850639, -0.007520959712564945, -0.019808543846011162, 0.05864539369940758, -0.03415083885192871, 0.05260894447565079, 0.021417286247015, 0.05901050195097923, 0.03708774968981743, 0.03313421085476875, 0.004212427418678999, 0.010964159853756428, 0.07464847713708878, 0.005659831687808037, -0.06818035244941711, -0.040163103491067886, -0.036391615867614746, 0.022919505834579468, 0.07319056987762451, 0.04253406077623367, 0.05340462550520897, -0.01013419684022665, 0.022505510598421097, -0.02016356773674488, -0.07786722481250763, 0.039560794830322266, -0.03574317693710327, 0.07932236045598984, 0.009270844981074333, 0.017653143033385277, 0.04294129088521004, -0.004231685306876898, -0.05384563282132149, -0.04783779755234718, 0.033293161541223526, 0.0009629465639591217, -0.0006640810170210898, 0.03313776105642319, 0.039083100855350494, -0.03693544119596481, 0.010071666911244392, 0.03574008122086525, -0.0400146022439003, -0.05770163610577583, 0.04272731766104698, 0.004638488404452801, -0.009189792908728123, 0.02892127074301243, -0.021931244060397148, -0.0028072006534785032, 0.02507135644555092, 0.04331132769584656, 0.03593317046761513, -0.0011493719648569822, 0.03370869904756546, 0.032060250639915466, 0.004112164489924908, 0.036039188504219055, 0.01182535570114851, 0.02827475778758526, 0.02177680842578411, 0.044390469789505005, -0.020909547805786133, -0.006041905842721462, 0.0033571578096598387, 0.04636387899518013, 0.05312906578183174, 0.026284225285053253, -0.07174181938171387, -0.024467287585139275, 0.05363456904888153, 0.07079050689935684, 0.005047635640949011, -0.0009417376713827252, 0.06310820579528809, 0.020906051620841026, -0.03673446923494339, 0.008320493623614311, 0.033392712473869324, 0.09041308611631393, -0.03583705797791481, 0.0015068671200424433, -0.012848964892327785, 0.004149049520492554, 0.03367604687809944, -0.035675130784511566, 0.025698229670524597, 0.02640416845679283, 0.04098265618085861, 0.052899666130542755, 0.023032573983073235, -0.03611373528838158, 0.03553178533911705, -0.0184408538043499, 0.05442464351654053, -0.0054645356722176075, -0.01352839358150959, 0.02894056774675846, -0.052358124405145645, -0.05489613115787506, 0.038247447460889816, 0.060522545129060745, 0.03184809908270836, 0.0387374609708786, 0.00344800460152328, 0.007321891374886036, -0.016010385006666183, 0.034417930990457535, -0.06253793090581894, 0.025012804195284843, 0.017945827916264534, -0.010278711095452309, -0.016966283321380615, 0.06692741811275482, 0.02422003261744976, -0.0037603729870170355, 0.00820304173976183, -0.05274408310651779, -0.0059659527614712715, -0.039230167865753174, 0.02305811084806919, 0.07702279090881348, 0.03962814062833786, -0.005698125343769789, 0.005217511206865311, 0.08046995103359222, 0.03151417151093483, 0.0293581485748291, -0.0468357615172863, 0.03638656437397003, -0.03826989233493805, 0.03481679409742355, -0.03155429661273956, -0.020367994904518127, 0.051671262830495834, -0.02860056608915329, 0.006374828051775694, 0.012865200638771057, 0.029550442472100258, -0.05616007745265961, -6.081780019124044e-33, 0.007210502866655588, -0.01609031669795513, -0.09302988648414612, -0.06978000700473785, -0.050205081701278687, 0.003412858583033085, 0.024941178038716316, 0.027182448655366898, 0.029277799651026726, -0.018156176432967186, -0.02769574522972107, 0.009340559132397175, 0.002837603911757469, 0.030664784833788872, 0.033611975610256195, -0.025950247421860695, -0.028335899114608765, -0.0016175444470718503, 0.0036346442066133022, 0.014948932453989983, 0.018001709133386612, 0.047742437571287155, -0.012335596606135368, -0.009959865361452103, -0.02985188364982605, -0.004428056068718433, -0.05298762768507004, 0.008292768150568008, -0.015754545107483864, -0.01925981417298317, -0.01696539670228958, -0.015508738346397877, -0.030572157353162766, -0.018251890316605568, 0.001732983160763979, -0.10430803894996643, 0.027692971751093864, -0.02113299071788788, -0.05098292976617813, 0.014743064530193806, -0.06147383153438568, 0.05087121203541756, 0.04063386097550392, -0.003406247589737177, -0.053500376641750336, 0.01874762400984764, 0.019712189212441444, 0.03182335942983627, -0.032667126506567, -0.009720331989228725, -0.039626482874155045, -0.02475021220743656, -0.021049747243523598, 0.003426474519073963, 0.024712175130844116, 0.004627987276762724, -0.00998812448233366, -0.04791821911931038, -0.05452343448996544, 0.013740114867687225, -0.004753511864691973, 0.024464726448059082, -0.004299320746213198, 0.007731569930911064, 0.04289814084768295, -0.007484490051865578, 0.03504649177193642, -0.009919176809489727, 0.029890280216932297, -0.0212639681994915, -0.021381214261054993, -0.0378551259636879, 0.018548816442489624, -0.013565479777753353, 0.049050722271203995, -0.037882596254348755, -0.046213991940021515, 0.009539313614368439, 0.004608294926583767, 0.029189549386501312, 0.036268990486860275, 0.003236602758988738, 0.007435905281454325, 0.017920617014169693, 0.022604888305068016, -0.08228287845849991, -0.017974210903048515, -0.004291978664696217, 0.006811439525336027, 0.029333794489502907, -0.027871718630194664, -0.006141339894384146, -0.00816328078508377, -0.03738068416714668, 0.042250316590070724, 0.02171178162097931, 0.015601009130477905, 0.011615730822086334, 0.035666726529598236, -0.028269559144973755, -0.04556584358215332, -0.026629306375980377, -0.02705361880362034, 0.002030721167102456, -0.005815710406750441, 0.0007940226350910962, 0.038819700479507446, -0.007351274602115154, -0.0039804307743906975, 0.0022737719118595123, -0.011721584014594555, 0.01967017911374569, 0.0004915661411359906, 0.013683623634278774, 0.054376013576984406, -0.08347921073436737, -0.001525391242466867, 0.11629441380500793, 0.021501902490854263, 0.026726746931672096, -0.0568128377199173, -0.03812441602349281, 0.006721261888742447, -0.027355412021279335, -0.011250292882323265, 0.05039132758975029, 0.00950232520699501, -0.05162325128912926, -0.0983729287981987, -0.06402236223220825, -0.001652016188018024, -0.028732657432556152, 2.7869128871316207e-07, -0.025655949488282204, 0.07274490594863892, -0.024156546220183372, 0.028081346303224564, 0.008443763479590416, -0.02206139825284481, -0.042061563581228256, -0.03969471901655197, -0.03878581523895264, 0.013297938741743565, 0.04239276796579361, -0.031169505789875984, 0.044053927063941956, 0.0085647227242589, -0.009609735570847988, -0.0491296648979187, -0.05991225689649582, 0.09455739706754684, -0.01345453318208456, -0.004027324728667736, 0.03709104284644127, 0.05117161199450493, -0.003011266468092799, -0.036246735602617264, 0.04854430630803108, 0.02053750492632389, 0.012047715485095978, 0.041207294911146164, 0.03551214188337326, -0.02527124620974064, 0.0028733559884130955, -0.04329828545451164, -0.049927812069654465, -0.030107222497463226, -0.01265321858227253, 0.030925452709197998, 0.012777894735336304, 0.04507465660572052, -0.011022677645087242, -0.041478902101516724, 0.05421361327171326, 0.04878390580415726, 0.06178981810808182, -0.0066832625307142735, 0.0326349250972271, 0.03548717871308327, 0.002827782416716218, -0.054154518991708755, 0.01519077643752098, -0.01293446496129036, 0.07187052816152573, -0.08364081382751465, 0.020009608939290047, -0.015642043203115463, -0.029289864003658295, 0.00352405640296638, -0.050839003175497055, 0.0027077756822109222, -0.007746879011392593, 0.08781782537698746, 0.005661582574248314, -0.019443994387984276, 0.022438272833824158, 0.12362787872552872, 0.06705159693956375, -0.016938306391239166, 0.00039242496131919324, 2.6735420556228068e-34, -0.0031354520469903946, 0.00227486714720726, -0.04117118939757347, 0.040515393018722534, -0.03699731454253197, -0.004363542422652245, 0.008811968378722668, 0.0033617715816944838, -0.009003223851323128, -0.009838555008172989, -0.011160497553646564]

['Peter Sarlin', 'Samuel Rönnqvist']

1306.3860v1

This paper takes an information visualization perspective to visual representations in the general SOM paradigm. This involves viewing SOM-based visualizations through the eyes of Bertin's and Tufte's theories on data graphics. The regular grid shape of the Self-Organizing Map (SOM), while being a virtue for linking visualizations to it, restricts representation of cluster structures. From the viewpoint of information visualization, this paper provides a general, yet simple, solution to projection-based coloring of the SOM that reveals structures. First, the proposed color space is easy to construct and customize to the purpose of use, while aiming at being perceptually correct and informative through two separable dimensions. Second, the coloring method is not dependent on any specific method of projection, but is rather modular to fit any objective function suitable for the task at hand. The cluster coloring is illustrated on two datasets: the iris data, and welfare and poverty indicators.

Cluster coloring of the Self-Organizing Map: An information visualization perspective

http://arxiv.org/pdf/1306.3860v1

Title Cluster coloring SelfOrganizing Map information visualization perspective Summary paper take information visualization perspective visual representation general SOM paradigm involves viewing SOMbased visualization eye Bertins Tuftes theory data graphic regular grid shape SelfOrganizing Map SOM virtue linking visualization restricts representation cluster structure viewpoint information visualization paper provides general yet simple solution projectionbased coloring SOM reveals structure First proposed color space easy construct customize purpose use aiming perceptually correct informative two separable dimension Second coloring method dependent specific method projection rather modular fit objective function suitable task hand cluster coloring illustrated two datasets iris data welfare poverty indicator Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.053234390914440155, 0.0032906015403568745, -0.03575795888900757, 0.008676453493535519, 0.002276625484228134, 0.007480278145521879, 0.0495477057993412, 0.0004183838318567723, 0.03684726729989052, 0.031026501208543777, -0.04252233728766441, 0.09190113842487335, 0.01388021744787693, 0.01407534908503294, 0.0033887289464473724, -0.12192969769239426, -0.002293840516358614, 0.025859052315354347, -0.025892972946166992, -0.008750805631279945, 0.023149672895669937, -0.013069827109575272, 0.0049736411310732365, -0.0014496336225420237, -0.06694499403238297, -0.01415688544511795, -0.02382567711174488, -0.007479515857994556, 0.00039590441156178713, -0.02745559811592102, -0.010167495347559452, 0.0456373505294323, -0.01650611311197281, -0.016914833337068558, 2.1358710000640713e-06, -0.06844717264175415, -0.04129570350050926, -0.00902656838297844, 0.05001587048172951, 0.03155848756432533, 0.05551062151789665, -0.04730528965592384, 0.0035980292595922947, -0.054854705929756165, -0.0007902615470811725, -0.009967447258532047, 0.013241478241980076, 0.07265274971723557, 0.06545060127973557, -0.09612052142620087, -0.0021505861077457666, -0.03378835693001747, -0.03931374102830887, 0.0038261404260993004, -0.018308699131011963, 0.04868986830115318, -0.00837478507310152, 0.06193803250789642, -0.02517867647111416, -0.00921458937227726, -0.06466216593980789, 0.041779495775699615, -0.009831140749156475, -0.006983403582125902, 0.04221406579017639, 0.039634522050619125, 0.029364291578531265, 0.001706122187897563, 0.0057085538282990456, 0.03851979970932007, -0.021270567551255226, 0.040589381009340286, 0.01524302177131176, 0.006132603157311678, -0.003952937666326761, 0.025247186422348022, -0.015945812687277794, 0.006902359426021576, -0.00027756846975535154, -0.0010414738208055496, -0.004349284339696169, 0.08715011179447174, -0.028295090422034264, -0.02160979062318802, -0.0422590970993042, 0.05441402271389961, -0.004593636374920607, -0.01195608265697956, -0.06664726883172989, -0.035671450197696686, -0.0071449317038059235, 0.00018079453730024397, -0.009125158190727234, 0.027357803657650948, 0.017049871385097504, -0.017967835068702698, 0.05247515067458153, -0.018914174288511276, 0.06606905907392502, 0.0017759972251951694, 0.0444774366915226, 0.024314874783158302, -0.005475708283483982, 0.014921634458005428, 0.05684910714626312, -0.009016621857881546, -0.011045796796679497, -0.011230608448386192, -0.0038217122200876474, -0.00852854922413826, -0.009206587448716164, 0.00816043559461832, -0.02933892421424389, -0.012098947539925575, -0.007185358088463545, 0.06993462890386581, -0.03357528895139694, 0.005999158136546612, -0.04024367034435272, -0.0339958555996418, 0.03169799968600273, -0.00519282091408968, 0.02822186052799225, 0.005093984305858612, -0.034951090812683105, -0.041623007506132126, -0.07960992306470871, 0.008022834546864033, -0.05732458457350731, 0.03817054256796837, 0.04438178613781929, 0.017143070697784424, -0.004607609007507563, 0.010780309326946735, -0.04070594906806946, 0.026164473965764046, 0.055445075035095215, 0.03281811252236366, -0.0823657363653183, -0.03213968127965927, -0.0015164489159360528, 0.017458761110901833, 0.012021124362945557, -0.03170322999358177, 0.014635779894888401, -0.04048474505543709, 0.0016435333527624607, 0.0473751462996006, -0.03909222409129143, -0.02220318093895912, -0.01673443242907524, 0.06178954243659973, -0.09610551595687866, 0.02575390413403511, 0.053827617317438126, -0.0042622750625014305, -0.00871935486793518, -0.025806158781051636, 0.019336655735969543, 0.005369429476559162, 0.04222387820482254, -0.09753971546888351, 0.018813656643033028, -0.037020884454250336, -0.03912973403930664, 0.01337822712957859, -0.010701363906264305, 0.0148154366761446, -0.010972967371344566, -0.03393187373876572, 0.03367495909333229, -0.01565730944275856, 0.013032328337430954, -0.024759402498602867, -0.013750363141298294, 0.10474095493555069, 0.07148528844118118, 0.017282651737332344, -0.05574449896812439, 0.0482485257089138, -0.013105867430567741, 0.007854382507503033, 0.03470417112112045, 0.041710928082466125, 0.0034549052361398935, -0.00877306330949068, -0.01625729724764824, 0.025181153789162636, -0.020699286833405495, -0.04050353541970253, 0.02481154352426529, 0.03914210945367813, 0.05634502321481705, -0.04180971160531044, 0.013493497855961323, 0.03671768307685852, 0.078373484313488, -0.05816466733813286, 0.04277753084897995, 0.005458052735775709, 0.008331608958542347, -0.012239629402756691, 0.05382122844457626, 0.017286159098148346, -0.033030927181243896, -0.0585605688393116, 0.001645200653001666, 0.016633983701467514, 0.03556108474731445, -0.00281419325619936, -0.035765912383794785, -0.004619883373379707, -0.028523758053779602, -0.048670414835214615, -0.01826055347919464, 0.0421488992869854, -0.011868922971189022, -0.03173163905739784, -0.028541620820760727, 0.008417895063757896, -0.003534436458721757, 0.0009088492952287197, 0.0020859765354543924, 0.022835835814476013, 0.09931400418281555, 0.09489063918590546, 0.02920514903962612, 0.023612869903445244, 0.009272738359868526, 0.02950514853000641, 0.044318508356809616, -0.01744985766708851, 0.06770283728837967, 0.0012901589507237077, 0.02790812961757183, 0.02627461589872837, -0.01850861683487892, -0.005038532428443432, -0.04208533465862274, -0.009471871890127659, 0.003927797544747591, -0.032720763236284256, -0.005166760180145502, -0.0384848415851593, 0.08122032880783081, 0.0020884533878415823, -0.0017566974274814129, 0.019643772393465042, -0.0009040610166266561, 0.009919964708387852, 0.05712537467479706, -0.03813723474740982, 0.03225058689713478, -0.032923027873039246, -0.03132506087422371, -0.04633167013525963, 0.027463607490062714, -0.01097473781555891, -0.007462930399924517, 0.0818169042468071, -0.05723060667514801, -0.007772829383611679, 0.015358122065663338, -0.045619793236255646, 0.0011378469644114375, -0.037362392991781235, 0.03660073131322861, -0.004958283621817827, -0.037857867777347565, 0.016916699707508087, 0.00531122786924243, 0.01751204952597618, -0.03341766819357872, -0.03458375856280327, -0.029480163007974625, 0.035185009241104126, 0.08045849204063416, 0.04566777125000954, -0.043027691543102264, 0.04324676841497421, -0.04473622888326645, -0.010433620773255825, 0.005270580295473337, -0.0030503824818879366, -0.004769369028508663, -0.027832457795739174, 0.070177361369133, -0.052849363535642624, -0.026017282158136368, -0.031933557242155075, 0.0023756460286676884, -0.009628367610275745, 0.009155781008303165, -0.011819038540124893, -0.00803025346249342, -0.0035559164825826883, 0.030400976538658142, -0.0036265624221414328, 0.034536704421043396, 0.01463688537478447, 0.030929379165172577, -0.06376196444034576, 0.0013502090005204082, 0.054042451083660126, -0.01138551626354456, 0.13307589292526245, 0.07728089392185211, -0.028940292075276375, 0.06785956770181656, -0.02390570379793644, 0.06669466197490692, -0.001772809773683548, 0.0014247819781303406, -0.023088550195097923, -0.006868390366435051, 0.030367311090230942, -0.05950785428285599, -0.014018272049725056, 0.009214289486408234, 0.0365922749042511, -0.03556189313530922, -0.033562760800123215, -0.033364687114953995, 0.014268353581428528, 0.015676533803343773, 0.03797182813286781, -0.031254637986421585, -0.026908785104751587, 0.020500775426626205, -0.0368647575378418, 0.010484392754733562, -0.04176630452275276, 0.005061331205070019, 0.0381021723151207, 0.015700863674283028, -0.028937630355358124, -0.004946562927216291, 0.004725285805761814, -0.03404238447546959, -0.05936276912689209, -0.0013965355465188622, 0.0008025011047720909, -0.027503492310643196, 0.004236541222780943, 0.06045101583003998, -0.06414876878261566, 0.07651343941688538, -0.012859970331192017, 0.03550180792808533, 0.07585442066192627, 0.016103748232126236, 0.00477550458163023, 0.04650545120239258, -0.018623553216457367, 0.04672858491539955, 0.01799592189490795, -0.07211078703403473, 0.012527483515441418, -0.03108290582895279, 0.012639733962714672, -0.0038214544765651226, 0.03854817897081375, -0.04551422595977783, 0.015476496890187263, -0.0011055530048906803, 0.0451238714158535, -0.00838983990252018, 0.008131254464387894, 0.013393973000347614, -0.06756746023893356, 0.021939212456345558, 0.0019196327775716782, 0.049923572689294815, 0.03656300902366638, 0.027074266225099564, -0.07233791798353195, 0.009655606001615524, -0.03813418000936508, -0.044420357793569565, 0.004667308647185564, 0.023825448006391525, 0.03175735846161842, 0.06269460171461105, -0.024040015414357185, 0.009728383272886276, -0.020051786676049232, -0.038933832198381424, 0.0010154466144740582, 0.012221000157296658, 0.007587573956698179, 0.009748382493853569, -0.0940355658531189, -0.04630478844046593, -0.013758992776274681, -0.00739202881231904, 0.011391042731702328, -0.04024209827184677, -0.01929750293493271, 0.023784581571817398, -0.01852932758629322, 0.005449135787785053, -0.11587837338447571, -0.008188222534954548, 0.014439845457673073, -0.047020554542541504, 0.029932746663689613, -0.0035889458376914263, 0.027401139959692955, -0.02280275896191597, -0.014048632234334946, -0.0041955383494496346, 0.03905965015292168, 0.00783826969563961, -0.043411098420619965, 0.059112563729286194, 0.03000536747276783, -0.024380970746278763, -0.0404340997338295, 0.026704944670200348, 0.037474941462278366, 0.01363179087638855, 0.0638284757733345, 0.010465827770531178, 0.024549437686800957, 0.002978880424052477, -0.030652634799480438, 0.0011574599193409085, -0.016033004969358444, -0.0318630188703537, 0.025849005207419395, -0.006025343667715788, 0.04261360317468643, -0.07380208373069763, 0.031736887991428375, 0.030590170994400978, -0.037705451250076294, 0.016529064625501633, -0.03390074148774147, 0.0022258206736296415, -0.024752940982580185, -0.009318266063928604, 0.028690777719020844, 0.05554964765906334, 0.005004087463021278, -0.04450463503599167, 0.0037784602027386427, -0.07953178137540817, -0.01616588793694973, -0.02220757305622101, -0.030334817245602608, -0.01418325025588274, 0.004926253575831652, -0.044156577438116074, -0.017403531819581985, 0.010444105602800846, 0.021181311458349228, -0.06126762554049492, 0.024298029020428658, 0.016972484067082405, 0.05992927774786949, 0.026963407173752785, -0.0023330471012741327, -0.05425485223531723, -0.04878963530063629, -0.027607155963778496, 0.015006804838776588, 0.005117998458445072, -0.020101262256503105, -0.02978219836950302, -0.10167611390352249, 0.003990992438048124, 0.014708258211612701, -0.014636439271271229, 0.06250491738319397, 0.06989994645118713, -0.017473287880420685, -0.03346073627471924, -0.08129020035266876, 0.06536182016134262, -0.021303661167621613, -0.026971714571118355, 0.09801720827817917, 0.044040605425834656, 0.009121094830334187, -0.02719750627875328, -0.026013614609837532, -0.02679147757589817, -0.0428268238902092, 0.019237341359257698, -0.015745125710964203, 0.037045665085315704, -0.004149360582232475, -0.009013048373162746, 0.038257475942373276, 0.0211031511425972, -0.0717872679233551, -0.017621729522943497, 0.024769172072410583, -0.0051201218739151955, 0.01555108092725277, -0.029018493369221687, 0.04947076365351677, 0.016467871144413948, 0.011843791231513023, -0.03446855768561363, 0.02162993513047695, 0.046874552965164185, -0.02028529718518257, 0.013987008482217789, 0.002471218118444085, -0.013761100359261036, 0.06499144434928894, 0.02722480706870556, 0.00743613438680768, 0.002937496639788151, -0.010165532119572163, -0.020870408043265343, 0.006646323949098587, -0.015699798241257668, 0.01122712530195713, -0.0193980373442173, 0.009873609989881516, 0.029381660744547844, 0.019590415060520172, -0.004366822075098753, 0.04531165957450867, -0.010806689970195293, -0.03864092007279396, -0.023540612310171127, 0.015114676207304, 0.005258759018033743, -0.06722640991210938, -0.025498446077108383, -0.03257131576538086, -0.038856182247400284, 0.06252928078174591, 0.009413205087184906, -0.00018208465189673007, -0.025539055466651917, -0.003284382401034236, -0.023457610979676247, -0.03697659820318222, 0.0047117541544139385, -0.008185095153748989, 0.025695474818348885, 0.06328802555799484, -0.0018029093043878675, -0.029051398858428, 0.010066993534564972, 0.019511954858899117, 0.03039136715233326, -0.00628324132412672, -0.04083101451396942, -0.07893464714288712, 0.014822248369455338, -6.46774477300891e-33, -0.031776923686265945, -0.09047175198793411, -0.015497757121920586, -0.03913382068276405, -0.01940820924937725, -0.041493915021419525, 0.02649424597620964, 0.030810080468654633, -0.025682613253593445, -0.007547433488070965, -0.007931641303002834, -0.009272552095353603, -0.016457829624414444, 0.024233950302004814, 0.04618864879012108, 0.07100608199834824, -0.008248545229434967, 0.03499000892043114, -0.012297244742512703, -0.023118428885936737, -0.041240394115448, 0.006575373467057943, 0.017380686476826668, -0.03308446332812309, -0.031088225543498993, 0.004446815699338913, -0.018273167312145233, 0.010054798796772957, -0.005569892935454845, -0.03411128371953964, -0.031490691006183624, 0.0018156594596803188, 0.030170252546668053, 0.029483765363693237, -0.060044702142477036, 0.013883532024919987, -0.044032711535692215, -0.05821792036294937, -0.05904681235551834, 0.022773178294301033, -0.07156175374984741, -0.010595716536045074, 0.019506489858031273, 0.03027745708823204, -0.0009768899763002992, 0.014537326991558075, 0.035329293459653854, -0.003673226572573185, 0.008037587627768517, 0.11400234699249268, 0.037771858274936676, 0.03785904496908188, -0.033082980662584305, 0.03666767105460167, 0.013757305219769478, -0.034791767597198486, 0.003937617875635624, 0.02774825133383274, -0.0528661273419857, 0.06117316707968712, -0.003576714778319001, -0.01172381266951561, 0.03020194172859192, 0.07865385711193085, 0.07550115138292313, -0.009931868873536587, -0.005275690462440252, 0.0023144730366766453, -0.04003138467669487, 0.018326139077544212, 0.002751024207100272, -0.018227633088827133, 0.011867024935781956, -0.01076598186045885, 0.001786787761375308, -0.028097720816731453, 0.014694372192025185, 0.03901778534054756, -0.05771942436695099, -0.0320855937898159, -0.07401975244283676, 0.044786904007196426, -0.021698065102100372, -0.029828166589140892, 0.019556432962417603, -0.06978466361761093, -0.035747043788433075, 0.013682625256478786, 0.036684051156044006, -0.022885825484991074, -0.050376731902360916, 0.05025678500533104, -0.056603774428367615, 0.008641907013952732, 0.010415378957986832, -0.015810057520866394, 0.00550629198551178, 0.02411208674311638, 0.009115111082792282, -0.037839192897081375, -0.04798232764005661, 0.006389070302248001, -0.018535032868385315, 0.04210500791668892, -0.03616124019026756, 0.02606886252760887, -0.01774551160633564, -0.021647943183779716, -0.05091613903641701, 0.0248301662504673, 0.06984122842550278, -0.04945823922753334, 0.04283595830202103, -0.10405769944190979, -0.006261449307203293, -0.05203289911150932, -0.0036708246916532516, 0.03947288542985916, 0.056292302906513214, 0.007274718023836613, 0.01698528788983822, -0.022361550480127335, -0.06532151252031326, -0.03268297761678696, 0.025794729590415955, -0.0009734606719575822, -0.022141072899103165, -0.03791827708482742, 0.029963864013552666, -0.0016464886721223593, -0.008772265166044235, -0.026183148846030235, 2.7858678208758647e-07, 0.03860333561897278, 0.04193641245365143, 0.015683600679039955, -0.020123446360230446, 0.00866031739860773, -0.027621544897556305, -0.007273058407008648, 0.03378556668758392, -0.05487248674035072, 0.0014299715403467417, 0.007684424053877592, 0.03702489659190178, 0.008739979937672615, 0.04984942823648453, -0.004659662954509258, 0.009557925164699554, 0.016100363805890083, -0.0020111759658902884, -0.053159765899181366, 0.011891734786331654, 0.03170373663306236, 0.029451383277773857, 0.04668734595179558, 0.0016571307787671685, 0.020753327757120132, 0.015143057331442833, 0.0007112631574273109, -0.013674372807145119, 0.0318039134144783, 0.01050620898604393, -0.05410333350300789, -0.0044237528927624226, -0.04113565385341644, 0.013338182121515274, 0.010567584075033665, -0.03729104995727539, -0.06315232068300247, -0.023592650890350342, 0.03132612630724907, 0.051538944244384766, 0.05004304274916649, 0.003147195093333721, 0.0334453359246254, -0.03475724533200264, -0.0009460809524171054, 0.01044247392565012, -0.024946866557002068, 0.046264804899692535, 0.04022999480366707, 0.06537383794784546, 0.06325607746839523, -0.008390095084905624, -0.051882144063711166, 0.014761636964976788, -0.01427213940769434, -0.024134114384651184, 0.0269485991448164, 0.01947210542857647, 0.02506604790687561, -0.025926467031240463, 0.0032197346445173025, 0.0002072458592010662, 0.011486457660794258, 0.05105846747756004, 0.006469917017966509, 0.0741892158985138, -0.015267882496118546, 2.6630971454672776e-34, -0.0009775584330782294, -0.017284590750932693, 0.007265494205057621, -0.06383796781301498, -0.0010634299833327532, -0.019672740250825882, -0.055304352194070816, -0.01869443617761135, 0.002410219982266426, -0.041986264288425446, -0.008620808832347393]

['An Bian', 'Xiong Li', 'Yuncai Liu', 'Ming-Hsuan Yang']

1306.4080v4

The recent years have witnessed advances in parallel algorithms for large scale optimization problems. Notwithstanding demonstrated success, existing algorithms that parallelize over features are usually limited by divergence issues under high parallelism or require data preprocessing to alleviate these problems. In this work, we propose a Parallel Coordinate Descent Newton algorithm using multidimensional approximate Newton steps (PCDN), where the off-diagonal elements of the Hessian are set to zero to enable parallelization. It randomly partitions the feature set into $b$ bundles/subsets with size of $P$, and sequentially processes each bundle by first computing the descent directions for each feature in parallel and then conducting $P$-dimensional line search to obtain the step size. We show that: (1) PCDN is guaranteed to converge globally despite increasing parallelism; (2) PCDN converges to the specified accuracy $\epsilon$ within the limited iteration number of $T_\epsilon$, and $T_\epsilon$ decreases with increasing parallelism (bundle size $P$). Using the implementation technique of maintaining intermediate quantities, we minimize the data transfer and synchronization cost of the $P$-dimensional line search. For concreteness, the proposed PCDN algorithm is applied to $\ell_1$-regularized logistic regression and $\ell_2$-loss SVM. Experimental evaluations on six benchmark datasets show that the proposed PCDN algorithm exploits parallelism well and outperforms the state-of-the-art methods in speed without losing accuracy.

Parallel Coordinate Descent Newton Method for Efficient $\ell_1$-Regularized Minimization

http://arxiv.org/pdf/1306.4080v4

Title Parallel Coordinate Descent Newton Method Efficient ell1Regularized Minimization Summary recent year witnessed advance parallel algorithm large scale optimization problem Notwithstanding demonstrated success existing algorithm parallelize feature usually limited divergence issue high parallelism require data preprocessing alleviate problem work propose Parallel Coordinate Descent Newton algorithm using multidimensional approximate Newton step PCDN offdiagonal element Hessian set zero enable parallelization randomly partition feature set b bundlessubsets size P sequentially process bundle first computing descent direction feature parallel conducting Pdimensional line search obtain step size show 1 PCDN guaranteed converge globally despite increasing parallelism 2 PCDN converges specified accuracy epsilon within limited iteration number Tepsilon Tepsilon decrease increasing parallelism bundle size P Using implementation technique maintaining intermediate quantity minimize data transfer synchronization cost Pdimensional line search concreteness proposed PCDN algorithm applied ell1regularized logistic regression ell2loss SVM Experimental evaluation six benchmark datasets show proposed PCDN algorithm exploit parallelism well outperforms stateoftheart method speed without losing accuracy Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.030086476355791092, 0.04530581086874008, -0.02558824047446251, 0.041539061814546585, -0.00472935801371932, 0.002932616975158453, 0.06619363278150558, -0.01286949310451746, -0.03168097138404846, 0.004646987188607454, 0.043116603046655655, 0.018544789403676987, 0.024947836995124817, -0.01588134653866291, -0.03970888629555702, -0.01990724727511406, -0.015113231725990772, 0.035319432616233826, -0.003662673756480217, -0.04452567920088768, 0.039575621485710144, 0.005536005366593599, -0.028182167559862137, -0.0008357149199582636, -0.07895124703645706, -0.03829537704586983, -0.018337829038500786, 0.0236651748418808, 0.027704430744051933, -0.008860856294631958, 0.03313133120536804, -0.0015049424255266786, 0.015142541378736496, 0.005765650421380997, 2.3828097255318426e-06, -0.03603005036711693, 0.02599451318383217, -0.0055769337341189384, 0.08048712462186813, 0.06811082363128662, -0.005356794223189354, -0.017748061567544937, 0.02864951826632023, -0.004682345315814018, -0.00046113700955174863, -0.0415179468691349, 0.012500406242907047, 0.024216189980506897, 0.008117795921862125, 0.01640387997031212, -0.0015737609937787056, 0.01025411207228899, 0.008333863690495491, -0.005804029759019613, -0.09316449612379074, -0.018438242375850677, 0.013223878107964993, 0.02219155803322792, -0.024808721616864204, 0.015011103823781013, 0.0017318697646260262, 0.045583661645650864, 0.021183578297495842, 0.006369730457663536, -0.0005916170193813741, 0.008735246025025845, 0.013472906313836575, 0.0007404417265206575, -0.04833744466304779, 0.019607188180088997, -0.022309934720396996, 0.009672925807535648, 0.022189605981111526, -0.003584587248042226, -0.012354894541203976, 0.005112186074256897, 0.019641121849417686, -0.00023102985869627446, -0.05287656560540199, 0.007035615388303995, -0.023267101496458054, -0.0714116320014, -0.007933266460895538, -0.02559896931052208, 0.014085270464420319, 0.011061579920351505, 0.008342831395566463, -0.0036569349467754364, 0.005853772629052401, 0.0023624359164386988, -0.0611482635140419, 0.010962058790028095, 0.05554076284170151, -0.04305819049477577, -0.03791516646742821, -0.017893731594085693, -0.004292151425033808, -0.10400521010160446, -0.00023522360424976796, -0.038442015647888184, 0.04114950820803642, -0.04703804478049278, 0.05715932324528694, 0.019326552748680115, 0.018628234043717384, 0.022177008911967278, -0.0398288369178772, -0.010961447842419147, -0.01772391051054001, 0.005142172798514366, -0.029929321259260178, -0.002783736679702997, -0.034980397671461105, 0.024441391229629517, -0.00866499450057745, 0.0019349480280652642, 0.0011741151101887226, -0.006608446128666401, -0.011383451521396637, -0.07400958240032196, 0.02149825543165207, 0.07550502568483353, 0.04362846165895462, 0.013363529928028584, 0.0385332927107811, 0.013468008488416672, -0.03718108683824539, 0.0039321016520261765, -0.037339258939027786, 0.0674472376704216, -0.0102747343480587, -0.006333459634333849, -0.0015736949862912297, 0.04467238858342171, -0.022634660825133324, -0.06215912103652954, 0.015688762068748474, 0.04506862536072731, -0.025454020127654076, 0.005728054326027632, -0.006718483287841082, 0.011592550203204155, -0.02870880253612995, -0.039021190255880356, 0.01353584136813879, -0.011740771122276783, 0.02059956081211567, 0.03133281320333481, -0.0071035693399608135, -0.043264612555503845, 0.00021943918545730412, 0.07168253511190414, -0.03829183429479599, -0.004223200026899576, 0.06582123786211014, 0.007695898413658142, -0.019531086087226868, 0.06326422840356827, -0.043966133147478104, 0.03995741531252861, -0.02161453105509281, -0.03424953669309616, -0.03254544734954834, -0.015206274576485157, -0.02676020935177803, -0.0362154021859169, -0.016692867502570152, -0.007043374236673117, 0.005711045116186142, 0.04998045414686203, 0.012096632272005081, -0.010588176548480988, 0.0006630196003243327, -0.0316157266497612, 0.023760467767715454, 0.047762591391801834, 0.07012636959552765, 0.03410027176141739, 0.026209888979792595, 0.04000167176127434, -0.02734597586095333, -0.035052329301834106, 0.043486300855875015, 0.018510933965444565, 0.0033628325909376144, -0.05956285819411278, -0.021704690530896187, 0.015027787536382675, -0.03241623565554619, -0.005919972434639931, 0.02397262677550316, 0.014749357476830482, -0.04606953635811806, 0.03538144379854202, 0.0004223983269184828, -0.03156650811433792, -0.01911841705441475, 0.01434713788330555, 0.06199556216597557, -0.02893318608403206, -0.08121990412473679, 0.04016195237636566, 0.009080763906240463, -0.05096342787146568, -0.04335103556513786, -0.029896831139922142, -0.051925234496593475, 0.004706119187176228, 0.09564461559057236, -0.037645306438207626, 0.012992212548851967, 0.015734288841485977, 0.00772063760086894, -0.025096043944358826, 0.010634128004312515, 0.055347271263599396, -0.002993422094732523, 0.028292324393987656, 0.018627451732754707, -0.0010083266533911228, -0.01649576798081398, 0.06285092234611511, 0.05534394457936287, 0.02124757319688797, -0.07070662081241608, 0.021870406344532967, 0.06136351451277733, 0.032034654170274734, 0.017196249216794968, -0.013486729003489017, 0.026343226432800293, -0.09823407977819443, 0.08029539883136749, -0.04471265897154808, 0.0010758599964901805, -0.024078460410237312, 0.026512710377573967, -0.06721984595060349, 0.05484313890337944, -0.02782907523214817, -0.010535834357142448, 0.11074727773666382, -0.010975112207233906, -0.014031215570867062, -0.02458186447620392, -0.019740117713809013, -0.01229160837829113, -0.05835537612438202, -0.009104705415666103, -0.046608809381723404, 0.018454205244779587, -0.015066184103488922, -0.01199925784021616, -0.0466013178229332, 0.036839958280324936, 0.00615842966362834, 0.03508168086409569, 0.027391783893108368, -0.005495539400726557, -0.008710917085409164, 0.014723343774676323, -0.01694362796843052, 0.01732763648033142, -0.00012134835560573265, 0.005816415883600712, 0.05530795827507973, 0.03632421791553497, -0.0690738707780838, 0.013626168482005596, -0.02709886245429516, -0.02762141078710556, 0.0348481722176075, 0.0013526936527341604, 0.024615244939923286, 0.002172376960515976, 0.0513015054166317, 0.1410278081893921, -0.04920512065291405, -0.04990299418568611, -0.011091463267803192, 0.0068541113287210464, -0.03321967273950577, 0.02749575302004814, -0.02714955434203148, 0.031821638345718384, 0.013094889000058174, 0.02139199711382389, 0.02871296927332878, -0.05538060516119003, 0.02976003848016262, -0.013221940957009792, 0.006507741287350655, -0.004191648680716753, -0.020061802119016647, -0.024093639105558395, -0.03784066066145897, -0.051704518496990204, 0.015867838636040688, 0.00625577149912715, -0.01861950382590294, 0.009738683700561523, 0.036975447088479996, -0.02078726328909397, 0.03960573673248291, -0.0183325856924057, 0.042991843074560165, 0.02962244674563408, 0.015384728088974953, 0.028213832527399063, 0.02386080101132393, 0.021776488050818443, -0.02381577529013157, 0.018954195082187653, -0.0414557158946991, 0.0011893566697835922, -0.06990579515695572, -0.0687250867486, 0.014486334286630154, -0.033064402639865875, -0.0509493425488472, 0.013384079560637474, -0.06439648568630219, 0.03354700282216072, 0.026866238564252853, 0.036329496651887894, -0.034031521528959274, -0.06126087158918381, -0.028027255088090897, 0.013071847148239613, -0.01664847880601883, -0.009431947022676468, -0.07993297278881073, -0.04093188792467117, 0.061443399637937546, 0.10178852826356888, 0.003873303299769759, -0.0013156296918168664, 0.009420838207006454, 0.02124776877462864, -0.0020873649045825005, 0.014486061409115791, -0.05488729104399681, -0.02567409537732601, -0.05471479147672653, 0.03073752112686634, 0.011913823895156384, 0.036601610481739044, -0.06024837866425514, -0.009263220243155956, 0.011247726157307625, -0.017824633046984673, 0.008847702294588089, -0.012975115329027176, -0.012060408480465412, 0.03089388646185398, 0.023729443550109863, -0.006472939159721136, -0.02868242748081684, -0.023881537839770317, -0.002415803726762533, 0.09541499614715576, -0.008667618036270142, 0.01744740642607212, 0.00040697978693060577, -0.08698933571577072, -0.0011425280245020986, -0.007363810203969479, 0.002804499352350831, -0.03876877948641777, -0.012340241111814976, -0.020697401836514473, -0.021316763013601303, 0.016424912959337234, 0.03485601022839546, 0.029170701280236244, -0.11347264051437378, -0.0469985157251358, -0.024947592988610268, 0.006495941895991564, 0.009441286325454712, -0.03615473583340645, -0.0011454682098701596, -0.015248107723891735, 0.007212006952613592, 0.005852691363543272, 0.05489611625671387, -0.001481377985328436, 0.023886846378445625, -0.035097021609544754, 0.018962876871228218, -0.02414732053875923, -0.0485549233853817, -0.0009951269021257758, -0.06452392786741257, -0.024645786732435226, -0.036606285721063614, 0.011986148543655872, 0.049724992364645004, -0.006785924080759287, -0.0037688135635107756, 0.030972857028245926, -0.004904883913695812, 0.06240694224834442, -0.0032718831207603216, -0.07495557516813278, -0.05422003194689751, -0.02737775258719921, 0.027760818600654602, -0.035563115030527115, -0.011116515845060349, 0.005852079018950462, 0.022066423669457436, -0.006094829179346561, -0.05443018302321434, -0.016954323276877403, 0.008827893994748592, 0.005060927476733923, -0.018741391599178314, 0.05775785073637962, -0.03789260610938072, 0.06667179614305496, 0.0595938116312027, 0.05904906243085861, 0.004965891130268574, 0.01962844654917717, -0.04905740171670914, 0.02127397619187832, 0.004756607580929995, -0.01027913112193346, -0.029506200924515724, -0.09989197552204132, -0.0019637327641248703, 0.017206605523824692, -0.021340973675251007, 0.02119748666882515, 0.10122383385896683, -0.004412749316543341, -0.006359020248055458, -0.048144422471523285, -0.04505613073706627, 0.05739365890622139, 0.028649942949414253, 0.021817345172166824, 0.004135852213948965, -0.01703299768269062, -0.019430946558713913, 0.006385955028235912, -0.060784488916397095, 0.02066991850733757, 0.06716036051511765, 0.0017319865291938186, -0.012314185500144958, 0.07897286862134933, 0.06280393898487091, -0.014892167411744595, 0.021982934325933456, 0.02639816701412201, -0.08500506728887558, -0.03653224930167198, 0.002202311297878623, 0.027866752818226814, -0.027308296412229538, 0.033844947814941406, -0.0182615015655756, -0.028513969853520393, -0.041277166455984116, 0.0227887611836195, 0.021694080904126167, 0.037327803671360016, -0.022770918905735016, -0.039108067750930786, 0.0013651951448991895, 0.01270709466189146, 0.019327115267515182, 0.051096707582473755, -0.0047567724250257015, -0.011947275139391422, -0.01270945742726326, -0.05082737281918526, -0.018191130831837654, 0.04219088330864906, 0.07157066464424133, 0.049779318273067474, -0.0527915321290493, -0.03724352642893791, 0.09113670140504837, 0.03517955169081688, 0.010751169174909592, -0.033105380833148956, 0.025392254814505577, -0.01753765344619751, 0.006758402567356825, -0.03377703204751015, 0.020839758217334747, 0.11808233708143234, -0.054867301136255264, -0.04354562982916832, 0.0315980426967144, -0.06365647166967392, 0.04872948303818703, -0.0089321443811059, 0.038453057408332825, 0.020722897723317146, -0.001319281873293221, 0.03058769181370735, 0.013569938950240612, -0.013048100285232067, -0.007301678415387869, -0.003650529310107231, 0.05742953345179558, -0.03803165629506111, -0.023287340998649597, 0.00047204637667164207, -0.0306253582239151, -0.011312204413115978, -0.012947880662977695, 0.06395112723112106, -0.003511172253638506, 0.025776337832212448, 0.0006493215914815664, -0.016967229545116425, -0.039677802473306656, 0.01738496497273445, -0.04786832258105278, 0.044103529304265976, 0.055490490049123764, -0.021039247512817383, -0.00377848744392395, 0.07236552983522415, 0.005049895029515028, -0.01843046210706234, -0.012623880058526993, 0.009162052534520626, -0.05202925577759743, -0.0374256856739521, 0.04355322942137718, 0.06515184789896011, 0.04497045651078224, -0.028326770290732384, -0.0253258366137743, 0.08047952502965927, 0.0027132397517561913, 0.05869448184967041, -0.01171528548002243, 0.031160427257418633, -0.011514058336615562, 0.020555520430207253, 0.0025946430396288633, -0.035397402942180634, 0.0022312107030302286, -0.008798928000032902, -0.012332162819802761, -0.04908011853694916, -0.007420655339956284, -0.021653495728969574, -5.4288931916040676e-33, 0.031338825821876526, -0.014677947387099266, -0.06714268028736115, 0.029742509126663208, -0.039235521107912064, 0.010073383338749409, 0.04167701303958893, -0.007912066765129566, 0.035871606320142746, 0.028221644461154938, 0.015492822974920273, 0.011221691034734249, -0.024089323356747627, 0.01795344427227974, 0.03152135759592056, 0.01921333558857441, 0.0046126157976686954, -0.01764311082661152, 0.0661105215549469, 0.010921171866357327, 0.028604088351130486, 0.08266325294971466, -0.017156079411506653, 0.0017355313757434487, -0.0889308899641037, -0.006854766979813576, 0.00843286793678999, -0.005602432414889336, -0.05199442058801651, -0.0006853294325992465, 0.010516566224396229, 0.02091924659907818, 1.446999522158876e-05, -0.04437299445271492, -0.010704243555665016, -0.015978975221514702, -0.042788032442331314, 0.01937389187514782, 0.009362694807350636, 0.00896825734525919, -0.03397088125348091, 0.02865043468773365, 0.034754518419504166, 0.0014540994307026267, -0.05693374201655388, -0.02314978837966919, 0.0337727926671505, 0.019110040739178658, -0.03176411986351013, -0.02210882306098938, -0.008265906013548374, -0.024591147899627686, -0.01947505585849285, -0.0042305076494812965, 0.05008426681160927, -0.0063670044764876366, -0.0509934239089489, -0.030668366700410843, 0.02080671489238739, 0.007693906780332327, -0.0061944168992340565, -0.004164174199104309, -0.02747044712305069, 0.04396085813641548, 0.07242468744516373, 0.0380777046084404, 0.07575161010026932, -0.02557176724076271, -0.015007385984063148, -0.009789606556296349, -0.013635033741593361, 0.007550298236310482, 0.054470665752887726, 0.018194686621427536, 0.046307746320962906, -0.04590204730629921, -0.112967848777771, 0.017002329230308533, -0.06050125136971474, -0.02233557403087616, 0.0049719857051968575, -0.011205198243260384, 0.036626920104026794, 0.01722010411322117, -0.009656662121415138, 0.028205057606101036, -0.006074916105717421, -0.022838080301880836, 0.024516290053725243, -0.008006423711776733, -0.021438036113977432, 0.048178914934396744, -0.017728572711348534, -0.06322398781776428, 0.07123535871505737, -0.0024307570420205593, -0.013380526565015316, 0.028353340923786163, 0.02923845872282982, -0.01380592118948698, -0.05461322143673897, 0.03861682862043381, -0.04550366476178169, -0.05160083249211311, 0.010572412051260471, -0.0004647185269277543, 0.03757080063223839, -0.04845548793673515, -0.004071892239153385, -0.01163824275135994, -0.012422175146639347, -0.004703014623373747, -0.028147533535957336, 0.08301860839128494, 0.04103732854127884, -0.040336914360523224, 0.02828551083803177, 0.05074184760451317, 0.028316661715507507, -0.008481568656861782, -0.03800775110721588, -0.03360955789685249, 0.016152508556842804, -0.0324091836810112, -0.028307000175118446, 0.011274910531938076, 0.012446609325706959, -0.06196482479572296, -0.022004030644893646, -0.06448836624622345, -0.008277411572635174, -0.011631150729954243, 2.6703037292463705e-07, -0.0260767824947834, 0.0521717295050621, -0.01634158566594124, -0.04313209280371666, -0.004433565307408571, -0.04503246396780014, -0.032870590686798096, 0.049381501972675323, -0.0026103761047124863, -0.03943866863846779, 0.06342142820358276, -0.022745003923773766, 0.06195422261953354, -0.010020128451287746, -0.08015929162502289, 0.015301928855478764, 0.0004624909779522568, 0.05974208936095238, -0.015462526120245457, 0.007665084209293127, 0.0022170438896864653, -0.0045135896652936935, 0.02588415890932083, -0.04276333376765251, 0.05132075026631355, 0.02462376095354557, 0.014570114202797413, -0.026972945779561996, -0.0017822510562837124, -0.04363691434264183, -0.012654993683099747, -0.013899369165301323, -0.018232572823762894, -0.012397415935993195, -0.001897729467600584, 0.022985899820923805, -0.019780082628130913, 0.017952682450413704, -0.01159216370433569, 0.003065928351134062, 0.052268676459789276, 0.044128067791461945, 0.015054364688694477, 0.0190808717161417, 0.022297779098153114, 0.06276661902666092, 0.012425410561263561, -0.06325503438711166, 0.04756245017051697, 0.00355593953281641, 0.08503597974777222, -0.03661493584513664, 0.051036059856414795, -0.00427251635119319, 0.0019066125387325883, -0.03727494552731514, -0.012526120990514755, -0.028304927051067352, 0.04009728133678436, 0.09156566113233566, -0.060952913016080856, -0.000612466421443969, 0.0280682984739542, 0.05934756621718407, 0.05217226967215538, 0.00022998636995907873, 0.008723565377295017, 2.4422633125097813e-34, -0.008431080728769302, -0.022724658250808716, -0.00916978344321251, 0.02483329363167286, -0.01952405832707882, -0.031071994453668594, -0.025071794167160988, -0.019311854615807533, -0.007597527466714382, -0.05328628048300743, -0.006923903711140156]

['Sumit Goswami', 'Mayank Singh Shishodia']

1306.4633v1

Fuzzy logic deals with degrees of truth. In this paper, we have shown how to apply fuzzy logic in text mining in order to perform document clustering. We took an example of document clustering where the documents had to be clustered into two categories. The method involved cleaning up the text and stemming of words. Then, we chose m number of features which differ significantly in their word frequencies (WF), normalized by document length, between documents belonging to these two clusters. The documents to be clustered were represented as a collection of m normalized WF values. Fuzzy c-means (FCM) algorithm was used to cluster these documents into two clusters. After the FCM execution finished, the documents in the two clusters were analysed for the values of their respective m features. It was known that documents belonging to a document type, say X, tend to have higher WF values for some particular features. If the documents belonging to a cluster had higher WF values for those same features, then that cluster was said to represent X. By fuzzy logic, we not only get the cluster name, but also the degree to which a document belongs to a cluster.

A Fuzzy Based Approach to Text Mining and Document Clustering

http://arxiv.org/pdf/1306.4633v1

Title Fuzzy Based Approach Text Mining Document Clustering Summary Fuzzy logic deal degree truth paper shown apply fuzzy logic text mining order perform document clustering took example document clustering document clustered two category method involved cleaning text stemming word chose number feature differ significantly word frequency WF normalized document length document belonging two cluster document clustered represented collection normalized WF value Fuzzy cmeans FCM algorithm used cluster document two cluster FCM execution finished document two cluster analysed value respective feature known document belonging document type say X tend higher WF value particular feature document belonging cluster higher WF value feature cluster said represent X fuzzy logic get cluster name also degree document belongs cluster Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.011140639893710613, -0.030188264325261116, -0.050049979239702225, 0.006859514396637678, -0.02102700248360634, 0.0006738764932379127, -0.012489521875977516, 0.04531959816813469, 0.030933158472180367, -0.03853463754057884, 0.022925982251763344, 0.05258285999298096, 0.047359153628349304, -0.019602209329605103, -0.013156933709979057, -0.037828654050827026, 0.0380888432264328, 0.028138214722275734, 0.04738858342170715, 0.013429527170956135, 0.06296450644731522, 0.0291050486266613, -0.012385373003780842, 0.0063803112134337425, -0.012153119780123234, 0.0205001849681139, 0.01011988427489996, -0.04083932936191559, -0.0016022815834730864, 0.03056700900197029, 0.030804211273789406, 0.029333295300602913, -0.02981148101389408, 0.030573729425668716, 2.0592949567799224e-06, -0.06998276710510254, -0.09035805612802505, 0.008439802564680576, 0.09073926508426666, -0.03629407659173012, 0.0864214077591896, 0.022544166073203087, -0.01622166484594345, 0.028877004981040955, -0.018603896722197533, 0.043150391429662704, -0.03799138590693474, 0.0358358658850193, 0.031693510711193085, 0.024541303515434265, 0.0064218295738101006, -0.06785595417022705, 0.0047085098922252655, 0.07775004953145981, 0.026400230824947357, 0.02255101129412651, 0.007022215519100428, 0.002430219203233719, 0.04536359757184982, 0.0008719501784071326, 0.010804218240082264, -0.022722702473402023, -0.06530973315238953, -0.031926799565553665, 0.011964048258960247, 0.033091045916080475, -0.026050888001918793, -0.003317097434774041, 0.049875736236572266, -0.00879070907831192, -0.011941131204366684, -0.0045152753591537476, 0.06602378934621811, 0.004448947496712208, -0.02794121764600277, 0.0110391890630126, -0.005198188591748476, 0.012212075293064117, -0.04125786945223808, 0.0031496798619627953, 0.02521950751543045, 0.08024728298187256, -0.03264239802956581, 0.008703533560037613, -0.007953166961669922, 0.05295339971780777, -0.019149187952280045, -0.011410802602767944, 0.0033357860520482063, -0.001451274030841887, 0.012486230581998825, -0.022708028554916382, 0.0565788708627224, 0.04597014933824539, 0.03966158255934715, -0.01071980595588684, -0.03680301830172539, -0.03716394305229187, 0.07078418880701065, -0.06179128587245941, -0.07136688381433487, -0.02388700284063816, 0.059696659445762634, 0.00616533262655139, -0.007783432956784964, -0.026114344596862793, 0.06705539673566818, -0.037130557000637054, -0.01085166446864605, -0.012973111122846603, -0.07051873207092285, 0.0010483257938176394, -0.02098735235631466, 0.027771230787038803, 0.01798439212143421, -0.009024406783282757, -0.04192669317126274, -0.005052508786320686, 0.01964508183300495, 0.024450039491057396, 0.004131037276238203, -0.017757540568709373, 0.021811578422784805, -0.006622599437832832, -0.020206356421113014, -0.01391786988824606, -0.051653359085321426, 0.05109015479683876, -0.03418884798884392, 0.04156133532524109, 0.05512973666191101, 0.022220805287361145, 0.047825463116168976, 0.007183071691542864, -0.019020818173885345, -0.01822669990360737, -0.026296989992260933, -0.0025146217085421085, -0.09670841693878174, -0.0413370281457901, 0.050449714064598083, -0.005906277801841497, -0.05843844637274742, -0.047394342720508575, -0.006530148442834616, -0.01399016473442316, -0.008174095302820206, 0.041528526693582535, -0.003929500002413988, 0.022612519562244415, -0.02740314230322838, 0.01822136901319027, -0.10388260334730148, -0.0024358921218663454, 0.10370828211307526, 0.013828921131789684, 0.02692730724811554, -0.010507289320230484, 0.021631667390465736, 0.0023027677088975906, 0.06437435746192932, -0.01180640235543251, 0.03758692368865013, -0.01960725709795952, -0.03017164207994938, -0.04182521253824234, 0.037890151143074036, 0.014650261960923672, -0.032050590962171555, -0.0005413833423517644, -0.009066790342330933, 0.02517085149884224, 0.006957695819437504, 0.014121383428573608, 0.014784887433052063, 0.10905499756336212, 0.045117489993572235, 0.04113774374127388, -0.0631137564778328, 0.07093814015388489, 0.01660192757844925, 0.031402431428432465, 0.06178811937570572, -0.006478503812104464, -0.06778416037559509, 0.008940659463405609, -0.0035159760154783726, 0.007461834233254194, -0.007726920302957296, -0.016738850623369217, -0.01228408608585596, 0.00612416910007596, 0.037274159491062164, -0.058239419013261795, 0.018121464177966118, 0.010464807040989399, 0.007932046428322792, -0.06662887334823608, 0.02114795707166195, -0.022149045020341873, 0.02966446429491043, 0.02308092825114727, 0.028609419241547585, 0.024311469867825508, 0.018610894680023193, -0.0793331041932106, 0.02812897600233555, -0.0008685004431754351, -0.06022856757044792, -0.05791989713907242, -0.05274030193686485, -0.0310574509203434, -0.05014694482088089, -0.031985726207494736, 0.028197087347507477, 0.039902254939079285, -0.014529731124639511, -0.0614858902990818, -0.01881529949605465, 0.05501449108123779, 0.0017312535783275962, 0.01671735942363739, -0.013739376328885555, 0.030707772821187973, 0.04628148302435875, 0.06100352481007576, 6.533253326779231e-05, -0.005870920605957508, -0.020206836983561516, -0.025252565741539, 0.010975277051329613, -0.007207697257399559, 0.04396767541766167, 0.035098765045404434, -0.03708922117948532, -0.023878267034888268, 0.045962948352098465, -0.038132186979055405, 0.005360660143196583, 0.01977977529168129, 0.011495511047542095, -0.07143586128950119, 0.015154361724853516, -0.009688877500593662, 0.004518608562648296, -0.03358617052435875, 0.002370081376284361, -0.014938510954380035, 0.041011299937963486, -0.03830978646874428, -0.0199500173330307, -0.04085826873779297, 0.07516579329967499, 0.019214235246181488, 0.026812933385372162, -0.07634443044662476, -0.03799604997038841, 0.010155540890991688, -0.0061067333444952965, 0.050691649317741394, -0.03853430598974228, -0.004557257052510977, 0.06056898459792137, 0.027659446001052856, -0.02939445525407791, -0.011668817140161991, -0.048514578491449356, 0.004814093001186848, -0.016241515055298805, 0.009421311318874359, -0.02087227813899517, 0.000489339348860085, -0.021313263103365898, -0.008564935065805912, 0.02619303949177265, -0.03315875679254532, 0.020611636340618134, 0.01843034289777279, -0.033630672842264175, 0.055569253861904144, -0.002040733117610216, 0.023297801613807678, -0.010801170952618122, 0.02546052075922489, -0.02456279844045639, 0.0007156895590014756, 0.031965773552656174, -0.03116515837609768, -0.042564500123262405, 0.046131376177072525, -0.017118118703365326, -0.010552460327744484, 0.015644507482647896, 0.0035752123221755028, -0.026280105113983154, -0.014211587607860565, -0.019313188269734383, -0.0037186481058597565, 0.06095128506422043, -0.003244130639359355, 0.022719884291291237, -0.027054835110902786, 0.016756970435380936, -0.015868932008743286, -0.001353563624434173, 0.0836528018116951, 0.03279545158147812, -0.019136345013976097, 0.058177728205919266, -0.042837899178266525, 0.05545070767402649, -0.03421724587678909, 0.01933608017861843, -0.005107389762997627, -0.04466431215405464, 0.06631852686405182, -0.025975732132792473, -0.05653301253914833, 0.03791303187608719, 0.04850068688392639, 0.029016725718975067, 0.01132990512996912, 0.03319944441318512, -0.026047827675938606, 0.009433936327695847, -0.10808361321687698, -0.04203357174992561, 0.016197076067328453, -0.02635500766336918, -0.032033082097768784, 0.02998228557407856, -0.01778888702392578, 0.0017016546335071325, 0.028239212930202484, -0.002774385502561927, 0.03760140761733055, 0.005832558497786522, -0.03148077428340912, -0.006736582610756159, -0.012770138680934906, 0.007053264882415533, 0.040665071457624435, 0.02128847874701023, -0.0019424634519964457, 0.033335328102111816, 0.016280479729175568, 0.06817769259214401, 0.007131571415811777, -0.017537198960781097, 0.03846000134944916, 0.03759422525763512, 0.01841709576547146, -0.0356442891061306, -0.03164702281355858, 0.008767879568040371, 0.03885716572403908, 0.00770826218649745, -0.08172731846570969, -0.015244515612721443, -0.01942208968102932, -0.041534457355737686, 0.06889589130878448, -0.03606048598885536, -0.055682454258203506, -0.016049867495894432, -0.009416547603905201, -0.00439914595335722, -0.09002784639596939, 0.012396857142448425, -0.019746504724025726, -0.027636108919978142, -0.016323981806635857, 0.0455826036632061, 0.07581854611635208, 0.06500422954559326, -0.08221971988677979, -0.01138978824019432, -0.0501091443002224, -0.03858911991119385, 0.011965524405241013, 0.030074002221226692, 0.013337448239326477, 0.006543576251715422, 0.008016001433134079, 0.0007524713291786611, -0.02192930318415165, -0.04812780022621155, 0.027813807129859924, -0.0027286713011562824, 0.018271703273057938, -0.0030311427544802427, -0.02903718128800392, -0.0015289108268916607, -0.023089446127414703, -0.025012627243995667, 0.014478961937129498, -0.07769578695297241, 0.01671740971505642, 0.0057737333700060844, -0.003051357576623559, -0.00560759799554944, -0.04821794107556343, -0.008797665126621723, -0.011633661575615406, -0.02171485684812069, -0.02216613106429577, -0.022194039076566696, 0.06623049080371857, -0.016089530661702156, 0.013145995326340199, -0.041227322071790695, -0.024177225306630135, 0.0016999520594254136, -0.032909832894802094, 0.0016169820446521044, -0.003768538823351264, 0.04508782550692558, -0.033228594809770584, 0.020580386742949486, 0.0441543310880661, 0.004572748206555843, 0.06996335834264755, 0.03638799116015434, 0.016741827130317688, -0.026615850627422333, -0.025571297854185104, 0.05267304554581642, -0.006490781437605619, -0.02665378339588642, -0.015057199634611607, 0.01936129480600357, 0.030694566667079926, -0.013220658525824547, 0.02186110056936741, 0.11251798272132874, -0.031479109078645706, -0.048695459961891174, -0.023272471502423286, -0.013531587086617947, -0.08593129366636276, -0.00676216185092926, 0.02038496918976307, 0.020279226824641228, 0.0002714587899390608, 0.03838483989238739, 0.0504484698176384, -0.024457231163978577, -0.03677007555961609, -0.044709403067827225, 0.06781376898288727, 0.00714140385389328, -0.04370763525366783, 0.0130342161282897, 0.03434870019555092, 0.024182835593819618, -0.013423332944512367, -0.05147264525294304, 0.026330171152949333, -0.01687653735280037, -0.018971886485815048, -0.036159250885248184, -0.0060515981167554855, -0.017723117023706436, -0.06420265883207321, -0.0732843428850174, 0.015908854082226753, 0.009327063336968422, -0.0906360000371933, -0.04451179876923561, -0.004550641868263483, -0.006870598532259464, 0.012245089747011662, -0.013742591254413128, 0.017341282218694687, 0.02100391313433647, -0.0637734979391098, -0.07938717305660248, -0.08707428723573685, -0.007976518012583256, -0.00673661706969142, 0.020227430388331413, 0.018714388832449913, 0.01775950752198696, 0.023638306185603142, -0.0008070232579484582, -0.021989256143569946, 0.0036496692337095737, -0.06081543490290642, 0.03503327816724777, -0.0014421207597479224, 0.021146059036254883, -0.009159592911601067, 0.0006606779643334448, -0.02367607317864895, 0.004848803393542767, -0.02265516296029091, 0.07887812703847885, 0.04936815798282623, 0.005833761766552925, 0.06881847232580185, -0.043933235108852386, -0.0015290266601368785, 0.006497387774288654, -0.05718216300010681, -0.015430336818099022, 0.06006666645407677, -0.05334075540304184, 0.002316845115274191, 0.009978213347494602, 0.008785041980445385, -0.0439680777490139, 0.030872929841279984, 0.012069694697856903, 0.040048304945230484, -0.025858964771032333, -0.015538308769464493, -0.01766994036734104, -0.03200381621718407, -0.02653902769088745, 0.007338049355894327, 0.0008114208467304707, 0.013977636583149433, 0.046769965440034866, -0.0035220375284552574, 0.0023515524808317423, -0.017021043226122856, 0.004387345630675554, -0.01600157469511032, -0.018378470093011856, 0.0438850000500679, -0.04428091645240784, -0.08592691272497177, 0.014953317120671272, -0.1080874651670456, -0.007089343387633562, 0.034404970705509186, 0.057936862111091614, 0.05722177028656006, -0.0072381929494440556, 0.02905932255089283, -0.010747361928224564, 0.05404757708311081, 0.010177792981266975, -0.016685007140040398, 0.029864873737096786, 0.02155950665473938, 0.04219290241599083, 0.05665886774659157, -0.0040565114468336105, 0.01705101877450943, -0.05773879587650299, -0.018788766115903854, 0.02751598320901394, -0.016237333416938782, 0.025023002177476883, -5.9302132468969565e-33, -0.03134381026029587, -0.06023892015218735, -0.025918958708643913, -0.008858457207679749, 0.025857415050268173, -0.04818293824791908, 0.005422884598374367, -0.004407195840030909, 0.008301358669996262, 0.011078521609306335, -0.0074222758412361145, 0.0037152902223169804, -0.00694286311045289, -0.05206195265054703, 0.0004188245511613786, 0.07518492639064789, -0.05234449729323387, 0.013930575922131538, -0.00420185225084424, 0.015041995793581009, 0.047659121453762054, 0.020805062726140022, 0.04775014892220497, -0.046216391026973724, -0.024233555421233177, 0.015200086869299412, -0.001278710551559925, -0.006387392524629831, 0.0022557605989277363, -0.027406394481658936, -0.003188548143953085, -0.014081872068345547, 0.01609249785542488, 0.03706538677215576, 0.008322887122631073, -0.057598624378442764, -0.007829752750694752, -0.06544788181781769, -0.030588621273636818, 0.02495666779577732, 0.07198916375637054, 0.01555169839411974, -0.001520856167189777, -0.0006326209404505789, -0.03583476319909096, 0.019133232533931732, 0.09714674204587936, -0.00320706469938159, -0.062077898532152176, 0.016327176243066788, -0.035826411098241806, 0.06685830652713776, -0.029436521232128143, 0.07286283373832703, -0.012705270200967789, -0.007290160283446312, -0.010167831555008888, 0.060791779309511185, -0.062484730035066605, 0.014125334098935127, -0.006341665517538786, 0.04991800710558891, -0.029749590903520584, -0.03621930629014969, 0.01980357989668846, 0.04870549589395523, -0.03029659017920494, -0.009476527571678162, -0.046861276030540466, 0.05199015513062477, 0.039445921778678894, 0.024613790214061737, 0.026512829586863518, 0.041215889155864716, 0.0050135767087340355, -0.07680758088827133, 0.0029234406538307667, 0.12757350504398346, 0.012195681221783161, -0.016024919226765633, -0.008989935740828514, 0.01419768389314413, -0.062575563788414, -0.06552474945783615, 0.03549225255846977, -0.011215580627322197, -0.0111392168328166, 0.018895551562309265, -0.056423068046569824, -0.01321556605398655, -0.04408681392669678, -0.025569528341293335, -0.04644317552447319, 0.002603774657472968, -0.0012351295445114374, -0.02190563455224037, -0.04004450887441635, 0.061040546745061874, -0.02572925016283989, -0.0043833511881530285, -0.04032960534095764, -0.026934970170259476, 0.0015770505415275693, 0.0033705104142427444, -0.014608087949454784, 0.0033462517894804478, -0.02107914164662361, -0.02495170570909977, -0.023242153227329254, 0.003305724821984768, 0.06883183866739273, -0.02898811735212803, 0.01690085232257843, -0.046415455639362335, -0.06724214553833008, -0.02817225083708763, 0.02350129932165146, 0.03064626455307007, 0.04044817388057709, 0.0032754724379628897, -0.00498983496800065, -0.022523824125528336, -0.008058540523052216, -0.008851616643369198, -0.014984403736889362, -0.003509029047563672, -0.02787192352116108, -0.003557689720764756, 0.07193604111671448, -0.02762529067695141, -0.006354036275297403, -0.017686963081359863, 2.712640423396806e-07, 0.04861266911029816, 0.022883107885718346, -0.01818411983549595, -0.03768095001578331, 0.006397693883627653, 0.04935968294739723, -0.0400003120303154, 0.008998166769742966, -0.013900311663746834, 0.09021533280611038, 0.027758408337831497, -0.01776409149169922, 0.009291408583521843, 0.06527739763259888, -0.0239444337785244, -0.036086566746234894, -0.036949340254068375, -0.07206358760595322, -0.035823456943035126, 0.0014393999008461833, -0.04661136865615845, 0.011773056350648403, 0.03641245886683464, -0.005686504766345024, 0.008227086625993252, -0.0493200458586216, 0.005209887865930796, 0.030369939282536507, 0.02617599442601204, 0.05260780453681946, 0.0135209821164608, -0.041566986590623856, -0.008799942210316658, 9.765863069333136e-06, -0.00595264695584774, 0.024960719048976898, 0.007992742583155632, 0.005749912466853857, -0.03519575670361519, 0.0409419909119606, 0.06635307520627975, -0.03673848882317543, -0.006626971997320652, -0.06191050261259079, 0.02614837884902954, 0.03908296674489975, -0.020846571773290634, 0.014129131101071835, 0.00457112118601799, -0.043651606887578964, -0.0004010728152934462, 0.01011470053344965, -0.06126336008310318, 0.050397973507642746, 0.004504815209656954, -9.063967445399612e-05, 0.00188383087515831, -0.015741772949695587, 0.027630167081952095, -0.018743235617876053, -0.002302083419635892, -0.018736479803919792, 0.03327195346355438, 0.025950472801923752, 0.024905983358621597, 0.00892528798431158, 0.040599994361400604, 2.666844722476745e-34, 0.01627972349524498, 0.016671473160386086, -0.07632031291723251, 0.003186141373589635, 0.02845056913793087, -0.017598602920770645, 0.0060224952176213264, 0.023196090012788773, 0.015474800951778889, -0.03415968641638756, 0.008075162768363953]

['Radim Belohlavek', 'Martin Trnecka']

1306.4905v1

We present new results on Boolean matrix factorization and a new algorithm based on these results. The results emphasize the significance of factorizations that provide from-below approximations of the input matrix. While the previously proposed algorithms do not consider the possibly different significance of different matrix entries, our results help measure such significance and suggest where to focus when computing factors. An experimental evaluation of the new algorithm on both synthetic and real data demonstrates its good performance in terms of good coverage by the first k factors as well as a small number of factors needed for exact decomposition and indicates that the algorithm outperforms the available ones in these terms. We also propose future research topics.

From-Below Approximations in Boolean Matrix Factorization: Geometry and New Algorithm

http://arxiv.org/pdf/1306.4905v1

Title FromBelow Approximations Boolean Matrix Factorization Geometry New Algorithm Summary present new result Boolean matrix factorization new algorithm based result result emphasize significance factorization provide frombelow approximation input matrix previously proposed algorithm consider possibly different significance different matrix entry result help measure significance suggest focus computing factor experimental evaluation new algorithm synthetic real data demonstrates good performance term good coverage first k factor well small number factor needed exact decomposition indicates algorithm outperforms available one term also propose future research topic Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.048890747129917145, -0.017493918538093567, -0.04875136911869049, 0.024611975997686386, -0.025318244472146034, -0.011500393971800804, 0.06071304529905319, 0.011198578402400017, -0.023797348141670227, 0.014743614941835403, 0.061896804720163345, 0.06311383843421936, 0.05349346995353699, 0.08246349543333054, -0.025831207633018494, 0.027798274531960487, -0.0030492546502500772, 0.006810981780290604, -0.05421099811792374, 0.011352572590112686, -0.01702699437737465, -0.009630371816456318, -0.03248671069741249, 0.01127463486045599, -0.07338918000459671, -0.0049009439535439014, -0.049079976975917816, -0.04576743394136429, 0.016317106783390045, -0.008849930949509144, -0.00610453262925148, 0.061981480568647385, -0.05708247050642967, -0.006738371215760708, 2.4032881356106373e-06, -0.04033335670828819, -0.02956719882786274, -0.0005975783569738269, 0.07342857122421265, 0.09260626137256622, 0.03095407225191593, 0.04372212290763855, -0.03406018763780594, -0.06456924974918365, -0.036336734890937805, -0.04851069673895836, -0.008700814098119736, 0.06582894921302795, -0.001423054258339107, -0.016637828201055527, 0.006843858398497105, 0.057295072823762894, -0.0027509997598826885, 0.03332800418138504, 0.00388688244856894, 0.0021034444216638803, 0.0034736916422843933, 0.002921638311818242, -0.04654773324728012, 0.018093876540660858, -0.034855492413043976, 0.04517155885696411, -0.01905115507543087, 0.023732667788863182, 0.04003263637423515, 0.015214405953884125, 0.013875428587198257, 0.015841305255889893, 0.01777178980410099, 0.05211791396141052, -0.014892357401549816, -0.008340849541127682, 0.02263110876083374, -0.02592974528670311, -0.005721099209040403, 0.05635519698262215, -0.00961760152131319, 0.00034441068419255316, -0.03232685104012489, -0.0220272708684206, -0.0041308351792395115, 0.033066485077142715, -0.03405230492353439, -0.020569797605276108, -0.0065907882526516914, 0.08712739497423172, 0.031369056552648544, 0.012797405011951923, -0.0577504001557827, -0.04828643426299095, 0.03651737794280052, -0.034830491989851, 0.0652809739112854, -0.018118413165211678, -0.004017798695713282, -0.07250373810529709, 0.0679868832230568, 0.019999416545033455, 0.0664392039179802, -0.046609412878751755, 0.02156636118888855, -0.02068435028195381, 0.027328629046678543, 0.03919464722275734, -0.03788359835743904, -0.01640680991113186, -0.019646162167191505, 0.05400016903877258, -0.04160529375076294, 0.06527663767337799, 0.019491806626319885, 0.034656327217817307, 0.020936133340001106, 0.03215216100215912, -0.003929543308913708, 0.019235488027334213, -0.014837002381682396, -0.020757844671607018, 0.0007804354536347091, -0.035211339592933655, 0.004230359103530645, 0.042255695909261703, 0.04862889647483826, -0.027008268982172012, 0.013646947219967842, -0.02611534669995308, -0.04359767213463783, 0.03386768326163292, -0.06304097175598145, 0.043323956429958344, 0.042748790234327316, -0.009362907148897648, 0.051424652338027954, -0.002124571008607745, 0.013522517867386341, -0.03738368675112724, 0.026248466223478317, -0.051348667591810226, -0.03224242478609085, 0.008219171315431595, -0.02331802248954773, -0.012144813314080238, -0.024348536506295204, -0.031377196311950684, 0.00748124485835433, -0.08931698650121689, -0.008915241807699203, 0.07023333758115768, 0.005267164204269648, -0.013687994331121445, 0.027813434600830078, 0.045206643640995026, 0.01618092507123947, -0.002112631918862462, 0.020162025466561317, 0.0130423279479146, 0.026865795254707336, -0.02231578342616558, 0.015885675325989723, 0.06466139853000641, -0.003363115480169654, -0.04519674554467201, -0.006622924469411373, -0.03154590725898743, -0.015890438109636307, -0.0229362603276968, -0.02114180102944374, -0.04564229026436806, -0.009041332639753819, -0.06456045806407928, -0.022033412009477615, -0.003555482253432274, 0.010875716805458069, 0.053241949528455734, 0.03305204585194588, 0.012325122021138668, 0.004692530259490013, 0.13016583025455475, -0.04336634278297424, 0.01652825064957142, 0.00031632932950742543, -0.04815234616398811, 0.053533848375082016, 0.037210237234830856, -0.050812967121601105, -0.02780594304203987, -0.005176502745598555, 0.030786709859967232, -0.007784485351294279, -0.04914030805230141, 0.03957318514585495, -0.034798260778188705, 0.030327413231134415, -0.0428437665104866, 0.03118646889925003, -0.01602134294807911, -0.02919061854481697, -0.05012570321559906, 0.04859469085931778, -0.0340091735124588, -0.03852466121315956, -0.005330701824277639, 0.0785985216498375, -0.10338582843542099, 0.005213657859712839, -0.051344260573387146, -0.007006749510765076, 0.010249067097902298, 0.007809063885360956, -0.08444195240736008, -0.009753837250173092, -0.026140296831727028, -0.0012394397053867579, -0.011358588933944702, 0.04269450530409813, 0.040787696838378906, 0.06897025555372238, -0.004633807577192783, -0.017157183960080147, 0.03406519442796707, 0.018125098198652267, 0.02460482344031334, 0.03197348117828369, -0.011259120889008045, 0.04042244330048561, 0.044836025685071945, 0.057848453521728516, 0.05565507709980011, 0.011132447980344296, 0.042414627969264984, 0.08479767292737961, -0.039590686559677124, 0.06208934634923935, -0.03415593132376671, -0.01671450212597847, -0.03329737111926079, 0.027825098484754562, -0.03250609338283539, 0.04724184051156044, -0.03954608365893364, -0.004234747961163521, 0.03305117040872574, -0.008612935431301594, 0.003917279653251171, 0.03415733203291893, -0.024502908810973167, -0.028093494474887848, -0.04338643699884415, 0.01400890201330185, -0.039209406822919846, -0.021209143102169037, -0.009361086413264275, 0.013907579705119133, -0.028727617114782333, 0.033340733498334885, -0.05611791834235191, -0.0664505660533905, 0.046751998364925385, 0.002032259711995721, 0.021558478474617004, -0.009307727217674255, -0.06237710639834404, -0.003450174583122134, -0.013340802863240242, 0.05004553124308586, 0.009525181725621223, 0.03457416966557503, -0.0025119632482528687, 0.010362989269196987, 0.011610928922891617, -0.03535265102982521, 0.03359499201178551, -0.021991536021232605, 0.04606739804148674, 0.0055935075506567955, 0.014173065312206745, 0.007605920545756817, 0.016038885340094566, -0.068595290184021, 0.03292958438396454, -0.02246754802763462, -0.04109872877597809, -0.026874931529164314, -0.03251156210899353, -0.04898478835821152, 0.010184718295931816, 0.03968195617198944, -0.022259637713432312, -0.005366174504160881, 0.06467253714799881, -0.012503104284405708, -0.04126704856753349, -0.010678140446543694, -0.057818152010440826, -0.016923164948821068, -0.0441330187022686, 0.012082424946129322, 0.041755836457014084, 0.03369586542248726, -0.034304048866033554, 0.035801127552986145, 0.007902092300355434, -0.0014898459194228053, 0.04575926065444946, -0.03992611914873123, 0.018613774329423904, 0.058565620332956314, -0.10285694152116776, 0.0315861850976944, -0.08163179457187653, 0.014123988337814808, 0.0004869008844252676, -0.010137591511011124, -0.009088989347219467, 0.005155302118510008, 0.007497909013181925, -0.06878282874822617, 0.027733461931347847, -0.027325548231601715, 0.05100709944963455, 0.016288217157125473, 0.03648542985320091, -0.01040572114288807, 0.004805286414921284, 0.008507872931659222, -0.016360986977815628, 0.0019225393189117312, 0.014796578325331211, -0.06911934912204742, -0.01555667445063591, 0.04066913202404976, -0.06995134055614471, -0.005828092340379953, 0.05627044290304184, -0.034939322620630264, -0.008748368360102177, -0.06636982411146164, -0.01155562698841095, 0.031029362231492996, -0.03537660092115402, 0.035099055618047714, -0.026098182424902916, -0.017192143946886063, 0.03690594434738159, 0.054414473474025726, -0.05288245901465416, -0.0021885570604354143, -0.007195969112217426, -0.005426026415079832, 0.020041605457663536, 0.009759013541042805, -0.0278096254914999, -0.02414892613887787, 0.013392387889325619, -0.014267642982304096, 0.06328817456960678, -0.026740754023194313, -0.006621639244258404, 0.016862759366631508, 0.0590352937579155, 0.005791583098471165, 0.03546809405088425, -0.04519816115498543, 0.06087109446525574, -0.05239313840866089, 0.01924082078039646, -0.019951989874243736, 0.02521662414073944, -0.006996705662459135, -0.00012374017387628555, -0.03698818013072014, 0.02702386863529682, 0.0006454145186580718, 0.012263278476893902, 0.04202067852020264, -0.042139068245887756, 0.009675798006355762, -0.020337052643299103, -0.07287539541721344, -0.0004517683119047433, 0.0072118681855499744, 0.02116730995476246, 0.03667815774679184, 0.017968596890568733, -0.042747318744659424, 0.026613811030983925, -0.028114281594753265, 0.03604978695511818, -0.07491649687290192, 0.013691253960132599, 0.006877637468278408, -0.01704021729528904, -0.12478072196245193, -0.08926358073949814, 0.010882711037993431, -0.05138840153813362, -0.08464167267084122, 0.028143344447016716, 0.014952016994357109, -0.03075955994427204, -0.020775655284523964, 0.007292536087334156, 0.03451937064528465, 0.027918895706534386, -0.036487042903900146, -0.023367928341031075, -0.08512410521507263, 0.05858784168958664, -0.025397440418601036, -0.08320492506027222, 0.0011365063255652785, 0.017160655930638313, -0.01902814395725727, -0.04164675623178482, 0.05928223580121994, 0.06719233840703964, 0.03467388078570366, -0.05542798712849617, 0.039071228355169296, -0.05066702887415886, -0.004602082073688507, 0.03413524106144905, 0.08404232561588287, 0.05346996709704399, 0.0446491464972496, -0.015989653766155243, 0.014972412027418613, -0.014426365494728088, -0.013589913956820965, -0.005032722372561693, -0.014894125983119011, -0.05231215059757233, 0.00602002814412117, 0.009739239700138569, -0.024831358343362808, -0.03848739340901375, 0.019049180671572685, -0.004438913427293301, -0.030126890167593956, -0.05961399897933006, 0.05277613177895546, 0.02882913313806057, 0.054174914956092834, -0.023510601371526718, -0.03117540292441845, -0.022332698106765747, -0.03608514741063118, 0.013256103731691837, -0.02577100321650505, 0.03729240968823433, 0.04589713364839554, 0.029010161757469177, 0.09439582377672195, -0.007010152563452721, -0.029558464884757996, -0.01575053110718727, -0.04065544530749321, -0.01752564311027527, 0.0010911842109635472, 0.009029887616634369, 0.09643235057592392, 0.00485513499006629, -0.07700791954994202, -0.038408733904361725, 0.024263747036457062, 0.019685912877321243, -0.01025409996509552, -0.011794238351285458, 0.034597884863615036, -0.005541473161429167, -0.014162051491439342, 0.001696817809715867, -0.006660074926912785, 0.04157159477472305, 0.014950062148272991, -0.013143478892743587, -0.017963901162147522, -0.04813025891780853, 0.014905460178852081, 0.024709168821573257, 0.015413746237754822, 0.036577824503183365, 0.06989507377147675, 0.004541229456663132, -0.03592667356133461, 0.03712954372167587, -0.0056731742806732655, -0.019349511712789536, 0.014810921624302864, 0.02606325037777424, 0.008516713976860046, -0.030752239748835564, -0.06256350874900818, -0.052127350121736526, -0.007447217591106892, 0.009311710484325886, 0.011591540649533272, -0.0033099916763603687, 0.015177656896412373, 0.0056443046778440475, 0.023778138682246208, 0.013020431622862816, 0.006227802950888872, -0.025483379140496254, 0.01660025492310524, 0.01988474279642105, 0.010111963376402855, -0.05084429681301117, -0.034339070320129395, -0.0091624790802598, -0.08947863429784775, 0.012805725447833538, 0.03023647330701351, 0.022626303136348724, -0.043617796152830124, 0.01763191446661949, 0.023144394159317017, 0.00716462591663003, 0.0035429915878921747, -0.0012404167791828513, -0.03513734042644501, -0.03043118305504322, 0.031772125512361526, -0.013882745057344437, 0.03195127844810486, 0.021434692665934563, 0.011754023842513561, -0.0181077029556036, -0.004830566234886646, -0.004830681253224611, 0.022579483687877655, -0.029872208833694458, -0.035410769283771515, -0.03916972503066063, -0.05024854838848114, 0.064872607588768, -0.01861550286412239, 0.11254951357841492, -0.058624882251024246, -0.05136830732226372, -0.04074694588780403, -0.0313088558614254, -0.02387876808643341, 0.02973058819770813, 0.03438043221831322, 0.02751532942056656, -0.023550409823656082, -0.026214148849248886, 0.02691073715686798, -0.025323836132884026, 0.007403744850307703, -0.021988557651638985, -0.03736729547381401, -0.019127700477838516, -0.05501759424805641, -5.905656802566294e-33, 0.0021643645595759153, -0.01025144662708044, -0.05511503666639328, 0.0071565075777471066, -0.015883514657616615, 0.026231693103909492, -0.003161140251904726, 0.04090464860200882, 0.032367605715990067, -0.013227762654423714, -0.046988051384687424, -0.01722957193851471, -0.0030979285947978497, -0.025565514340996742, 0.004971414804458618, 0.026409270241856575, -0.012851396575570107, 0.023125531151890755, -0.010750840418040752, -0.003266894491389394, -0.00730489008128643, 0.012952091172337532, -0.014977822080254555, -0.02780728228390217, -0.06292872130870819, 0.003430089447647333, -0.04202356934547424, -0.0178381260484457, -0.11402540653944016, 0.020660901442170143, -0.01111892331391573, 0.004479854833334684, 0.030401239171624184, 0.03761998936533928, 0.011021859012544155, -0.06108396500349045, -0.036721933633089066, -0.025085145607590675, 0.004129329696297646, 0.041427694261074066, -0.03233930468559265, 0.012917743995785713, 0.0036071166396141052, 0.02177565172314644, -0.03878648206591606, -0.0075201597064733505, 0.03150108829140663, -0.017157262191176414, -0.009529183618724346, -0.010599331930279732, 0.024982867762446404, -0.01034021656960249, -0.03680836409330368, -0.004194885026663542, 0.04217703267931938, -0.019182292744517326, -0.06060772389173508, 0.005110447760671377, 0.032382797449827194, 0.029205631464719772, 0.05655912682414055, 0.010049191303551197, 0.0016565646510571241, -0.02956232987344265, 0.0030210823751986027, 0.010663633234798908, 0.012468847446143627, -0.023600295186042786, -0.01864481158554554, -0.051918208599090576, 0.009222090244293213, 0.06247209757566452, 0.007153145503252745, 0.04110858961939812, 0.10555468499660492, -0.048506978899240494, -0.05492940545082092, 0.04651261493563652, -0.07045426964759827, 0.013666299171745777, -0.025161901488900185, -0.007947717793285847, 0.031034469604492188, 0.010290546342730522, 0.002942141145467758, 0.01741611585021019, -0.027148695662617683, 0.0052262176759541035, -0.005668963771313429, 0.018497919663786888, -0.07670002430677414, -0.029884738847613335, -0.028102247044444084, -0.007405484095215797, 0.07990551739931107, 0.006286380812525749, -0.020885473117232323, 0.040631409734487534, 0.006456502713263035, -0.03834057226777077, -0.03420171141624451, 0.012758752331137657, -0.030392376706004143, -0.07841044664382935, -0.019356725737452507, -0.002294522477313876, -0.01657581329345703, -0.010871360078454018, -0.030971650034189224, -0.004217273090034723, 0.04591070115566254, -0.06020065024495125, 0.03781067207455635, -0.005037139635533094, 0.0014331189449876547, -0.03664563223719597, 0.0032077215146273375, 0.02277802862226963, 0.024052632972598076, 0.025328755378723145, -0.019919216632843018, -0.01420578919351101, -0.02955629862844944, 0.0030626943334937096, -0.01000144425779581, -0.030916359275579453, -0.02657395415008068, -0.038057196885347366, 0.03961915150284767, -0.018562838435173035, -0.02597593516111374, 0.0026933865156024694, 2.91119789608274e-07, 0.0016377430874854326, 0.03988943248987198, -0.017673008143901825, 0.024547772482037544, -0.004266414791345596, 0.007664418313652277, -0.017179986461997032, 0.028535787016153336, 0.005115277599543333, 0.008488818071782589, 0.031933724880218506, 0.008350368589162827, -0.009824302978813648, 0.0038436190225183964, 0.0005187226925045252, 0.05437004938721657, 0.05311098322272301, -0.0069895414635539055, -0.04746547341346741, 0.0114904111251235, 0.01213458739221096, -0.018590033054351807, 0.06146177276968956, -0.007868236862123013, 0.04413357377052307, 0.01917426288127899, -0.009826775640249252, -0.004661028739064932, -0.008565411902964115, 0.03421254828572273, -0.01145817432552576, -0.07351001352071762, -0.022341977804899216, 0.026281069964170456, 0.030191659927368164, -0.002201829804107547, 0.02571079693734646, 0.04596501961350441, 0.050465185195207596, 0.01968751661479473, 0.02546655386686325, -0.011361061595380306, 0.03271012380719185, -0.009880761615931988, 0.05401062220335007, 0.051635030657052994, 0.0116234440356493, -0.03491348773241043, -0.01381484605371952, 0.0486377589404583, 0.06232753396034241, 0.010585257783532143, -0.0026608193293213844, 0.012569616548717022, -0.025699803605675697, 0.012343546375632286, 0.0533975325524807, 0.008529897779226303, 0.07521720230579376, 0.014812589623034, -0.014977047219872475, -0.03485677018761635, 0.07663299143314362, 0.04118732362985611, 0.06649512052536011, -0.008367573842406273, -0.008773604407906532, 3.263950623712609e-34, -0.032948341220617294, 0.048157770186662674, 0.043556537479162216, 0.020136835053563118, 0.014585253782570362, 0.01691633276641369, 0.004031436983495951, -0.03659561648964882, 0.005692314822226763, -0.02212238684296608, -0.0006841693539172411]

['Nir Ailon', 'Mehryar Mohri']

0710.2889v2

This paper describes an efficient reduction of the learning problem of ranking to binary classification. The reduction guarantees an average pairwise misranking regret of at most that of the binary classifier regret, improving a recent result of Balcan et al which only guarantees a factor of 2. Moreover, our reduction applies to a broader class of ranking loss functions, admits a simpler proof, and the expected running time complexity of our algorithm in terms of number of calls to a classifier or preference function is improved from $\Omega(n^2)$ to $O(n \log n)$. In addition, when the top $k$ ranked elements only are required ($k \ll n$), as in many applications in information extraction or search engines, the time complexity of our algorithm can be further reduced to $O(k \log k + n)$. Our reduction and algorithm are thus practical for realistic applications where the number of points to rank exceeds several thousands. Much of our results also extend beyond the bipartite case previously studied. Our rediction is a randomized one. To complement our result, we also derive lower bounds on any deterministic reduction from binary (preference) classification to ranking, implying that our use of a randomized reduction is essentially necessary for the guarantees we provide.

An efficient reduction of ranking to classification

http://arxiv.org/pdf/0710.2889v2

Title efficient reduction ranking classification Summary paper describes efficient reduction learning problem ranking binary classification reduction guarantee average pairwise misranking regret binary classifier regret improving recent result Balcan et al guarantee factor 2 Moreover reduction applies broader class ranking loss function admits simpler proof expected running time complexity algorithm term number call classifier preference function improved Omegan2 log n addition top k ranked element required k n many application information extraction search engine time complexity algorithm reduced Ok log k n reduction algorithm thus practical realistic application number point rank exceeds several thousand Much result also extend beyond bipartite case previously studied rediction randomized one complement result also derive lower bound deterministic reduction binary preference classification ranking implying use randomized reduction essentially necessary guarantee provide Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0024763764813542366, 0.030878223478794098, -0.01544097624719143, 0.027395382523536682, -0.005162136163562536, -0.013755304738879204, 0.0027574694249778986, 0.021947966888546944, 0.03966595232486725, -0.04275768995285034, -0.023283904418349266, 0.04110220819711685, -0.004983637016266584, 0.0005360005307011306, -0.043492574244737625, -0.030825648456811905, 0.015834011137485504, 0.01812080107629299, -0.006899459753185511, -0.0682699978351593, 0.004680444486439228, -0.01925775036215782, -0.003119748318567872, 0.008510634303092957, 0.05205655097961426, 0.010737081989645958, -0.0044386861845850945, -0.010590426623821259, 0.0031631062738597393, 0.00979568064212799, 0.05585777387022972, 0.07904583215713501, -0.02093268558382988, 0.006702335551381111, 2.4264127205242403e-06, -0.06257816404104233, -0.06764796376228333, -0.018174506723880768, -0.015325664542615414, -0.007660469505935907, -0.036205828189849854, 0.033379025757312775, 0.026288850232958794, 0.022107375785708427, -0.034126151353120804, -0.002048690803349018, 0.004844565875828266, 0.046018343418836594, 0.034466877579689026, -0.023703906685113907, 0.009315993636846542, -0.008175341412425041, -0.04913716018199921, -0.04310748353600502, 0.015413915738463402, -0.01713542640209198, 0.023088669404387474, -0.04603343456983566, -0.03484172001481056, -0.003199484432116151, -0.023390213027596474, -0.03434884920716286, -0.005382090341299772, 0.03335250914096832, 0.037079617381095886, 0.03267664462327957, -0.02646581456065178, 0.010331111028790474, -0.009398244321346283, 0.03406309336423874, -0.033442623913288116, -0.006851693615317345, -0.006190963089466095, 0.01578115113079548, -0.002135189948603511, -0.010872989892959595, -0.002005095826461911, 0.009713391773402691, -0.03266425058245659, 0.03640315681695938, -0.011299408972263336, 0.08045891672372818, -0.030070126056671143, 0.026111677289009094, -0.00920677836984396, 0.052112191915512085, -0.005395666696131229, -0.02238273434340954, 0.05026428401470184, 0.025010311976075172, -0.009430110454559326, -0.03585199639201164, 0.04723459109663963, -0.03176761418581009, -0.052930768579244614, -0.02434658445417881, 0.027973944321274757, 0.014561604708433151, 0.03788834810256958, -0.047947678714990616, 0.01456050667911768, -0.04360117390751839, 0.04708198830485344, 0.026088165119290352, -0.0010782591998577118, 0.029691485688090324, 0.04874219745397568, 0.01840859279036522, 0.005872940644621849, 0.051194291561841965, -0.01140707079321146, 0.022277599200606346, 0.011150779202580452, 0.10133867710828781, -0.007997644133865833, 0.028658894822001457, -0.08063579350709915, -0.03598589822649956, -0.050482429563999176, 0.01473255455493927, 0.03409957513213158, 0.03548401594161987, -0.003701457753777504, 0.02461288869380951, -0.039205074310302734, -0.016111284494400024, 0.00951659306883812, 0.0399036630988121, -0.07547923922538757, 0.01907992549240589, 0.04963613674044609, 0.0051530203782022, 0.0059935166500508785, -0.006323742214590311, 0.019597847014665604, 0.03130978345870972, -0.018984386697411537, -0.006066786590963602, 0.004314837045967579, -0.0033694927114993334, 0.01955011487007141, 0.006452534347772598, -0.06872153282165527, -0.07005917280912399, 0.017506081610918045, -0.03473241627216339, 0.0006390243652276695, 0.03566592186689377, -0.003964757546782494, -0.007531930226832628, -0.05587701126933098, 0.04663495719432831, 0.005259510595351458, -0.0027207203675061464, 0.08475512266159058, 0.045576415956020355, 0.003367772325873375, 0.002562852343544364, -0.008464949205517769, 0.08091290295124054, 0.01430185791105032, -0.05112062394618988, -0.039978910237550735, 0.0010819261660799384, -0.0008892876212485135, -0.05885930359363556, 0.004123041406273842, 0.014379806816577911, -0.010564735159277916, -0.024135315790772438, 0.006209234707057476, 0.035176172852516174, -0.0053576636128127575, -0.04395758733153343, 0.014547046273946762, -0.0281407181173563, 0.03320141136646271, 0.04218690097332001, -0.06353826820850372, 0.03666272014379501, -0.034297551959753036, 0.0021685343235731125, -0.007430932018905878, 0.05276692658662796, -0.01946352981030941, -0.051115211099386215, 0.042999185621738434, -0.025880996137857437, -0.03381112590432167, -0.06102685257792473, 0.014311373233795166, 0.015488404780626297, -0.002396986121311784, 0.031178971752524376, 0.028943808749318123, -0.013881607912480831, -0.012589365243911743, -0.019483713433146477, 0.04534405469894409, 0.018009372055530548, -0.034931257367134094, -0.06180350482463837, -0.004979629069566727, 0.023421630263328552, -0.005204470828175545, -0.053073685616254807, 0.030505279079079628, 0.0009778989478945732, -0.030420741066336632, -0.10994237661361694, 0.025435034185647964, -0.04550431668758392, 0.03209182992577553, -0.012643232941627502, -0.014814116060733795, 0.05813974514603615, 0.021147560328245163, 0.021602552384138107, 0.01235437672585249, 0.016964105889201164, -0.015411817468702793, 0.039904456585645676, -0.013915743678808212, 0.0013669828185811639, 0.056918978691101074, 0.00440089451149106, 0.10230574756860733, 0.04066523164510727, 0.04674387723207474, -0.008972573094069958, 0.03156881406903267, -0.03962472453713417, 0.056586459279060364, -0.014730174094438553, -0.03093312494456768, -0.0352511927485466, 0.04228392615914345, -0.056133877485990524, -0.0010504275560379028, -0.01269350852817297, 0.015538059175014496, 0.1205725446343422, -0.03867436572909355, -0.013318900018930435, -0.02381318062543869, 0.000367878470569849, -0.013502408750355244, -0.02856609970331192, 0.0016889784019440413, 9.637312177801505e-05, -0.022890225052833557, -0.04012768715620041, 0.08492335677146912, -0.024350883439183235, 0.041059527546167374, 0.00012603394861798733, -0.11503604054450989, 0.015976816415786743, -0.05116821080446243, -0.006566050462424755, 0.006348549388349056, -0.041133373975753784, 0.026501497253775597, 0.009066475555300713, 0.02883174642920494, -0.006828726269304752, 0.00016675735241733491, -0.02846682071685791, 0.019957510754466057, 0.008754443377256393, 0.006542612798511982, 0.0016306452453136444, -0.01503998227417469, 0.05558335408568382, -0.04838906601071358, -0.03594905510544777, -0.018785428255796432, -0.014574801549315453, 0.009068243205547333, 0.028060374781489372, -0.0034784709569066763, -0.001561820157803595, -0.010740892961621284, -0.035958874970674515, 0.02989237755537033, 0.03331483155488968, 0.0031222342513501644, -0.024291621521115303, -0.006564856041222811, 0.047011151909828186, -0.029961861670017242, -0.003828642191365361, 0.0034324019216001034, 0.003621781477704644, -0.023997046053409576, -0.03154701739549637, -0.0325993187725544, 0.01922685094177723, 0.0679529532790184, 0.0644991472363472, 0.09072402864694595, 0.06939660012722015, -0.042945168912410736, 0.008654292672872543, -0.00934589747339487, 0.019410809502005577, 0.03990637883543968, -0.0021348875015974045, -0.015492436476051807, -0.00634969724342227, 0.02201111428439617, -0.01383993774652481, -0.0008812476880848408, -0.0039014245849102736, 0.01787327602505684, -0.040024079382419586, -0.12848946452140808, 0.027272485196590424, -0.004813272040337324, 0.015864359214901924, -0.0011896849609911442, -0.0052077448926866055, 0.015746047720313072, 0.05237075313925743, 0.020604699850082397, -0.04708027467131615, -0.04106885939836502, 0.027038468047976494, -0.0016239045653492212, 0.016705743968486786, 0.06182774901390076, -0.0828583836555481, 0.0024769878946244717, -0.039126262068748474, -0.014351514168083668, 0.051804713904857635, -0.07860223203897476, -0.019496716558933258, 0.0021748621948063374, -0.008229106664657593, -0.028171032667160034, -0.09348952025175095, -0.01956373080611229, -0.005834560841321945, 0.03613310679793358, -0.022733308374881744, 0.02562698721885681, 0.027209855616092682, -0.0007394008571282029, -0.005472708493471146, -0.027817314490675926, 0.023244570940732956, 0.01381006184965372, -0.03689231723546982, 0.07017248868942261, 0.05690480023622513, 0.013172981329262257, 0.006409750320017338, -0.03830335661768913, 0.015980148687958717, 0.027105866000056267, 0.0779239609837532, 0.00038038651109673083, 0.014137156307697296, -0.03294573724269867, 0.003211163217201829, 0.04406706988811493, -0.07233963906764984, -0.034983545541763306, -0.007955366745591164, -0.0450807623565197, -0.0025383708998560905, 0.06819967925548553, 0.054931823164224625, 0.05240160599350929, -0.07688262313604355, 0.005109503865242004, -0.002757064998149872, -0.007784730289131403, 0.002029701601713896, 0.021948406472802162, -0.06674027442932129, 0.011308392509818077, -0.020123109221458435, 0.00872365664690733, -0.00867551937699318, -0.04123822599649429, -0.0018492210656404495, -0.10437504947185516, 0.04116755723953247, -0.016856836155056953, -0.011995624750852585, -0.009377971291542053, -0.048982344567775726, 0.007361381780356169, -0.07508449256420135, -0.07921791821718216, 0.019047811627388, 0.023966312408447266, 0.012400074861943722, 0.03572211042046547, -0.058924075216054916, 0.013241362757980824, 0.04642122983932495, -0.03568371385335922, 0.005644875578582287, -0.027478616684675217, 0.06845391541719437, -0.037159182131290436, -0.019963538274168968, -0.0246792770922184, -0.014382398687303066, -0.03573169559240341, -0.041725751012563705, 0.04998287558555603, 0.010151304304599762, 0.030119411647319794, -0.021476753056049347, 0.022356266155838966, 0.05224844813346863, 0.050568029284477234, 0.04221787303686142, 0.06516827642917633, 0.002102863509207964, 0.012062303721904755, 0.015910420566797256, 0.00038840039633214474, 8.762955985730514e-05, 0.0196208693087101, -0.03384524583816528, -0.04071398824453354, -0.007079560309648514, -0.02979559823870659, 0.03414631634950638, 0.01166225504130125, -0.021760327741503716, 0.012327688746154308, -0.025023775175213814, -0.033852703869342804, -0.0532122477889061, 0.02668519876897335, 0.014827665872871876, 0.02126445434987545, -0.04627104476094246, 0.04052894562482834, -0.08177582919597626, 0.019830217584967613, -0.06026901304721832, -0.0780806764960289, 0.044353924691677094, 0.021338922902941704, -0.034410759806632996, -0.005499867722392082, 0.0008877636282704771, -0.036021143198013306, -0.054795436561107635, -0.08150473237037659, 0.047538675367832184, -0.021642928943037987, -0.027684232220053673, 0.07874631881713867, 0.022906003519892693, -0.011431724764406681, -0.013245971873402596, -0.021033288910984993, 0.015816176310181618, 0.0788930132985115, 0.02580651082098484, 0.005207891575992107, 0.026372458785772324, 0.003084306139498949, -0.04449213296175003, 0.043396856635808945, -0.02256469987332821, 0.06077566742897034, -0.017515383660793304, -0.048100732266902924, -0.055766794830560684, -0.0006529878592118621, 0.020338770002126694, 0.06685830652713776, 0.0657847449183464, 0.008995233103632927, -0.026518911123275757, -0.024212609976530075, 0.0714651569724083, 0.012320888228714466, -0.05124711990356445, 0.008656732738018036, 0.028548628091812134, 0.03965276479721069, 0.04934212937951088, -0.040378447622060776, -0.04871460422873497, 0.07307305186986923, -0.04233243316411972, -0.03888478875160217, 0.019463354721665382, -0.008571851067245007, 0.02405400760471821, 0.02039208635687828, 0.037615399807691574, -0.02989584393799305, -0.023997630923986435, 0.0938911885023117, 0.05870968475937843, -0.025750044733285904, -0.06290363520383835, 0.00697105098515749, 0.046989668160676956, -0.040621258318424225, 0.05085941404104233, 0.02181592956185341, -0.01653498411178589, -0.01244593970477581, 0.003070819890126586, 0.01268309447914362, -0.008507739752531052, -0.013027486391365528, 0.010204590857028961, -0.01229441910982132, -0.032906778156757355, 0.006196453236043453, -0.010284262709319592, -0.01663029193878174, 0.02762356773018837, 0.007105144672095776, 0.006027157884091139, 0.07133030146360397, 0.10026400536298752, 0.034840937703847885, -0.03890412673354149, -0.037210941314697266, -0.07856275886297226, -0.06666544824838638, 0.004370373673737049, -0.01218358427286148, 0.026139745488762856, 0.003614673623815179, -0.01316723134368658, -0.02139355055987835, 0.010892211459577084, -0.008819892071187496, -0.018018508329987526, 0.10159467905759811, -0.03244173526763916, 0.004794804845005274, 0.01948300190269947, 0.027046702802181244, 0.04263012483716011, -0.04962272197008133, -0.03920215368270874, -0.03883432224392891, -0.02673165686428547, -0.04868309199810028, -6.286732601977694e-33, -0.003412555670365691, -0.04478100687265396, -0.032168470323085785, 0.0013865206856280565, -0.03167666494846344, 0.022522687911987305, 0.03622480109333992, -0.03305401653051376, 0.025973577052354813, -0.0016883374191820621, 0.00425081979483366, -0.03261156007647514, 0.0028091645799577236, -0.02067536674439907, 0.03428150713443756, -0.007346668746322393, 0.02865838073194027, 0.0025789362844079733, -0.024218635633587837, 0.027002649381756783, 0.044073570519685745, 0.01480143889784813, -0.025952963158488274, -0.035748038440942764, -0.04800878092646599, 0.04008273780345917, -0.051867302507162094, 0.00807110033929348, -0.05425252765417099, 0.024979127570986748, 0.004456286784261465, 0.03371104970574379, 0.03136594220995903, -0.08668659627437592, 0.046667058020830154, -0.012108050286769867, -0.04690183326601982, -0.04043874889612198, -0.04915266111493111, 0.01721363328397274, 0.027004577219486237, 0.021565310657024384, 0.042197078466415405, 0.05417562648653984, -0.03403851389884949, -0.03131354600191116, 0.037770602852106094, -0.022574199363589287, -0.06187056750059128, -0.043570008128881454, 0.0323447659611702, -0.001800052123144269, -0.012061169371008873, 0.011516384780406952, 0.02055424638092518, 0.040030587464571, -0.03573458269238472, 0.012550062499940395, -0.03603552654385567, 0.03689127042889595, -0.012813454493880272, 0.08593397587537766, -0.035747136920690536, -0.02283823862671852, -0.01782429777085781, 0.026775604113936424, 0.01036899071186781, 0.0009704242111183703, 0.0441490039229393, 0.004510955885052681, -0.03428514674305916, 0.031512003391981125, 0.008082838729023933, 0.0270099975168705, 0.0784219428896904, -0.058952007442712784, -0.07039262354373932, 0.09089057147502899, 0.042968153953552246, -0.04217888414859772, -0.032320234924554825, 0.013920951634645462, -0.031407661736011505, -0.03525325655937195, 0.01842113584280014, -0.006727767176926136, -0.024322638288140297, -0.03413810580968857, 0.0110086714848876, 0.03828650340437889, -0.055964790284633636, -0.008059577085077763, -0.036454569548368454, -0.04192274436354637, -0.04545937851071358, -0.013814520090818405, -0.006390092894434929, 0.02258416637778282, 0.009050672873854637, -0.04102424904704094, -0.024030331522226334, 0.030158841982483864, -0.01852809078991413, -0.042855605483055115, 0.019858531653881073, 0.019257375970482826, 0.006951298099011183, 0.006473556160926819, -0.023884106427431107, 0.020755453035235405, 0.02118830569088459, -0.03920450434088707, -0.0053217653185129166, 0.05135653540492058, -0.03503064438700676, -0.031382039189338684, 0.016584429889917374, 0.03754297271370888, 0.019368784502148628, 0.03463781252503395, -0.03690071403980255, -0.017690079286694527, -0.005650447681546211, -0.009176237508654594, -0.01734490506350994, 0.031231513246893883, 0.005681962240487337, -0.008961250074207783, -0.011074897833168507, -0.007010326255112886, -0.0428428128361702, -0.046620383858680725, 2.9096344178469735e-07, 0.018990250304341316, -0.00452544866129756, -0.04920581728219986, -0.04679892584681511, 0.009368074126541615, 0.018236318603157997, -0.008073613047599792, 0.0650087222456932, 0.004982800222933292, 0.06174240633845329, 0.04664584621787071, -0.03138479217886925, 0.027380265295505524, 0.024734579026699066, -0.05685283616185188, -0.049383874982595444, -0.038338787853717804, -0.019482184201478958, -0.041963618248701096, -0.011567333713173866, 0.01620657928287983, 0.01935110241174698, 0.048862274736166, -0.031548380851745605, -0.023269889876246452, 0.055778782814741135, -0.009325751103460789, -0.04281286522746086, 0.017667658627033234, -0.044305380433797836, 0.056837089359760284, -0.018033239990472794, -0.04060745611786842, 0.006697531323879957, -0.04052112624049187, -0.017359187826514244, 0.02770041860640049, 0.028115512803196907, -0.010154320858418941, 0.034545984119176865, 0.042802900075912476, 0.009373657405376434, 0.0393020324409008, -0.01577513851225376, 0.06458911299705505, 0.02493647113442421, -0.014069335535168648, 0.010173068381845951, -0.011989422142505646, -0.01936471089720726, 0.06236441060900688, 0.030399512499570847, -0.030483759939670563, -0.005469072610139847, -0.028594987466931343, 0.002643764019012451, 0.023124944418668747, -0.021690165624022484, 0.029414571821689606, 0.033277202397584915, 0.006895744241774082, -0.042856790125370026, 0.05922870710492134, 0.03803139925003052, 0.013519804924726486, -0.04205687716603279, 0.005940768402069807, 2.9302172164321035e-34, 0.015155300498008728, 0.030507514253258705, 0.0018867041217163205, -0.009072737768292427, 0.00992912333458662, -0.03154812380671501, 0.007812160067260265, -0.02697906270623207, 0.03575306013226509, -0.019450198858976364, -0.026780270040035248]

['Dev Rajnarayan', 'David Wolpert']

0810.0877v1

In this paper, we examine the CE method in the broad context of Monte Carlo Optimization (MCO) and Parametric Learning (PL), a type of machine learning. A well-known overarching principle used to improve the performance of many PL algorithms is the bias-variance tradeoff. This tradeoff has been used to improve PL algorithms ranging from Monte Carlo estimation of integrals, to linear estimation, to general statistical estimation. Moreover, as described by, MCO is very closely related to PL. Owing to this similarity, the bias-variance tradeoff affects MCO performance, just as it does PL performance. In this article, we exploit the bias-variance tradeoff to enhance the performance of MCO algorithms. We use the technique of cross-validation, a technique based on the bias-variance tradeoff, to significantly improve the performance of the Cross Entropy (CE) method, which is an MCO algorithm. In previous work we have confirmed that other PL techniques improve the perfomance of other MCO algorithms. We conclude that the many techniques pioneered in PL could be investigated as ways to improve MCO algorithms in general, and the CE method in particular.

Bias-Variance Techniques for Monte Carlo Optimization: Cross-validation for the CE Method

http://arxiv.org/pdf/0810.0877v1

Title BiasVariance Techniques Monte Carlo Optimization Crossvalidation CE Method Summary paper examine CE method broad context Monte Carlo Optimization MCO Parametric Learning PL type machine learning wellknown overarching principle used improve performance many PL algorithm biasvariance tradeoff tradeoff used improve PL algorithm ranging Monte Carlo estimation integral linear estimation general statistical estimation Moreover described MCO closely related PL Owing similarity biasvariance tradeoff affect MCO performance PL performance article exploit biasvariance tradeoff enhance performance MCO algorithm use technique crossvalidation technique based biasvariance tradeoff significantly improve performance Cross Entropy CE method MCO algorithm previous work confirmed PL technique improve perfomance MCO algorithm conclude many technique pioneered PL could investigated way improve MCO algorithm general CE method particular Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0180228129029274, -0.0007563043036498129, -0.023768780753016472, -0.011033621616661549, 0.019885364919900894, -0.01915842480957508, 0.03705586493015289, 0.038528140634298325, 0.012448343448340893, 0.005005483981221914, 0.008443606086075306, 0.045210957527160645, 0.04688160866498947, -0.04519105702638626, 0.00812187884002924, -0.05941595509648323, -0.021399205550551414, 0.002429432701319456, 0.01110087800770998, -0.011416854336857796, 0.01919340342283249, -0.031949494034051895, 0.022900205105543137, 0.018936043605208397, -0.052935946732759476, 0.025809893384575844, 0.007346610073000193, -0.005924492608755827, 0.046120259910821915, -0.05914673954248428, 0.05429147928953171, 0.016940439119935036, -0.047234971076250076, 0.045198556035757065, 2.396306172158802e-06, -0.03422652184963226, -0.03818780928850174, 0.007928200997412205, 0.058502160012722015, 0.0029144573491066694, 0.07554956525564194, 0.009815463796257973, 0.004250382073223591, 0.02978624776005745, -0.0019909068942070007, -0.028580516576766968, 0.04731558635830879, 0.059084270149469376, 0.035565558820962906, 0.04379164054989815, -0.007575944531708956, -0.010988938622176647, 0.007107923738658428, -0.009786183014512062, 0.04172009602189064, -0.050921473652124405, 0.025978287681937218, 0.013836102560162544, -0.054181210696697235, -0.032462719827890396, -0.018289826810359955, 0.017127642408013344, 0.01603025756776333, 0.032375212758779526, -0.0090902429074049, 0.031826600432395935, 0.0032389601692557335, 0.029924483969807625, -0.03644658997654915, 0.04651283472776413, -0.09426441788673401, -0.010138357989490032, 0.02793043479323387, -0.032709043473005295, -0.046517275273799896, 0.034090131521224976, -0.01649654097855091, -0.006317819934338331, -0.023146890103816986, -0.021089015528559685, -0.04015854746103287, 0.07914988696575165, -0.004648993257433176, -0.005229491740465164, -0.0016925556119531393, 0.04205407574772835, -0.012202446348965168, -0.03388163819909096, 0.03472772240638733, -0.008876897394657135, -0.00547970412299037, -0.02145499177277088, -0.011344310827553272, -0.005009442567825317, -0.038742534816265106, -0.027624813839793205, 0.0037975877057760954, -0.040304895490407944, 0.04138350114226341, -0.043732017278671265, 0.03373439237475395, -0.021701257675886154, -0.0016965731047093868, -0.007645072415471077, -0.04748058319091797, -0.015616459771990776, -0.05916660279035568, -0.0011779528576880693, -0.042767852544784546, -0.006550382822751999, -0.03601421043276787, 0.013347938656806946, -0.0015380994882434607, 0.04965795576572418, 0.04973767697811127, 0.020724276080727577, -0.09149793535470963, 0.01579885184764862, 0.006083874963223934, -0.046095047146081924, 0.05310909077525139, 0.020265357568860054, 0.03903082385659218, 0.025889357551932335, -0.009037250652909279, 0.011177449487149715, -0.0502118282020092, 0.0545378178358078, -0.0619165375828743, -0.01893380656838417, 0.028587548062205315, 0.023936863988637924, -0.020574457943439484, -0.008685030974447727, 0.04151191934943199, 0.05912233889102936, 0.055094167590141296, 0.017133180052042007, -0.0706540122628212, -0.0020556985400617123, -0.005281479097902775, -0.05138980224728584, -0.0010663963621482253, -0.06019064038991928, -0.006248714867979288, -0.05560161918401718, -0.01108207181096077, 0.045566581189632416, 0.004490998573601246, -0.07599711418151855, -0.03865288943052292, 0.062008388340473175, -0.009937195107340813, -0.022185688838362694, 0.10847671329975128, -0.017416594550013542, 0.02577049843966961, 0.08367005735635757, 0.04442337155342102, 0.01158061157912016, 0.013879181817173958, -0.02495569922029972, 0.020731166005134583, -0.030173195526003838, -0.002075380878522992, -0.03790215775370598, -0.035264745354652405, -0.042553771287202835, 0.01087026298046112, 0.024189380928874016, 0.008897143416106701, -0.029974166303873062, -0.017373457551002502, -0.003952555824071169, 0.01793106459081173, -0.045260101556777954, 0.04556143283843994, -0.020292392000555992, 0.01868184469640255, -0.01837790012359619, -0.01159620564430952, -0.012970014475286007, 0.02770175039768219, 0.033113040030002594, -0.07250823825597763, -0.024373820051550865, 0.030514342710375786, -0.013363003730773926, -0.05590148642659187, -0.05059672147035599, 0.0006064670160412788, -0.016393965110182762, -0.05636010691523552, -0.03526533022522926, 0.055285658687353134, -0.024956146255135536, 0.005781648680567741, -0.0014790470013394952, 0.04599202796816826, -0.014390984550118446, -0.09362424165010452, -0.03818938881158829, 0.02384578250348568, -0.05023480951786041, -0.0225474052131176, -0.058151815086603165, 0.022349027916789055, -0.011895040050148964, -0.0010566498385742307, -0.08408874273300171, 0.03137927129864693, 0.02403123676776886, 0.043983425945043564, -0.04510611295700073, -0.02958032675087452, 0.05058199167251587, 0.014993054792284966, 0.027136217802762985, 0.012312117964029312, 0.06009220704436302, 0.0321149006485939, -0.029302021488547325, 0.010854504071176052, 0.00054478261154145, 0.0293243620544672, -0.016414256766438484, 0.07801435142755508, 0.03413597121834755, 0.030122581869363785, -0.0017956331139430404, 0.01907331310212612, -0.03399956598877907, 0.00030379596864804626, 0.0018377267988398671, -0.04792788252234459, 0.03504988178610802, 0.0011359596392139792, -0.03137025609612465, -0.00039670238038524985, -0.0421900600194931, 0.03112456016242504, -0.030029097571969032, -0.04314722493290901, -0.0421888567507267, 0.025140680372714996, -0.007946000434458256, -0.008014746941626072, -0.024630257859826088, 0.03582198917865753, -0.034084927290678024, 0.05860994756221771, -0.027625950053334236, 0.04518299922347069, 0.005794453900307417, 0.02090715989470482, -0.05475575849413872, -0.01382412388920784, 0.0507364347577095, -0.027490969747304916, 0.02051655203104019, -0.0037814422976225615, -0.00829401332885027, -0.004161214921623468, 0.019926927983760834, 0.028093703091144562, -0.002639597747474909, -0.02726171538233757, -0.06537950783967972, -0.003691854188218713, 0.007336914073675871, -0.034038931131362915, 0.011608791537582874, -0.0021157183218747377, -0.0020232312381267548, 0.02137376368045807, 0.025969551876187325, 0.04543139412999153, -0.03692805767059326, -0.03448969125747681, 0.031104613095521927, -0.02979256957769394, -0.002531129866838455, 0.0026504681445658207, -0.05947202444076538, -0.03030124120414257, 0.08272360265254974, 0.03556080907583237, -0.004097976256161928, -0.038263797760009766, 0.0033138198778033257, 0.0014767859829589725, -0.015186644159257412, 0.011550727300345898, -0.018216311931610107, -0.040412500500679016, -0.03352807089686394, -0.01958969049155712, 0.06996507197618484, 0.023149752989411354, -0.03517866134643555, 0.009175550192594528, 0.027987172827124596, -0.005355373956263065, 0.02743108756840229, 0.0005976606043986976, -0.016526635736227036, 0.07615157961845398, -0.02787131443619728, -0.009369056671857834, 0.02233373187482357, 0.03982741758227348, 0.023630116134881973, -0.012183118611574173, 0.03793436661362648, 0.03258274123072624, -0.015178310684859753, -0.025648821145296097, 0.02874964475631714, 0.004023625049740076, 0.0017872770549729466, 0.022240299731492996, -0.019982606172561646, 0.023185115307569504, -0.0015489030629396439, 0.03137855604290962, -0.009014206007122993, 0.0159599706530571, 0.027687398716807365, -0.0727066621184349, 0.016794180497527122, 0.044183988124132156, -0.011848355643451214, -0.03196828067302704, 0.010680143721401691, -0.020665911957621574, 0.052099619060754776, -0.03030109405517578, -0.08179096132516861, 0.030690887942910194, -0.020415693521499634, 0.010054784826934338, 0.04180075600743294, -0.028086191043257713, 0.026499412953853607, 0.03088783472776413, -0.050082504749298096, -0.03253083676099777, -0.004775242414325476, 0.02004948817193508, 0.017828859388828278, -0.013973331078886986, 0.045364461839199066, -0.026595888659358025, -0.03232191875576973, 0.01152610220015049, 0.04198242351412773, 0.00043988466495648026, -0.0672304630279541, -0.005940133240073919, 0.03155555948615074, 0.0396268256008625, -0.010547509416937828, 0.0506957471370697, 0.08243592828512192, -0.121735580265522, 0.029680119827389717, -0.04015754535794258, -0.019110267981886864, -0.0020403277594596148, 0.010510268621146679, -0.005186975467950106, -0.01024677138775587, 0.06044647470116615, 0.0701928362250328, -0.002022735308855772, -0.0791759192943573, -0.025835974141955376, -0.01372441090643406, -0.024277521297335625, -0.027046222239732742, 0.018915293738245964, -0.004541042726486921, -0.01406592596322298, -0.027181390672922134, 0.02769589051604271, -0.059951093047857285, -0.04366304352879524, 0.037686657160520554, -0.0745997354388237, 0.03866637125611305, -0.010728482156991959, -0.04770372807979584, -0.05672740936279297, -0.057546038180589676, -0.011726916767656803, -0.05112849920988083, -0.0029463565442711115, 0.009734265506267548, 0.023114753887057304, -0.02563657984137535, 0.029799925163388252, -0.06890006363391876, -0.03128063306212425, -0.012177868746221066, -0.09242327511310577, -0.023202812299132347, 0.01947537623345852, 0.05000472068786621, -0.04969251900911331, -0.013790305703878403, 0.04420369863510132, -0.040496814996004105, 0.006261675618588924, -0.05703981965780258, 0.10759975761175156, 0.024141138419508934, 0.011370192281901836, 0.026029793545603752, 0.06590775400400162, 0.0440596379339695, 0.042187441140413284, 0.023936225101351738, 0.04661102592945099, 0.015008783899247646, -0.024272259324789047, 0.003711945842951536, 0.020284857600927353, 0.03693407401442528, -0.015233186073601246, -0.006995222996920347, -0.02910332754254341, -0.06406685709953308, 0.0031585250981152058, 0.000855153426527977, 0.017434410750865936, 0.045084673911333084, -0.001972371246665716, 0.007126066368073225, -0.07883749902248383, -0.07660933583974838, 0.0056692203506827354, -0.009696297347545624, 0.0759376809000969, 0.007530092261731625, 0.03215120732784271, -0.017108911648392677, -0.004780617076903582, -0.03970571979880333, -0.043103575706481934, 0.049298666417598724, 0.03044227696955204, -0.0013293122174218297, 0.04642269387841225, 0.005970155820250511, -0.04042208939790726, -0.020220452919602394, -0.0438527874648571, -0.04004880040884018, -0.06055421754717827, -0.0030841201078146696, 0.08296087384223938, 0.0031085102818906307, 0.02604554407298565, -0.04131167009472847, -0.04331643506884575, 0.11600764095783234, 0.018698211759328842, 0.023741472512483597, 0.03643258661031723, 0.050547149032354355, 0.016153894364833832, 0.004410309251397848, -0.023510854691267014, 0.015057574957609177, 0.04246257618069649, 0.013543796725571156, -0.06526123732328415, -0.040924787521362305, -0.042910005897283554, -0.02963348850607872, 0.022086450830101967, 0.08761940896511078, 0.005886180326342583, 0.006707610096782446, -0.023458676412701607, 0.05030079931020737, 0.023350559175014496, 0.002117466414347291, 0.008617348037660122, -0.011830875650048256, 0.04672563821077347, 0.0188261978328228, -0.016836507245898247, -0.03297938033938408, 0.020132718607783318, -0.07127488404512405, 0.01905040442943573, 0.034342922270298004, -0.010684104636311531, 0.10980955511331558, -0.06384225934743881, -0.009634329006075859, 0.024829884991049767, -0.010694309137761593, 0.05568389967083931, 0.03509232774376869, 0.005054008215665817, 0.026832304894924164, -0.009359517134726048, 0.006886556278914213, -0.04103599116206169, 0.012396533973515034, -0.007286107633262873, -2.621702333271969e-05, -0.06199260428547859, 0.025935297831892967, 0.045132819563150406, -0.028468187898397446, 0.008880192413926125, -0.01291132066398859, 0.035735610872507095, -0.02437703125178814, 0.05005018040537834, -0.008175291121006012, 0.07098202407360077, 0.03828592598438263, -0.02662789076566696, -0.0326843187212944, 0.03426538035273552, 0.0028554447926580906, 0.0556936077773571, 0.029431521892547607, -0.07003387063741684, -0.014928200282156467, -0.029412178322672844, 0.037976767867803574, -0.00022952354629524052, -0.01111468207091093, -0.035384368151426315, 0.007462924346327782, -0.0003560077166184783, 0.028239497914910316, 0.03186456114053726, -0.016519630327820778, 0.07555589079856873, 0.014199960045516491, -0.014543878845870495, 0.02207198739051819, -0.06026540696620941, 0.005744160618633032, -0.03062780573964119, -0.06593909114599228, -0.0023592873476445675, 0.02218092978000641, -0.017322096973657608, -6.135948268177873e-33, -0.011022127233445644, -0.02735784277319908, -0.05750742554664612, 0.0017683841288089752, -0.027563979849219322, -0.02287544310092926, -0.02288808859884739, 0.02490818500518799, 0.029147636145353317, -0.03575762361288071, -0.0027820738032460213, 0.0029668353963643312, 0.016008315607905388, -0.01314114686101675, 0.026227915659546852, -0.014208645559847355, -0.019920647144317627, -0.016805499792099, 0.017956463620066643, -0.0067821079865098, 0.0031463750638067722, 0.032994452863931656, 0.019948801025748253, -0.04857189953327179, -0.033594198524951935, 0.059642381966114044, -0.046797800809144974, -0.01706605590879917, -0.022302377969026566, -0.00192936637904495, 0.040399786084890366, -0.004821253474801779, -0.026528730988502502, -0.019811667501926422, 0.00609637051820755, -0.012777409516274929, 0.015013939701020718, -0.054668791592121124, -0.053991951048374176, 0.04454214870929718, 0.013213271275162697, -0.027907950803637505, 0.066075399518013, 0.015495291911065578, -0.05849403887987137, -0.007237384561449289, 0.039370495826005936, 0.0008832748862914741, 0.00826865155249834, -0.03898568078875542, -0.011547855101525784, 0.0230953898280859, -0.012690207920968533, 0.038238171488046646, 0.031223230063915253, 0.016196832060813904, -0.023403389379382133, 0.03422393277287483, 0.003823032369837165, 0.027245745062828064, 0.032540593296289444, 0.047593843191862106, -0.007299602497369051, 0.03244718164205551, 0.07068042457103729, -0.010180147364735603, 0.03789471462368965, -0.06461678445339203, -0.012348506599664688, -0.0011596475960686803, 0.0049956482835114, 0.02759511210024357, 0.04053065553307533, 0.05457881838083267, 0.061824917793273926, -0.07876795530319214, -0.06255590170621872, 0.07817588746547699, 0.005079206544905901, 0.03523767739534378, -0.023993125185370445, -0.0537937693297863, -0.025539573282003403, 0.020964179188013077, -0.0058678328059613705, -0.09311819821596146, -0.018938127905130386, -0.003206647699698806, 0.004977561999112368, -0.019444597885012627, -0.036959458142519, -0.0015464723110198975, -0.0005991006619296968, -0.031265296041965485, 0.06126055493950844, 0.00418277271091938, -0.011065265163779259, 0.044018566608428955, 0.030508210882544518, -0.04624537378549576, -0.03350994363427162, -0.08537860214710236, 0.006326194852590561, 0.01389279030263424, 0.047124359756708145, -0.0018676248146221042, 0.0060514649376273155, -0.004896138794720173, -0.0153041435405612, 0.017408888787031174, 0.021167472004890442, -0.03350289911031723, 0.008737495169043541, 0.005211520474404097, -0.008131014183163643, -0.07211939990520477, -0.017719198018312454, 0.01675824075937271, 0.02598387748003006, -0.002010346855968237, -0.03767748922109604, -0.009507098235189915, 0.01525831501930952, 0.014500952325761318, -0.03541138768196106, 0.007903587073087692, 0.013322779908776283, -0.08488298207521439, -0.018189487978816032, -0.028411637991666794, -0.02324714884161949, -0.01363991666585207, 2.889530890115566e-07, -0.015778154134750366, 0.0320572555065155, -0.014987415634095669, -0.03730678930878639, -0.0004957304336130619, 0.02766447886824608, -0.02974066510796547, -0.02227696217596531, -0.040346659719944, -0.002480873605236411, 0.07843658328056335, -0.05300169438123703, 0.03843970224261284, 0.013233180157840252, -0.023091506212949753, -0.0420934334397316, 0.014423738233745098, 0.10366739332675934, -0.013056044466793537, 0.015640633180737495, 0.013708885759115219, 0.05392255261540413, 0.028238927945494652, -0.03271309286355972, 0.07261590659618378, 0.02631778083741665, 0.028261538594961166, 0.0020210188813507557, 0.06622208654880524, 0.00496158329769969, -0.004049205221235752, -0.00948221143335104, -0.0013574347831308842, 0.022411523386836052, -0.015940912067890167, 0.05452915281057358, 0.0193941593170166, 0.007788090500980616, -0.01350277941673994, 0.000920024118386209, 0.05343693494796753, 0.04935427010059357, 0.04130111634731293, -0.05786721408367157, 0.05137812718749046, 0.04362078756093979, -0.00775339687243104, -0.0752720907330513, -0.012242283672094345, 0.00834165420383215, 0.0878867655992508, -0.005392339546233416, 0.006752865854650736, -0.005500197410583496, -0.022639119997620583, -0.01554784830659628, 0.0278907660394907, -0.02102378010749817, -0.010814988985657692, 0.01375496108084917, -0.004847829230129719, -0.013697636313736439, 0.05060935392975807, 0.0018682919908314943, 0.09468703716993332, 0.005352908745408058, -0.02778884582221508, 2.7144887482947703e-34, -0.014173599891364574, -0.028863493353128433, -0.005488320253789425, -0.017661090940237045, -0.039768289774656296, 0.011245038360357285, -0.01214373204857111, -0.028871925547719002, -0.0021570592653006315, 0.00828592199832201, -0.006009883247315884]

['Omar Mehanna', 'Ahmed Sultan', 'Hesham El Gamal']

0810.1430v1

We consider the design of cognitive Medium Access Control (MAC) protocols enabling an unlicensed (secondary) transmitter-receiver pair to communicate over the idle periods of a set of licensed channels, i.e., the primary network. The objective is to maximize data throughput while maintaining the synchronization between secondary users and avoiding interference with licensed (primary) users. No statistical information about the primary traffic is assumed to be available a-priori to the secondary user. We investigate two distinct sensing scenarios. In the first, the secondary transmitter is capable of sensing all the primary channels, whereas it senses one channel only in the second scenario. In both cases, we propose MAC protocols that efficiently learn the statistics of the primary traffic online. Our simulation results demonstrate that the proposed blind protocols asymptotically achieve the throughput obtained when prior knowledge of primary traffic statistics is available.

Blind Cognitive MAC Protocols

http://arxiv.org/pdf/0810.1430v1

Title Blind Cognitive MAC Protocols Summary consider design cognitive Medium Access Control MAC protocol enabling unlicensed secondary transmitterreceiver pair communicate idle period set licensed channel ie primary network objective maximize data throughput maintaining synchronization secondary user avoiding interference licensed primary user statistical information primary traffic assumed available apriori secondary user investigate two distinct sensing scenario first secondary transmitter capable sensing primary channel whereas sens one channel second scenario case propose MAC protocol efficiently learn statistic primary traffic online simulation result demonstrate proposed blind protocol asymptotically achieve throughput obtained prior knowledge primary traffic statistic available Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04277150705456734, 0.011317020282149315, 0.009561115875840187, -0.048743076622486115, -0.05371557176113129, -0.022219672799110413, -0.02741030417382717, 0.0031638327054679394, 0.005328529514372349, -0.02505956031382084, -0.025606373324990273, 0.044697754085063934, -0.007434394210577011, 0.024592142552137375, -0.00812468770891428, 0.06602346152067184, 0.011789701879024506, -0.007249023765325546, 0.07609374076128006, 0.0032760812900960445, 0.009658492170274258, -0.022823691368103027, -0.046717569231987, -0.011314642615616322, 0.016006529331207275, -0.03424891084432602, -0.03513247147202492, 0.005623667500913143, -0.047893986105918884, -0.028705041855573654, 0.008270672522485256, 0.010269972495734692, 0.018454086035490036, 0.05696394667029381, 2.183365040764329e-06, -0.00101687281858176, 0.03142951428890228, -0.034787774085998535, 0.011277123354375362, -0.015017883852124214, -0.04358163848519325, 0.03523971140384674, 0.0016081276116892695, 0.020588651299476624, 0.01822473667562008, 0.041785452514886856, 0.014135187491774559, 0.05267322063446045, 0.013013044372200966, 0.015147141180932522, -0.023306287825107574, 0.04914334788918495, -0.00230196351185441, -0.030930520966649055, 0.03881499543786049, -0.014967421069741249, 0.04552347958087921, -0.012161312624812126, -0.03369633108377457, -0.06139479950070381, 0.015287770889699459, -0.011121019721031189, 0.02397039346396923, -0.03734832629561424, 0.03525089845061302, 0.0116886580362916, -0.04938008263707161, 0.0010336245177313685, -0.018762817606329918, 0.008747090585529804, 0.01847442425787449, -0.015592454932630062, 0.009448036551475525, 0.03600841760635376, -0.013754735700786114, 0.015955816954374313, -0.03813712298870087, 0.001142216264270246, -0.03375411406159401, 0.027718141674995422, -0.04180363565683365, 0.0405745804309845, -0.001849774387665093, 0.010066705755889416, -0.04835578426718712, 0.048706136643886566, -0.025865674018859863, -0.03342378884553909, 0.04080786556005478, -0.023491567000746727, -0.02799677476286888, 0.002269763732329011, -0.010795950889587402, 0.0243756752461195, -0.03736179322004318, -0.05844824016094208, -0.032565828412771225, -0.007105609402060509, -0.029704952612519264, -0.07632652670145035, 0.05474083870649338, -0.012415449135005474, -0.010886630043387413, 0.019812004640698433, -0.0012501953169703484, -0.05325091630220413, -0.050750721246004105, 0.03153127431869507, 0.008575855754315853, 0.0037542700301855803, 0.005286000669002533, -0.04028194025158882, -0.003922221250832081, 0.11966468393802643, -0.00912726391106844, -0.022328289225697517, -0.0647146925330162, 0.037989791482686996, -0.012597299180924892, -0.06649267673492432, -0.013259143568575382, -0.018462350592017174, -0.03892051428556442, 0.019580256193876266, -0.0060640862211585045, -0.005677098408341408, 0.046014443039894104, 0.0833967849612236, -0.010939854197204113, -0.04140041768550873, -0.005951724946498871, 0.02271542139351368, -0.028922656551003456, 0.006072338204830885, -0.0398324616253376, 0.06380762159824371, -0.03583722561597824, 0.022572221234440804, -0.05450703576207161, 0.0003163779038004577, 0.08228545635938644, -0.007705576252192259, -0.016307389363646507, -0.0025912246201187372, -0.050828274339437485, -0.02390446700155735, 0.002805266994982958, 0.02829742059111595, 0.014091392047703266, -0.00853060558438301, -0.0052189272828400135, 0.046571213752031326, -0.026346072554588318, -0.023186447098851204, 0.12065121531486511, 0.020483117550611496, -0.03915729373693466, 0.06804800778627396, 0.007673510350286961, -0.010310713201761246, 0.013762662187218666, 0.006080981809645891, 0.023676762357354164, -0.027151670306921005, 0.024437716230750084, -0.03467002138495445, -0.03760675713419914, -0.004542303271591663, 0.04669759422540665, -0.0012192822759971023, -0.01884113810956478, 0.029165711253881454, 0.02391231618821621, 0.044174548238515854, 0.015414959751069546, 0.00647073844447732, 0.07251573354005814, -0.07791917026042938, -0.024256540462374687, 0.04582357779145241, -0.007917412556707859, 0.02127917855978012, 0.01703549176454544, 0.04142506793141365, -0.06543387472629547, -0.05337801203131676, 0.023662174120545387, -0.031046856194734573, 0.0026454757899045944, -0.014209057204425335, 0.04180383309721947, -0.056926753371953964, -0.023285651579499245, 0.011382858268916607, -0.0028216526843607426, -0.04027054086327553, 0.07881322503089905, -0.00900101475417614, 0.04190096631646156, -0.023102261126041412, -0.060091424733400345, -0.02209186740219593, -0.015293690375983715, -0.06503669917583466, 0.03109251894056797, 0.03271668031811714, 0.04459245875477791, -0.016605153679847717, 0.012361723929643631, -0.02835381031036377, -0.04337793588638306, 0.006630559451878071, 0.007174422033131123, -0.01979350671172142, -0.0008067985181696713, 0.0398123525083065, -0.0028600781224668026, 0.005228921305388212, -0.09749043732881546, 0.065543033182621, -0.01786131039261818, 0.035137444734573364, -0.0004046967951580882, 0.01904628612101078, 0.036451052874326706, 0.010709891095757484, -0.01920485682785511, 0.007568657398223877, 0.041319988667964935, -0.01416548527777195, -0.004158968571573496, 0.03140593320131302, 0.0217409897595644, -0.033581528812646866, 0.01516047865152359, 0.043025221675634384, -0.058446746319532394, 0.02894766628742218, -0.019008338451385498, -0.023211093619465828, 0.08851619064807892, 0.06817851215600967, 0.04252365976572037, -0.048317451030015945, -0.018854422494769096, -0.0133208641782403, 0.013317513279616833, -0.025201942771673203, 0.030045567080378532, -0.01957371085882187, -0.003382825292646885, 0.02315405011177063, 0.025425486266613007, 0.016759701073169708, 0.007193808909505606, 0.026888102293014526, -0.031023606657981873, 0.05770908668637276, -0.017104987055063248, 0.06386755406856537, 0.023216594010591507, -0.016871251165866852, -0.03466690331697464, -0.03432958573102951, 0.017695695161819458, 0.03311244398355484, 0.005320812109857798, -0.031220335513353348, -0.01872694119811058, -0.03235308453440666, 0.003530217334628105, 0.028160709887742996, 0.013088580220937729, -0.003125913208350539, -0.03183548524975777, -0.049246907234191895, 0.06353773176670074, -0.03614293783903122, -0.02147398330271244, -0.016250107437372208, -0.027013590559363365, 0.016439693048596382, -0.003352600149810314, 0.0010329076321795583, 0.0006888300995342433, -0.016566447913646698, 0.0733274593949318, -0.06505792587995529, -0.021143345162272453, -0.007820244878530502, -0.009599373675882816, 0.03291650116443634, -0.042613107711076736, 0.03300514072179794, 0.027860401198267937, 0.01221590954810381, -0.035508718341588974, -0.026018651202321053, 0.03313058242201805, 0.027669766917824745, 0.013109169900417328, 0.0021660232450813055, -0.015449781902134418, -0.009245777502655983, 0.043515466153621674, 0.028983935713768005, -0.044023822993040085, 0.012710047885775566, 0.011704477481544018, 0.026547018438577652, -0.03747383877635002, 0.019714927300810814, -0.007192500866949558, -0.02453117072582245, 0.01024207565933466, -0.055930931121110916, -0.0956876203417778, -0.012903884053230286, -0.011200880631804466, -0.022411329671740532, 0.0192161425948143, 0.004174146801233292, 0.01444293837994337, 0.02335304766893387, -0.0053443992510437965, -0.01960526593029499, -0.03776096925139427, -0.0017129373736679554, 0.049114011228084564, 0.0012059599393978715, -0.014956245198845863, 0.020139850676059723, -0.04202800244092941, -0.026969043537974358, -0.0018655776511877775, 0.021429888904094696, -0.021750619634985924, -0.05965776741504669, -0.03237595781683922, 0.008544554933905602, -0.04060227423906326, 0.007865603081882, -0.02901315502822399, 0.0636257752776146, 0.027240920811891556, 0.0029526480939239264, 0.0021089676301926374, 0.029267949983477592, -0.005217333789914846, -0.00031555857276543975, 0.018307875841856003, 0.021975208073854446, -0.013922623358666897, -0.015658266842365265, -0.005015098489820957, 0.033855609595775604, 0.04718655347824097, 0.001799514633603394, -0.027721675112843513, 0.04571041837334633, 0.02635801210999489, 0.041824374347925186, -0.01142034400254488, 0.05213218182325363, 0.03940553590655327, 0.04974381625652313, 0.0005543332081288099, 0.010615312494337559, 0.015243396162986755, 0.00843770895153284, 0.0871153250336647, 0.004033446777611971, 0.04874860495328903, 0.045078523457050323, -0.02375122345983982, -0.13898275792598724, -0.057259347289800644, -0.030837638303637505, -0.07895392179489136, 0.03107515536248684, -0.012214855290949345, -0.059161193668842316, 0.011655345559120178, -0.02046406827867031, 0.05849196016788483, -0.01832924224436283, -0.03362683951854706, -0.026606569066643715, 0.0015298877842724323, -0.017166610807180405, -0.016703607514500618, 0.02718731202185154, 0.03782006725668907, -0.030137749388813972, -0.01001863181591034, -0.01292170025408268, 0.03359239548444748, -0.0016811356181278825, 0.01133185438811779, -0.010661612264811993, 0.01064329780638218, -0.005138800945132971, -0.03179854899644852, -0.010582424700260162, 0.0037503407802432775, 0.06911767274141312, -0.0478399395942688, 0.02766476385295391, 0.003303880337625742, -0.08101446181535721, 0.013369846157729626, -0.13057217001914978, -0.02643422782421112, -0.0006597712635993958, -0.06836467981338501, 0.01698579080402851, 0.0004597710503730923, -0.03100789710879326, 0.054798390716314316, 0.06780119240283966, 0.030527720227837563, 0.0053977989591658115, -0.039124995470047, -0.041895877569913864, -0.012646523304283619, -0.024964168667793274, 0.013636672869324684, 0.028711020946502686, 0.024822916835546494, 0.012575315311551094, 0.0065411049872636795, -0.022820230573415756, -0.004675140604376793, -0.006437347736209631, -0.02573898248374462, 0.030933842062950134, 0.020513148978352547, 0.04990130290389061, -0.06383194774389267, -0.018564963713288307, -0.007488321512937546, 0.024906454607844353, 0.03949051350355148, 0.013453644700348377, 0.14352869987487793, 0.06390107423067093, 0.006324253976345062, -0.02328757755458355, -0.04754793271422386, 0.027722762897610664, -0.03193790838122368, -0.0269780196249485, 0.006691302172839642, -0.04843823239207268, -0.01267487183213234, 0.0041076019406318665, -0.051736921072006226, -0.0007455041049979627, -0.032254409044981, 0.049502357840538025, -0.014433344826102257, 0.0129208043217659, -0.01883433200418949, -0.02350398153066635, -0.03140819072723389, -0.0695587620139122, 0.0343460775911808, -0.09117388725280762, 0.04124750196933746, 0.01581619493663311, 0.02890956401824951, -0.004167554434388876, 0.015392463654279709, -0.0001118041982408613, 0.05782513692975044, 0.005643830634653568, -0.006841424386948347, -0.0026962831616401672, 0.0614328496158123, 0.03946099057793617, 0.01503725629299879, 0.011378751136362553, 0.025693856179714203, 0.07069069147109985, 0.02640869840979576, 0.0626312717795372, -0.07013647258281708, 0.02555025927722454, -0.025430727750062943, 0.01261249091476202, -0.013302966021001339, 0.005196000915020704, 0.07653548568487167, -0.09487844258546829, 0.010596474632620811, -0.055367521941661835, 0.00829547643661499, 0.03673049435019493, -0.06789571791887283, 0.009484516456723213, 0.006894912105053663, -0.01681738719344139, -0.0026154574006795883, 0.02111104503273964, 0.048493631184101105, 0.03757602721452713, -0.024278167635202408, 0.04502182826399803, 0.0006901107844896615, 0.003718843450769782, -0.016603272408246994, -0.0010318279964849353, 0.040499042719602585, 0.006643191445618868, 0.08615778386592865, 0.08546680957078934, 0.038137227296829224, 0.08259808272123337, -0.06692451238632202, 0.009493828751146793, 0.04516134038567543, -0.02960745245218277, 0.017257602885365486, -0.028352422639727592, 0.019518136978149414, 0.023025376722216606, 0.04082067683339119, -0.01575581543147564, 0.03800235688686371, -0.0032544047571718693, 0.0030430525075644255, -0.02282792329788208, -0.05938033387064934, 0.0033956526312977076, -0.016699299216270447, 0.05758853256702423, 0.050450537353754044, 0.04762575030326843, -0.023180801421403885, 0.05191454663872719, 0.011284816078841686, 0.02980947680771351, 0.08094798028469086, -0.03727586194872856, 0.0710766538977623, -0.030236031860113144, 0.0318664088845253, 0.00048530439380556345, -0.023952607065439224, -0.043294619768857956, 0.017676854506134987, 0.0010320923756808043, 0.005654970649629831, -0.0019804220646619797, -0.032996196299791336, -6.381736055411152e-33, 0.008069208823144436, 0.001483184634707868, -0.02234414964914322, -0.01086385641247034, -0.0025458652526140213, -0.027409153059124947, -0.00587039440870285, 0.006728008855134249, 0.02575458399951458, -0.042580097913742065, 0.011248080991208553, 0.02297046221792698, 0.029834462329745293, 0.034288082271814346, 0.003978968132287264, 0.012953534722328186, -0.029373057186603546, -0.034844379872083664, -0.017515335232019424, -0.012839499861001968, 0.03333650529384613, 0.017555732280015945, -0.030074404552578926, -0.00585514772683382, -0.0017280025640502572, -0.009936312213540077, -0.022383173927664757, -0.031077582389116287, -0.04997418448328972, -0.016795609146356583, -0.012115693651139736, -0.004350283183157444, 0.0222017802298069, 0.036987707018852234, 0.045083511620759964, 0.054378122091293335, -0.0014239992015063763, -0.023974521085619926, -0.05472032353281975, -0.022015824913978577, -0.06474225968122482, 0.02413300983607769, -0.018785512074828148, 0.01408444344997406, -0.09011295437812805, 0.07313529402017593, 0.02269754931330681, 0.00023348529066424817, -0.03704671934247017, 0.03100690431892872, 0.03687926009297371, -0.010852154344320297, -0.014901232905685902, 0.041627272963523865, 0.01798027753829956, -0.042300257831811905, -0.04196556657552719, -0.0594828724861145, -0.07500558346509933, 0.01280065905302763, -0.03912971541285515, 0.01288518775254488, -0.04189189150929451, -0.013405876234173775, 0.030175937339663506, 0.05281992629170418, -0.031283795833587646, -0.0605485700070858, -0.03147395700216293, -0.015253225341439247, -0.02158522978425026, 0.004409013316035271, 0.002076433040201664, -0.03361817076802254, -0.0004811309918295592, -0.040081482380628586, -0.0506647527217865, 0.0195130817592144, 0.05608292296528816, 0.025608377531170845, -0.030703462660312653, 0.008917449973523617, -0.04796239361166954, -0.0029057480860501528, 0.050376567989587784, 0.01507469080388546, -0.009862834587693214, 0.01712934486567974, -0.0031782148871570826, 0.0192679762840271, 0.018065070733428, -0.029624827206134796, -0.0180773064494133, 0.00822344608604908, -0.02175118587911129, -0.05039367824792862, 0.05833154171705246, 0.01258721761405468, -0.021346520632505417, -0.019827257841825485, -0.10178574919700623, 0.017301000654697418, 0.06350388377904892, 0.05506685748696327, 0.03296780586242676, 0.006815850269049406, 0.01428582426160574, 0.04770061746239662, 0.004635239019989967, -0.0033760706428438425, -0.01649211160838604, 0.024783656001091003, 0.06822746992111206, 0.008181292563676834, 0.013497400097548962, -0.10857397317886353, 0.01596766710281372, -0.032748397439718246, -0.05471644178032875, -0.1030973568558693, -0.020259229466319084, -0.02477552928030491, 0.01738620363175869, 0.0630907267332077, -0.015621861442923546, 0.031967200338840485, -0.053162649273872375, 0.03791511803865433, -0.0070170629769563675, -0.04116930067539215, 0.0005510398768819869, -0.02021097019314766, 2.915868151376344e-07, -0.040377162396907806, -0.045170124620199203, 0.017560254782438278, 0.015713056549429893, 0.023277228698134422, -0.0365164615213871, -0.04372875764966011, 0.042142342776060104, 0.0025599109940230846, 0.036133937537670135, -0.04144355654716492, -0.04893908277153969, 0.02961474284529686, -0.03378615155816078, -0.016962694004178047, 0.00913920346647501, -0.02023208886384964, 0.04158657789230347, -0.009365018457174301, -0.024335874244570732, 0.02266598306596279, -0.045204151421785355, -0.025760525837540627, -0.0067030517384409904, 0.050919193774461746, -0.015910755842924118, 0.008116113021969795, 0.01624959148466587, 0.038978759199380875, -0.03103805147111416, 0.06529708206653595, 0.041462574154138565, -0.05437517911195755, 0.025677787140011787, -0.006645792163908482, -0.0004675515810959041, -0.027185499668121338, 0.006153790280222893, -0.017383119091391563, 0.004423059057444334, 0.005489319562911987, 0.029242772608995438, 0.02168627828359604, 0.02036456950008869, 0.030249305069446564, -0.044866785407066345, -0.06921934336423874, 0.05036187544465065, 0.04207906499505043, 0.03564571961760521, -0.005034651607275009, 0.02845066972076893, 0.004955093376338482, -0.09172467887401581, -0.004390121903270483, 0.02919740043580532, 0.025095771998167038, 0.00220581516623497, 0.01708960346877575, -0.02796556055545807, 0.019390251487493515, -0.012701060622930527, -0.042772017419338226, -0.0218608770519495, 0.06308263540267944, -0.05522945523262024, 0.03512468934059143, 2.0290701605335354e-34, -0.011777155101299286, 0.004729560576379299, -0.00028713952633552253, 0.013681267388164997, -0.06672292947769165, -0.07113821059465408, 0.03439735621213913, 0.012118094600737095, 0.0026009941939264536, -0.009258287958800793, 0.015950672328472137]

['Nir Ailon']

0810.2764v1

The LETOR website contains three information retrieval datasets used as a benchmark for testing machine learning ideas for ranking. Algorithms participating in the challenge are required to assign score values to search results for a collection of queries, and are measured using standard IR ranking measures (NDCG, precision, MAP) that depend only the relative score-induced order of the results. Similarly to many of the ideas proposed in the participating algorithms, we train a linear classifier. In contrast with other participating algorithms, we define an additional free variable (intercept, or benchmark) for each query. This allows expressing the fact that results for different queries are incomparable for the purpose of determining relevance. The cost of this idea is the addition of relatively few nuisance parameters. Our approach is simple, and we used a standard logistic regression library to test it. The results beat the reported participating algorithms. Hence, it seems promising to combine our approach with other more complex ideas.

A Simple Linear Ranking Algorithm Using Query Dependent Intercept Variables

http://arxiv.org/pdf/0810.2764v1

Title Simple Linear Ranking Algorithm Using Query Dependent Intercept Variables Summary LETOR website contains three information retrieval datasets used benchmark testing machine learning idea ranking Algorithms participating challenge required assign score value search result collection query measured using standard IR ranking measure NDCG precision MAP depend relative scoreinduced order result Similarly many idea proposed participating algorithm train linear classifier contrast participating algorithm define additional free variable intercept benchmark query allows expressing fact result different query incomparable purpose determining relevance cost idea addition relatively nuisance parameter approach simple used standard logistic regression library test result beat reported participating algorithm Hence seems promising combine approach complex idea Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.015464811585843563, 0.04464423656463623, -0.031032683327794075, -0.01561696082353592, 0.022333424538373947, 0.01567869819700718, 0.014889342710375786, 0.0184719767421484, 0.06474267691373825, -0.06456004828214645, -0.015644965693354607, 0.03018501028418541, -0.008599051274359226, 0.0477600023150444, -0.017810475081205368, -0.02242419496178627, 0.007687675300985575, 0.03761626407504082, -0.009851320646703243, -0.021184751763939857, 0.029846172779798508, 0.01192967314273119, 0.013949977234005928, -0.016339385882019997, 0.06633980572223663, 0.05402597039937973, -0.010257027111947536, 0.0016847860533744097, 0.0050124796107411385, 0.020111484453082085, 0.022256534546613693, 0.05245397239923477, -0.016224173828959465, 0.024152597412467003, 2.228713356089429e-06, -0.06672854721546173, -0.07945416867733002, -0.019375314936041832, 0.020066095516085625, -0.017529282718896866, -0.008480139076709747, 0.01931712031364441, 0.052939873188734055, 0.0172585379332304, -0.05309552326798439, -0.014868187718093395, -0.024754386395215988, 0.022567588835954666, 0.02790917456150055, -0.004680059850215912, 0.021524395793676376, -0.027859454974532127, -0.05574124678969383, 0.002160655800253153, 0.0654669776558876, -0.022836919873952866, -0.014608679339289665, 0.028859006240963936, 0.013233492150902748, 0.052536740899086, -0.00841270200908184, 0.0014392910525202751, -0.0601399801671505, -0.014942559413611889, 0.05998845770955086, 0.0021707676351070404, -0.04452156648039818, 0.027672981843352318, 0.027190543711185455, 0.047659073024988174, 0.03106559067964554, -0.006399095524102449, -0.010583448223769665, 0.014103271067142487, 0.020509669557213783, -0.014834582805633545, -0.03841416910290718, 0.006451378110796213, -0.01719684898853302, 0.020786575973033905, -0.0500020906329155, 0.05115562677383423, -0.013689299114048481, 0.004822497256100178, 0.015904871746897697, 0.03203420341014862, -0.0038299376610666513, -0.029435953125357628, 0.05351720377802849, 0.006359914783388376, 0.02973041497170925, -0.016790010035037994, 0.009948971681296825, -0.01873725652694702, -0.04814384505152702, -0.02098044753074646, 0.01969190314412117, -0.023902785032987595, 0.03242481127381325, -0.06572818011045456, 0.02789922244846821, -0.028225326910614967, 0.05948808416724205, 0.0488714836537838, 0.014765726402401924, 0.05991977080702782, -0.004853369668126106, 0.03788527101278305, -0.003346177050843835, 0.03376485034823418, -0.062701515853405, -0.0199788399040699, 0.012498889118432999, 0.08276408165693283, 0.0005749993724748492, 0.030973101034760475, -0.05761668458580971, -0.01056897733360529, 0.016205238178372383, -0.03868911787867546, 0.010500694625079632, 0.032647132873535156, 0.02369553968310356, 0.07953637093305588, -0.02398565225303173, 0.0024789278395473957, -0.006651708390563726, -0.016057780012488365, -0.051771026104688644, 0.010054460726678371, 0.058474961668252945, 0.023951087146997452, 0.007298589684069157, 0.014668400399386883, 0.031758371740579605, 0.02883855439722538, 0.031858302652835846, 0.020214350894093513, -0.025862887501716614, -0.02980227954685688, 0.040750931948423386, 0.0019507467513903975, -0.057369329035282135, -0.04029771313071251, 0.01752222329378128, 0.015023944899439812, -0.00428499560803175, 0.022992491722106934, 3.0015657102921978e-05, 0.02922237664461136, -0.06536444276571274, 0.07655415683984756, 0.02210402674973011, -0.009660298936069012, 0.04635322093963623, 0.007046893239021301, 4.209835606161505e-05, 0.02386951446533203, -0.015974193811416626, 0.038605231791734695, 0.06401227414608002, 0.0029129739850759506, -0.02617197483778, -0.034266091883182526, -0.03537992015480995, -0.029800748452544212, 0.010211699642241001, 0.03599508851766586, -0.042219970375299454, -0.004006297327578068, -0.040441885590553284, 0.018568407744169235, -0.00024259704514406621, 0.005674045532941818, 0.01249797735363245, -0.025528499856591225, 0.05276652052998543, -0.019603166729211807, -0.030716584995388985, 0.09216151386499405, -0.014901813119649887, -0.03029894456267357, 0.004125748295336962, 0.05052219331264496, -0.05276719480752945, -0.02893555723130703, 0.01987611874938011, 0.016088321805000305, -0.02691332995891571, -0.04970243573188782, -0.0049880631268024445, 0.04690903052687645, -0.014193742536008358, 0.00529195461422205, 0.041458290070295334, -0.0346686877310276, -0.009793763980269432, -0.06158331036567688, -0.007485240697860718, -0.030585981905460358, -0.0016189677407965064, -0.030898887664079666, -0.0035282832104712725, 0.05889961123466492, 0.006317374296486378, -0.06025257334113121, 0.012714408338069916, -0.010875292122364044, 0.02269708551466465, -0.06379613280296326, 0.028124142438173294, -0.019255660474300385, -0.032667092978954315, -0.007126982323825359, -0.028013009577989578, 0.03913811221718788, -0.012973330914974213, -0.009043718688189983, -0.015956325456500053, 0.040815502405166626, 0.024216128513216972, 0.005511399358510971, 0.009701802395284176, 0.011875045485794544, 0.005396837834268808, 0.01313734706491232, 0.0672493577003479, -0.008051266893744469, 0.030241865664720535, 0.03082788735628128, 0.029973987489938736, 0.018916107714176178, 0.060157738626003265, 0.007025653030723333, -0.06415481865406036, -0.018398569896817207, 0.11056184768676758, -0.019108394160866737, 0.008782055228948593, -0.018989669159054756, 0.060676705092191696, 0.07306718081235886, -0.0053414530120790005, 0.00827160757035017, -0.01278402004390955, -0.006973853800445795, 0.013561289757490158, -0.008858006447553635, 0.022747812792658806, -0.010994895361363888, -0.04368934780359268, -0.092323437333107, 0.06200200691819191, 0.00553515600040555, 0.06774367392063141, 0.001928421901538968, -0.024795671924948692, -0.00594489136710763, -0.01141353603452444, -0.010817290283739567, -0.03938126191496849, -0.025685898959636688, 0.028618788346648216, -0.02096952311694622, 0.0104755237698555, -0.04109439253807068, 0.01144331693649292, -0.07168082147836685, 0.003557281568646431, 0.028984135016798973, -0.037475649267435074, -0.004942949395626783, -0.00879781786352396, 0.028248455375432968, -0.03070719726383686, -0.03764582797884941, -0.03526940941810608, 0.003493927652016282, 0.02483881451189518, 0.005022862460464239, 0.016621457412838936, 0.007385008968412876, -0.030464734882116318, -0.03480488806962967, -0.013196277432143688, 0.02674313634634018, 0.048401981592178345, -0.017939994111657143, -0.02227325178682804, -0.02769995853304863, -0.06746471673250198, 0.0007593734771944582, -0.003505445783957839, 0.0004478501505218446, -0.02727482095360756, -0.04071352258324623, -0.05406155064702034, 0.024877198040485382, 0.053016774356365204, -0.020962145179510117, 0.06778042763471603, -0.010866560973227024, -0.06915707886219025, 0.004113287199288607, -0.022082097828388214, 0.035997580736875534, 0.040446557104587555, -0.01999957300722599, 0.025274168699979782, -0.06112276017665863, 0.03811702877283096, -0.027390429750084877, -0.01764383539557457, 0.05672036483883858, -0.028720321133732796, -0.029811717569828033, -0.13619861006736755, 0.02206716313958168, 0.020449073985219002, 0.0623929537832737, 0.0223349928855896, -0.049081381410360336, 0.010197989642620087, 0.0502321831882, 0.02184661477804184, -0.034221041947603226, -0.010329104028642178, -0.03334428742527962, 0.0010246664751321077, -0.02343285270035267, 0.04201541468501091, -0.11213353276252747, 0.019994376227259636, 0.010928777977824211, 0.03966832906007767, 0.03821086138486862, -0.06818709522485733, 0.021489886566996574, 0.008627733215689659, -0.009087684564292431, 0.022500520572066307, -0.01680050604045391, -0.0295296348631382, -0.020757479593157768, 0.05074495077133179, -0.01821119338274002, 0.030223408713936806, -0.010764554142951965, -0.0045619229786098, 0.015594073571264744, 0.013049650937318802, 0.011997570283710957, -0.037949349731206894, -0.050004102289676666, 0.06461178511381149, 0.021291520446538925, 0.009367831982672215, -0.04355806112289429, -0.010216392576694489, 0.02041998691856861, 0.010804594494402409, 0.04691959172487259, 0.027031129226088524, -0.041298579424619675, 0.010363145731389523, 0.024307962507009506, 0.059789158403873444, -0.062197089195251465, -0.007442389149218798, -0.021623719483613968, -0.0688207820057869, 0.02921224571764469, 0.013519234023988247, 0.06294647604227066, 0.08822643011808395, -0.04729423671960831, -0.04919848591089249, -0.05537106469273567, 0.03652056306600571, 0.04293102025985718, 0.05273636430501938, -0.015836983919143677, 0.04470117390155792, 0.004863784182816744, 0.059712812304496765, -0.0308392196893692, -0.04385127127170563, -0.002590336836874485, -0.08081710338592529, 0.04285075515508652, -0.025100277736783028, -0.002061029663309455, -0.0320681668817997, -0.0934835895895958, -0.029069382697343826, -0.05963826924562454, -0.09226460009813309, 0.06063919514417648, -0.017887640744447708, 0.008866118267178535, -0.005701079964637756, -0.014107117429375648, 0.028866102918982506, 0.003599340794607997, -0.0003534410207066685, -0.02405385486781597, -0.027728822082281113, 0.04233783483505249, -0.019039057195186615, -0.006832001265138388, -0.027503591030836105, -0.01130686979740858, -0.04433415085077286, -0.06905584782361984, 0.08939789980649948, -0.025680052116513252, 0.014090892858803272, -0.04524742066860199, -0.0018267391715198755, 0.0036701031494885683, 0.08758734166622162, 0.03593037277460098, 0.04026602953672409, -0.03966371715068817, 0.05915260687470436, -0.05144132673740387, 0.017592694610357285, -0.0287071093916893, 0.002850501798093319, -0.029874488711357117, -0.037178412079811096, 0.027140237390995026, -0.017711719498038292, 0.006548470351845026, 0.016328010708093643, -0.06201343238353729, 0.014332899823784828, -0.03716565668582916, -0.036622025072574615, -0.06969277560710907, -0.027140552178025246, 0.01922842301428318, 0.028556879609823227, -0.014334934763610363, 0.04376035928726196, -0.06527843326330185, -0.006091684103012085, -0.050975311547517776, -0.053047094494104385, 0.03662092238664627, 0.005972101353108883, -0.03532065451145172, 0.006165981292724609, 0.056941043585538864, -0.02429226227104664, -0.06872604042291641, -0.054239675402641296, 0.001969082746654749, -0.024158941581845284, -0.02770128846168518, 0.04201271012425423, 0.017618242651224136, -0.008683248423039913, -0.05491597577929497, -0.0016299951821565628, -0.03962255269289017, -0.014824608340859413, 0.034008678048849106, -0.013586591929197311, -0.024685142561793327, -0.009092404507100582, 0.017191587015986443, 0.01082929503172636, -0.06233188509941101, 0.03499745577573776, -0.01612011156976223, -0.02487264946103096, -0.0360303670167923, -0.03740888833999634, 0.04128224402666092, 0.06958279758691788, 0.0283527635037899, 0.0385727696120739, -0.05347021669149399, -0.011697007343173027, 0.049688659608364105, -0.04642191529273987, -0.07184531539678574, -0.04178718477487564, -0.006990911439061165, 0.033810634166002274, 0.028291815891861916, -0.030991055071353912, -0.02705920673906803, -0.008839167654514313, 0.004091970156878233, -0.04637232795357704, 0.02867598831653595, -0.051459912210702896, 0.0333402045071125, -0.012850918807089329, -0.009093034081161022, 0.00011159127461723983, -0.04974155128002167, 0.03252759575843811, 0.04996756464242935, -0.03905392438173294, -0.01843341812491417, 0.0017771676648408175, 0.010384012944996357, -0.013892957009375095, 0.036759085953235626, -0.021096164360642433, -0.023182867094874382, -0.029352914541959763, -0.022406410425901413, -0.020013339817523956, -0.01711038500070572, 0.0030652573332190514, 0.050825316458940506, -0.019174596294760704, 0.0037353942170739174, 0.00867613684386015, 0.01859644241631031, -0.0009864792227745056, 0.006687343120574951, 0.02534574456512928, 0.011216364800930023, 0.05636711046099663, 0.08340369164943695, 0.0330694280564785, -0.05512392148375511, -0.018224047496914864, -0.08894361555576324, -0.015998199582099915, 0.03391006216406822, 0.028693577274680138, 0.01658329926431179, 0.005452070385217667, -0.030802294611930847, -0.041286617517471313, 0.0057435124181210995, 0.025210948660969734, -0.054231490939855576, 0.03968778997659683, 0.019659554585814476, 0.05041199550032616, 0.046897631138563156, -0.012633892707526684, 0.014232010580599308, -0.05989629402756691, -0.0435168594121933, -0.048809219151735306, -0.029502304270863533, -0.011486418545246124, -6.408005415416153e-33, -0.0030668277759104967, -0.04538435861468315, -0.043317846953868866, -0.02444165199995041, -0.01630590856075287, 0.009754178114235401, 0.0748470202088356, -0.01232872437685728, -0.026605667546391487, -0.04958570376038551, 0.016405826434493065, -0.023373281583189964, 0.021484090015292168, -0.009271316230297089, 0.03043520078063011, -0.008812662214040756, -0.04941580072045326, 0.009573512710630894, -0.0024290659930557013, -0.0016620093956589699, 0.042294323444366455, 0.048506755381822586, -0.0062903654761612415, -0.0853320062160492, 0.015590507537126541, 0.0013036789605394006, -0.032723743468523026, 0.033306561410427094, -0.05837099999189377, 0.0502052940428257, 0.043379876762628555, 0.017241209745407104, 0.037793464958667755, -0.026718536391854286, 0.02635948546230793, -0.0072690946981310844, -0.006275794003158808, -0.041596315801143646, -0.011216383427381516, -0.027215758338570595, 0.04540640115737915, 0.07367502897977829, 0.03447144851088524, -0.010269518941640854, -0.012489186599850655, -0.01005760207772255, 0.08809638768434525, 0.0031491764821112156, -0.031145265325903893, -0.00644171517342329, 0.039628881961107254, 0.005235564894974232, -0.023791087791323662, 0.0749344453215599, 0.02764042094349861, 0.08765764534473419, -0.03384975716471672, 0.07816410809755325, 0.004399185534566641, 0.047081124037504196, -0.031171247363090515, 0.08840183913707733, 0.002181760501116514, -5.2593295549741015e-05, -0.003196334233507514, 0.03369467332959175, 0.004203041084110737, -0.033692583441734314, 0.0013047753600403666, -0.028919752687215805, -0.022319752722978592, 0.00012377665552776307, 0.02761213481426239, -0.004951628856360912, 0.006189956795424223, -0.01314920000731945, -0.058051470667123795, 0.05390116199851036, -0.023495325818657875, -0.02410091646015644, -0.03288524970412254, -0.003132607787847519, -0.06933848559856415, -0.027599617838859558, -0.02356123924255371, 0.03382914140820503, -0.06689365208148956, -0.04643433541059494, 0.0551811046898365, 0.0019676967058330774, -0.05792766436934471, -0.020178303122520447, -0.045882582664489746, -0.006895195692777634, -0.047271911054849625, 0.015366180799901485, 0.020790955051779747, 0.021585898473858833, -0.01490957010537386, -0.015456972643733025, -0.01797594502568245, 0.0377318412065506, -0.025236107409000397, -0.03512116149067879, -0.024607839062809944, -0.032719213515520096, 0.010125244967639446, -0.03241484984755516, -0.025473836809396744, -0.013190995901823044, 0.06080285832285881, -0.03434309363365173, -0.03437021002173424, 0.043829385191202164, -0.03495136648416519, 0.005762203596532345, -0.02274766005575657, 0.04950082302093506, 0.05392667278647423, 0.04882917180657387, -0.03384026885032654, -0.058825258165597916, 0.007865188643336296, -0.044682394713163376, -0.023978309705853462, 0.017660465091466904, 0.03916982188820839, 0.016967248171567917, 0.006763500161468983, -0.016300804913043976, -0.026334812864661217, -0.0233331099152565, 2.8659792405960616e-07, 0.05981278419494629, 0.027687083929777145, -0.04939878359436989, 0.013387617655098438, -0.02507792040705681, -0.02268260344862938, -0.002358686178922653, 0.03639644756913185, 0.027587221935391426, 0.06667967885732651, 0.022579820826649666, -0.013566470704972744, 0.02534877322614193, 0.03233807533979416, -0.07935455441474915, -0.05071137100458145, 0.023947473615407944, -0.04316512495279312, -0.032952338457107544, -0.03079948201775551, 0.06267194449901581, 0.03806270658969879, 0.048982132226228714, 0.007038526237010956, -0.030315199866890907, 0.006974396295845509, -0.024889005348086357, -0.010009081102907658, -0.0276309996843338, 0.002557095605880022, 0.056929800659418106, 0.012674258090555668, -0.022009726613759995, 0.025492757558822632, -0.039395272731781006, -0.0034759007394313812, 0.05398120358586311, 0.01443902961909771, -0.03948909789323807, 0.009274633601307869, 0.046593956649303436, -0.0026315562427043915, 0.02800704538822174, 0.007415838539600372, 0.0501672588288784, 0.05458845570683479, 0.020441079512238503, 0.05813774839043617, -0.03851192817091942, 0.0057164691388607025, 0.027255354449152946, -0.02581063285470009, -0.058110855519771576, 0.007689189165830612, -0.011393871158361435, 0.004369829315692186, 0.025718586519360542, 0.0020801490172743797, 0.0248781219124794, 0.0035751303657889366, -0.009078571572899818, -0.046698976308107376, 0.008591427467763424, 0.06810522824525833, 0.00030447469907812774, 0.012732725590467453, 0.008898774161934853, 3.174376347058768e-34, 0.05613580346107483, 0.03846747800707817, 0.02014927938580513, -0.0005628814687952399, 0.009898358955979347, -0.012296208180487156, 0.036079127341508865, -0.006302366033196449, 0.016162684187293053, -0.03845922648906708, 0.010967745445668697]

['Barbara Hammer', 'Alexander Hasenfuß', 'Fabrice Rossi']

0909.0638v1

Median clustering extends popular neural data analysis methods such as the self-organizing map or neural gas to general data structures given by a dissimilarity matrix only. This offers flexible and robust global data inspection methods which are particularly suited for a variety of data as occurs in biomedical domains. In this chapter, we give an overview about median clustering and its properties and extensions, with a particular focus on efficient implementations adapted to large scale data analysis.

Median topographic maps for biomedical data sets

http://arxiv.org/pdf/0909.0638v1

Title Median topographic map biomedical data set Summary Median clustering extends popular neural data analysis method selforganizing map neural gas general data structure given dissimilarity matrix offer flexible robust global data inspection method particularly suited variety data occurs biomedical domain chapter give overview median clustering property extension particular focus efficient implementation adapted large scale data analysis Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.01303925458341837, -0.025741061195731163, -0.05598577484488487, 0.004705770406872034, 0.013110506348311901, 0.030037209391593933, 0.03153739497065544, 0.030976535752415657, 0.006725549232214689, 0.03527587279677391, 0.013210621662437916, -0.058681029826402664, 0.026022279635071754, -0.002915631514042616, 0.015122253447771072, -0.09474397450685501, -0.017112091183662415, -0.002591752912849188, 0.07762040197849274, -0.015764813870191574, -0.013657434843480587, -0.04439190402626991, 0.004908572416752577, 0.01988551765680313, -0.012710890732705593, -0.0293195229023695, 0.04377853497862816, -0.02755136601626873, 0.03196953609585762, -0.0373280830681324, 0.03772401064634323, 0.01842728815972805, -0.026252102106809616, -0.006412539631128311, 2.1792516236018855e-06, -0.06413797289133072, -0.0045750923454761505, 0.0048394156619906425, 0.031363945454359055, 0.006227761972695589, 0.06241970509290695, 0.05772627517580986, -0.04546092450618744, -0.06429313123226166, -0.0005077820969745517, -0.04734504222869873, 0.025707338005304337, 0.05338841304183006, 0.058624595403671265, -0.02488117478787899, -0.02054668590426445, -0.015033982694149017, 0.04805520176887512, -0.0005540241836570203, 0.02872239053249359, 0.012397426180541515, 0.008703992702066898, 0.016632424667477608, -0.020900191739201546, 0.01658414676785469, 0.005986995063722134, 0.03993694484233856, 0.027083054184913635, 0.056328535079956055, 0.0191968847066164, 0.0618073008954525, 0.0023197862319648266, -0.009679633192718029, 0.010108849965035915, 0.02026291750371456, -0.06956670433282852, 0.014133788645267487, 0.04030786454677582, 0.023198356851935387, -0.007383745163679123, -0.049246449023485184, -0.027293682098388672, 0.028530606999993324, -0.04007039591670036, -0.010497855953872204, -0.01723909005522728, 0.06759028881788254, 0.004643669351935387, -0.029642628505825996, -0.06374742090702057, -0.03359674662351608, -0.016578707844018936, 0.017702676355838776, -0.06220102682709694, -0.029498230665922165, -0.06812458485364914, 0.002789050340652466, 0.01149043720215559, 0.003645674092695117, -0.009323429316282272, -0.05081389471888542, 0.04291617497801781, -0.0554157979786396, 0.08656693249940872, -0.05039643868803978, 0.038485970348119736, -0.009013166651129723, -0.026020556688308716, 0.025834277272224426, -0.03612130880355835, -0.02038811519742012, -0.07536806166172028, 0.06609034538269043, 0.016881927847862244, -0.006976503878831863, 0.00034308279282413423, 0.017406664788722992, 0.024580826982855797, 0.03634115681052208, -0.011624910868704319, 0.022363953292369843, -0.0421861931681633, -0.017672689631581306, -0.01735030487179756, -0.03483659774065018, -0.019692420959472656, 0.06358570605516434, 0.022296538576483727, 7.042496145004407e-05, 0.012608557008206844, -0.025355864316225052, -0.05414345860481262, 0.026378732174634933, -0.002770282793790102, 0.03627811744809151, 0.04218027740716934, 0.03140202909708023, -0.023218005895614624, 0.04138949513435364, -0.032184623181819916, 0.025684010237455368, 0.013606286607682705, 0.03565146401524544, -0.07916620373725891, 0.009462393820285797, -0.023325854912400246, 0.011068297550082207, -0.01659686304628849, -0.05069103464484215, 0.03125321492552757, 0.011959654279053211, -0.02797890640795231, 0.009421274065971375, -0.042966004461050034, -0.023054921999573708, -0.04709211364388466, 0.062067095190286636, -0.05055506154894829, -0.03619449958205223, 0.11551147699356079, 0.0243404321372509, -0.0007732745143584907, -0.04303928464651108, 0.06697692722082138, 0.01425930391997099, 0.011568257585167885, -0.0020318194292485714, -0.003354776883497834, -0.043674286454916, -0.015318884514272213, -0.06856822222471237, -0.03178089112043381, -0.02719779685139656, 0.018589111045002937, 0.040914811193943024, 0.0014880072558298707, 0.03706057742238045, 0.009908287785947323, -0.05239657312631607, 0.013005453161895275, 0.12214251607656479, 0.04991792514920235, 0.06320410966873169, -0.058071039617061615, -0.005225790664553642, -0.031119849532842636, -0.03371123969554901, 0.03389643877744675, 0.048655103892087936, -0.02866777405142784, -0.00029695010744035244, -0.022424718365073204, 0.06185689941048622, -0.008713169023394585, -0.042421046644449234, 0.018961142748594284, 0.0010510544525459409, -0.028346577659249306, -0.09629563987255096, -0.0046477667056024075, -0.019235949963331223, 0.05720667541027069, -0.06055368483066559, -0.012945421040058136, -0.008926253765821457, -0.014414746314287186, -0.023470871150493622, -0.018128419294953346, -0.06400415301322937, -0.03017578460276127, -0.04681151360273361, -0.006546497344970703, 0.009716033935546875, 0.021776635199785233, -0.05986093729734421, -0.03701463341712952, 0.020250113680958748, 0.017861705273389816, -0.08905743807554245, -0.009510274976491928, 0.034780483692884445, -0.0032273121178150177, -0.026312900707125664, -0.033610060811042786, 0.03765073046088219, -0.010714861564338207, -0.07512152194976807, 0.027084922417998314, 0.0048692114651203156, -0.038823243230581284, 0.0610029511153698, 0.03346442058682442, 0.04878144711256027, -0.0037008204963058233, -0.0024655081797391176, 0.0039383056573569775, -0.05755237862467766, 0.04606415331363678, -0.005672356579452753, 0.0060335490852594376, 0.0008716695592738688, 0.009724152274429798, 0.005729259457439184, -0.026758892461657524, -0.014863485470414162, -0.021860020235180855, -0.044942792505025864, -0.027543148025870323, -0.03344736620783806, 0.003600872354581952, 0.0024614245630800724, -0.017310576513409615, -0.016082415357232094, 0.02026258409023285, 0.009505314752459526, 0.024370569735765457, -0.037688516080379486, 0.042318832129240036, -0.0056918286718428135, -0.008174343034625053, 0.01816045120358467, -0.037572216242551804, 0.019300205633044243, -0.018427012488245964, -0.005115509498864412, -0.020308956503868103, -0.025923794135451317, -0.011234245263040066, -0.019748110324144363, 0.026081224903464317, -0.00048429518938064575, -0.017820581793785095, -6.866369949420914e-05, -0.011534052900969982, 0.00382353737950325, 0.015246269293129444, 0.024276042357087135, -0.014888052828609943, 0.0014987008180469275, -0.047631751745939255, 0.012038116343319416, 0.030425043776631355, 0.022179530933499336, -0.05446362867951393, 0.1123322993516922, -0.014732034876942635, 0.020531099289655685, -0.010306054726243019, -0.010069189593195915, -0.007183645851910114, 0.03644417226314545, 0.02114618755877018, -0.05083956941962242, 0.03834142908453941, 0.020544707775115967, -0.0194245595484972, 0.028639115393161774, 0.021029286086559296, -0.07071247696876526, -0.0044813817366957664, 0.010220992378890514, 0.023965904489159584, 0.06403609365224838, 0.07615827769041061, -0.013494785875082016, 0.001171802286989987, 0.05303916707634926, 0.0340239442884922, -0.004525858908891678, -0.017298376187682152, 0.037830546498298645, 0.03444782271981239, -0.025038547813892365, 0.027485519647598267, 0.0172534491866827, 0.06939617544412613, -0.004171420820057392, 0.020960332825779915, -0.010892740450799465, 0.01610645279288292, 0.030895810574293137, -0.06540865451097488, 0.05082780495285988, -0.02878708764910698, 0.03247031569480896, -0.04770011082291603, -0.010708626359701157, 0.051192738115787506, 0.014444006606936455, 0.002777168294414878, -0.010222467593848705, -0.025965962558984756, 0.019355786964297295, -0.06956387311220169, 0.0003778336977120489, 0.03246432542800903, -0.05075492337346077, -0.025575263425707817, -0.011156645603477955, -0.005065867677330971, -0.029616182669997215, -0.03489728271961212, -0.005407108925282955, -0.00746877258643508, -0.044810522347688675, 0.03553846478462219, 0.006398423109203577, -0.03368275985121727, 0.09097114205360413, 0.08779137581586838, -0.03474462032318115, 0.0616164356470108, -0.005815553013235331, 0.02340742014348507, 0.06655962765216827, 0.03182877227663994, 0.04439530149102211, -0.0054930709302425385, -0.027055900543928146, 0.002847769996151328, 0.06564341485500336, -0.04124431312084198, 0.04039449244737625, 0.001976634608581662, 0.041077498346567154, 0.048722535371780396, 0.05847406014800072, 0.007877632044255733, 0.00790250115096569, -0.05033961310982704, 0.026419615373015404, -0.046571698039770126, 0.021318253129720688, 0.0003257113858126104, -0.03612932562828064, 0.05499941110610962, 0.016305863857269287, 0.02104412391781807, 0.045088447630405426, 0.01840137131512165, -0.08193530887365341, -0.00349249760620296, -0.017931004986166954, -0.044160667806863785, -0.00819181464612484, -0.009213929995894432, 0.03284882381558418, 0.05903858318924904, -0.030941616743803024, -0.004600322339683771, 0.00018961563182529062, -0.05279894918203354, 0.03518843278288841, 0.03558697924017906, 0.040972188115119934, 0.009746328927576542, -0.09708434343338013, -0.019170479848980904, -0.0287695974111557, -0.004087876528501511, -0.015256978571414948, -0.0409993901848793, -0.03473362699151039, 0.02956048585474491, -0.04535409063100815, 0.001274780952371657, -0.03531248867511749, 0.027749786153435707, 0.016217853873968124, -0.10133452713489532, 0.04403512924909592, -0.019715065136551857, 0.024397404864430428, 0.009643001481890678, 0.03817322105169296, 0.029188605025410652, -0.03623456135392189, 0.027782144024968147, -0.028581341728568077, 0.09114424884319305, 0.08298305422067642, -0.007499899715185165, -0.0775214359164238, 0.046175841242074966, 0.015551353804767132, 0.01937277428805828, -0.007311240304261446, 0.052603304386138916, -0.012530521489679813, 0.030120186507701874, -0.06802020967006683, 0.02274475246667862, -0.010759220458567142, -0.035894326865673065, 0.0075478884391486645, 0.016615211963653564, -0.019806435331702232, -0.05200576037168503, 0.0990450382232666, 0.05260643735527992, -0.023919880390167236, 0.027504727244377136, -0.03291536867618561, 0.012586633674800396, -0.01930094324052334, 0.019349679350852966, -0.0013715351233258843, 0.048338573426008224, 0.0035454973112791777, -0.019150033593177795, 0.021907612681388855, -0.0711863562464714, -0.025417042896151543, 0.013500719331204891, 0.05104432255029678, -0.026250388473272324, -0.03503748029470444, -0.0036473495420068502, 0.061689343303442, 0.0010309169301763177, -0.013925471343100071, -0.054134584963321686, -0.013277602382004261, -0.009356550872325897, -0.007489487994462252, 0.04173213988542557, 0.0053987870924174786, -0.01811511628329754, -0.04323072358965874, -0.05329582467675209, 0.13744504749774933, 0.02308971807360649, -0.020762847736477852, 0.0016037005698308349, -0.02016088180243969, -0.03959932178258896, -0.013632403686642647, -0.014540070667862892, 0.021176008507609367, 0.05475198104977608, 0.004435483366250992, -0.028486890718340874, -0.011575768701732159, 0.004882731940597296, -0.02968856319785118, -0.01849505864083767, 0.13713975250720978, 0.040848735719919205, -0.04487714171409607, -0.01933068037033081, -0.009831985458731651, 0.009705358184874058, 0.024822626262903214, 0.03670213371515274, 0.016185618937015533, 0.020520836114883423, 0.07002121955156326, -0.05539733171463013, -0.005024504382163286, 0.05384693667292595, -0.028012393042445183, 0.0063958195969462395, -0.0014885328710079193, -0.0259944349527359, -0.0028312536887824535, -0.026768598705530167, 0.04987470060586929, -0.008019928820431232, -0.0351925827562809, -0.021532243117690086, 0.022191062569618225, 0.031453389674425125, -0.008642759174108505, 0.023483986034989357, 0.057093024253845215, -0.03601393848657608, 0.0777633786201477, -0.03177132457494736, -0.012042826972901821, -0.02549874596297741, 0.009762722998857498, -0.003937509376555681, 0.019910737872123718, -0.01076722051948309, 0.005490046460181475, 0.01689104735851288, -0.0195879265666008, 0.02920706383883953, -0.03475122153759003, 0.04070821404457092, -0.0035913102328777313, -0.004073554649949074, -0.002535835839807987, -0.030950920656323433, 0.04065509885549545, -0.02962525561451912, -0.036721549928188324, -0.038261521607637405, -0.029293684288859367, -0.055701591074466705, 0.04958983138203621, 0.009398382157087326, -0.017998868599534035, -0.03203548863530159, -0.009329604916274548, 0.0032466615084558725, -0.022163348272442818, -0.018001621589064598, 0.021225018426775932, 0.0009688811842352152, 0.021585654467344284, -0.024175215512514114, -0.015394210815429688, 0.000559136678930372, -0.022268380969762802, 0.043236248195171356, -0.014682699926197529, -0.02401457540690899, -0.04541981592774391, -0.008636035956442356, -6.0539266804813096e-33, 0.020041758194565773, -0.054223768413066864, 0.00039683631621301174, -0.03735202178359032, -0.0006453188834711909, -0.010086404159665108, -0.009769629687070847, -0.0008034395286813378, -0.005463367328047752, 0.0032017158810049295, 0.0002730584819801152, -0.024834079667925835, -0.016660943627357483, 0.021160444244742393, 0.02146519534289837, 0.04408325254917145, 0.0036896171513944864, -0.010924382135272026, -0.004829736892133951, 0.010260091163218021, 0.007455078884959221, 0.0029961219988763332, 0.010501726530492306, -0.02365242689847946, -0.09775909781455994, 0.05133461207151413, 0.019027559086680412, 0.016628338024020195, -0.03160613775253296, 0.007231967058032751, 0.03033168613910675, 0.008993856608867645, 0.0075784414075315, 0.017871148884296417, -0.016689643263816833, -0.048852548003196716, -0.04620201513171196, -0.032501500099897385, -0.04565955698490143, -0.008664057590067387, 0.05244056507945061, 0.0007400071481242776, 0.07229546457529068, -0.04587702080607414, 0.008276999928057194, -0.007208917755633593, 0.0714629739522934, -0.035088054835796356, -0.011873940005898476, 0.03011481836438179, 0.04273835942149162, 0.028415298089385033, -0.0341019444167614, 0.026116857305169106, -0.005086014978587627, -0.0018930919468402863, -0.031736962497234344, 0.04360475018620491, -0.09511490911245346, 0.055780235677957535, -0.0014367663534358144, -0.022288847714662552, -0.0025965170934796333, 0.011114111170172691, 0.06514894217252731, 0.02938484214246273, 0.0763569176197052, -0.02893764339387417, -0.02264285460114479, 0.009476699866354465, -0.0022867966908961535, 0.005605367943644524, -0.004242952447384596, -0.010598036460578442, 0.06516008824110031, -0.05483679100871086, -0.006254955194890499, 0.08128128945827484, -0.07971575856208801, 0.004900527652353048, -0.06222078576683998, -0.01929878257215023, -0.02647980861365795, -0.021009262651205063, 0.05435923486948013, -0.06976432353258133, -0.03148043528199196, -0.024001574143767357, 0.003278430551290512, -0.04563899338245392, -0.016992781311273575, 0.0020496263168752193, -0.014468787238001823, -0.024107905104756355, 0.04584657400846481, -0.012852765619754791, 0.036969177424907684, 0.026260072365403175, 0.03973285108804703, 0.005747639574110508, 0.006371779832988977, -0.014588098973035812, -0.005089642480015755, -6.771887274226174e-05, -0.014396381564438343, 0.0036928411573171616, -0.02507074736058712, -0.0377923920750618, -0.0040471116080880165, 0.006024327129125595, 0.06555429846048355, -0.041892848908901215, -0.0014896730426698923, 0.003766779089346528, -0.022476745769381523, -0.0793585255742073, 0.0037347646430134773, 0.03937552496790886, 0.03351772576570511, 0.02725432999432087, -0.036788731813430786, 0.013373129069805145, -0.04521845281124115, -0.005399198271334171, -0.0007602254627272487, 0.0018570133252069354, -0.06589438021183014, -0.017373299226164818, -0.019469397142529488, -0.02536950260400772, -0.02076108753681183, -0.00874179694801569, 2.826163836289197e-07, 0.02648439258337021, 0.052857402712106705, 0.030672293156385422, -0.013049419969320297, -0.0036190287210047245, -0.022386591881513596, -0.00241300230845809, -0.0265347957611084, -0.028350360691547394, 0.01047399640083313, 0.04165894538164139, -0.00999663956463337, -0.0062093064188957214, 0.002653713570907712, -0.011342031881213188, 0.0008524423465132713, -0.027274848893284798, -0.0015629032859578729, -0.009453728795051575, 0.009138396009802818, 0.03626300022006035, 0.01242308970540762, -0.028047045692801476, -0.03159307688474655, 0.047599293291568756, -0.003010172164067626, -0.01821892149746418, -0.06304209679365158, 0.049125686287879944, -0.004305878654122353, 0.01594671420753002, -0.021411024034023285, 0.02684662491083145, 0.0012637573527172208, 0.03314856067299843, -0.012021450325846672, -0.03972291201353073, -0.019884910434484482, 0.0003645571123342961, -0.004139257594943047, 0.05502284690737724, 0.031881194561719894, 0.05413345247507095, -0.07676218450069427, -0.025154616683721542, -0.02797740511596203, -0.011986837722361088, 0.0008096865494735539, 0.0608963705599308, 0.009816356934607029, 0.07874099910259247, -0.03302153944969177, 0.005127341952174902, -0.0015296677593141794, -0.00650038244202733, -0.00692141056060791, 0.06926769763231277, 0.03217305988073349, 0.03860517218708992, 0.09305040538311005, -0.012849603779613972, -0.04086139053106308, 0.0416618250310421, 0.024852383881807327, 0.04678524285554886, 0.043251726776361465, -0.019190607592463493, 2.6349084695103226e-34, 0.0007547165732830763, -0.011760863475501537, -0.0073947967030107975, -0.031073125079274178, -0.03469626605510712, 0.010444785468280315, 0.028336655348539352, -0.030496804043650627, -0.07114677876234055, -0.01180353108793497, -0.024793976917862892]

['Laure Berti-Equille', 'Anish Das Sarma', 'Xin', 'Dong', 'Amelie Marian', 'Divesh Srivastava']

0909.1776v1

The Web has enabled the availability of a huge amount of useful information, but has also eased the ability to spread false information and rumors across multiple sources, making it hard to distinguish between what is true and what is not. Recent examples include the premature Steve Jobs obituary, the second bankruptcy of United airlines, the creation of Black Holes by the operation of the Large Hadron Collider, etc. Since it is important to permit the expression of dissenting and conflicting opinions, it would be a fallacy to try to ensure that the Web provides only consistent information. However, to help in separating the wheat from the chaff, it is essential to be able to determine dependence between sources. Given the huge number of data sources and the vast volume of conflicting data available on the Web, doing so in a scalable manner is extremely challenging and has not been addressed by existing work yet. In this paper, we present a set of research problems and propose some preliminary solutions on the issues involved in discovering dependence between sources. We also discuss how this knowledge can benefit a variety of technologies, such as data integration and Web 2.0, that help users manage and access the totality of the available information from various sources.

Sailing the Information Ocean with Awareness of Currents: Discovery and Application of Source Dependence

http://arxiv.org/pdf/0909.1776v1

Title Sailing Information Ocean Awareness Currents Discovery Application Source Dependence Summary Web enabled availability huge amount useful information also eased ability spread false information rumor across multiple source making hard distinguish true Recent example include premature Steve Jobs obituary second bankruptcy United airline creation Black Holes operation Large Hadron Collider etc Since important permit expression dissenting conflicting opinion would fallacy try ensure Web provides consistent information However help separating wheat chaff essential able determine dependence source Given huge number data source vast volume conflicting data available Web scalable manner extremely challenging addressed existing work yet paper present set research problem propose preliminary solution issue involved discovering dependence source also discus knowledge benefit variety technology data integration Web 20 help user manage access totality available information various source Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03068949282169342, 0.07921994477510452, -0.019842253997921944, -0.028879866003990173, -0.0487246997654438, -0.01633930578827858, 0.048578131943941116, 0.03289419785141945, 0.006658266298472881, -0.044955167919397354, 0.016412336379289627, 0.02467702142894268, 0.018943561241030693, 0.07999381422996521, -0.04091501608490944, -0.03611364588141441, 0.03531138598918915, 0.025372114032506943, -0.010825389996170998, -0.010058983229100704, 0.01287702564150095, -0.00216072634793818, -0.008678347803652287, -0.02954336442053318, 0.0223399568349123, -0.02902030013501644, 0.01667286641895771, -0.026170508936047554, -0.016795648261904716, -0.07001519948244095, 0.019478924572467804, 0.03997802734375, -0.012376349419355392, 0.05757100507616997, 2.7574783416639548e-06, -0.022747425362467766, -0.04136651009321213, 0.010063489899039268, -0.03249804675579071, 0.017020825296640396, -0.0035941526293754578, 0.01026694942265749, 0.04528067260980606, 0.0024768603034317493, 0.00010387176735093817, -0.022666029632091522, 0.033125001937150955, 0.02022084780037403, 0.025130271911621094, 0.004196971654891968, 0.0021104784682393074, -0.01825636811554432, -0.01640021614730358, -0.005066965240985155, 0.048476677387952805, 0.010290645062923431, 0.005642339121550322, 0.039405129849910736, 0.033899515867233276, 0.028216425329446793, 0.0003040208830498159, 0.034845080226659775, -0.03140663728117943, 0.0015445512253791094, 0.06337553262710571, 0.016020121052861214, -0.022129317745566368, -0.035951387137174606, 0.00574251776561141, 0.04751334339380264, 0.09816781431436539, -0.04349103197455406, 0.027395885437726974, 0.011084828525781631, -0.028530484065413475, 0.07247862219810486, -0.03330549970269203, 0.03959420323371887, -0.030939722433686256, -0.005797018762677908, -0.012187028303742409, 0.05995895341038704, -0.016524238511919975, 0.032250914722681046, -0.015750836580991745, 0.045132704079151154, 0.005026441533118486, -0.005847605876624584, -0.035616688430309296, -0.022245433181524277, 0.10016030818223953, -0.077911876142025, 0.020456166937947273, -0.0210475642234087, -0.0011858971556648612, -0.011492667719721794, 0.001235291245393455, -0.012250695377588272, 0.04636196419596672, -0.08680573105812073, -0.005220198072493076, -0.006516983732581139, 0.01370606105774641, 0.048387669026851654, 0.09759367257356644, -0.039300721138715744, -0.04743674769997597, -0.0227150097489357, 0.0562843456864357, 0.028040016070008278, -0.04868970066308975, 0.001127137104049325, 0.02366679534316063, 0.06517305225133896, -0.03187995031476021, -0.005739231128245592, -0.014510508626699448, 0.012948689982295036, -0.019880708307027817, 0.02186453528702259, 0.016827434301376343, 0.004648162052035332, -0.0012836090754717588, -0.0006583662470802665, -0.04112428426742554, 0.03792642429471016, -0.0285789854824543, 0.0061217183247208595, -0.012975269928574562, -0.011842022649943829, 0.05400216951966286, -0.0009231913136318326, 0.05272676423192024, -0.003312270389869809, 0.0001024217126541771, 0.05578295513987541, 0.04547877982258797, 0.006177290342748165, -0.09307494014501572, -0.05659988150000572, 0.023499909788370132, -0.030296554788947105, -0.03772984445095062, -0.0471925251185894, 0.005161245819181204, -0.011388109996914864, -0.008383125998079777, 0.012355511076748371, -0.014142288826406002, -0.0062240008264780045, -0.030640264973044395, 0.03542051464319229, -0.09401078522205353, -0.00925190094858408, 0.07977660745382309, 0.04636850580573082, 0.07244069129228592, 0.015321477316319942, -0.035605642944574356, 0.028582433238625526, 0.046709537506103516, 0.0271502286195755, 0.0118913184851408, -0.07165522873401642, -0.025006625801324844, -0.01463667955249548, 0.04652704671025276, 0.03574318066239357, -0.03566858544945717, -0.02609657123684883, -0.07866732776165009, 0.026852376759052277, -0.04177223518490791, 0.07283884286880493, 0.07914896309375763, -0.02099078893661499, 0.03952156752347946, 0.0439164862036705, -0.030279887840151787, 0.052731502801179886, 0.020185448229312897, -0.022994596511125565, -0.008308245800435543, 0.07904744148254395, -0.03879960998892784, -0.018202204257249832, 0.0031518423929810524, 0.023499393835663795, -0.018863199278712273, -0.02750570885837078, -0.009934714995324612, -0.03819074109196663, -0.06207164376974106, -0.010518403723835945, 0.012425216846168041, -0.006831006612628698, 0.029170140624046326, -0.006466784980148077, 0.022816874086856842, -0.016902286559343338, -0.01297068316489458, -0.003545657265931368, 0.02235773392021656, 0.09073212742805481, 0.01701998896896839, -0.029925186187028885, -0.005942079238593578, -0.02484752982854843, 0.038946278393268585, 0.02874363400042057, 0.010317454114556313, 0.012945892289280891, -0.022625545039772987, 0.005195011384785175, 0.01571681909263134, 0.032718971371650696, 0.010991673916578293, 0.004179764539003372, 0.009470445103943348, 0.0611063577234745, -0.013704793527722359, 0.02701152302324772, -0.026971299201250076, -0.008665435947477818, 0.0386379212141037, -0.01601056009531021, -0.03687470033764839, 0.021614449098706245, 0.02373300865292549, 0.04293081909418106, -0.02429572120308876, 0.00991258304566145, 0.021430063992738724, 0.0025515800807625055, -0.10733834654092789, 0.016270579770207405, 0.07058893889188766, 0.10606034845113754, 0.0024702136870473623, -0.07952511310577393, 0.026797940954566002, 0.0032422738149762154, 0.026271309703588486, -0.0202706977725029, 0.011983218602836132, -0.017889294773340225, 0.014649981632828712, 0.03589077293872833, -0.007345573045313358, 0.009769489988684654, 0.016231952235102654, 0.0006073382101021707, 0.03711586073040962, -0.0002558874257374555, 0.02496141567826271, -0.033748701214790344, -0.0527864508330822, 0.01352077815681696, 0.013268185779452324, -0.004017629195004702, 0.008249374106526375, -0.025588685646653175, 0.011349673382937908, 0.020792769268155098, -0.012431245297193527, -0.040746524930000305, 0.04862070828676224, -0.03859885782003403, -0.016328606754541397, 0.004767545498907566, 0.00921954307705164, 0.029934613034129143, 0.01918698661029339, 0.00339999096468091, -0.023570597171783447, 0.003468615235760808, -0.03525439649820328, -0.003503417829051614, 0.0061111049726605415, 0.03405597805976868, 0.03202902898192406, -0.0028502263594418764, -0.04965556785464287, -0.014994153752923012, -0.002976741176098585, 0.01774441823363304, 0.10115408897399902, -0.039631929248571396, -0.03937075287103653, -0.03579292818903923, -0.05049877613782883, 0.0007653653738088906, 0.021536746993660927, -0.002274441532790661, -0.04104650393128395, -0.006473030429333448, -0.05485057458281517, -0.008455666713416576, 0.014228184707462788, 0.0017246318748220801, 0.026353642344474792, -0.016690872609615326, 0.004593441728502512, -0.02433651126921177, -0.0069124442525208, 0.04879559203982353, 0.05143537372350693, -0.02589399181306362, 0.03802245482802391, -0.04605751112103462, 0.029550792649388313, 0.029754040762782097, 0.005257785320281982, 0.03257259353995323, -0.03306696191430092, 0.020249471068382263, -0.034387387335300446, -0.05803008750081062, -0.01261345949023962, 0.056067224591970444, 0.02555428445339203, -0.011230142787098885, 0.019436955451965332, -0.007653730921447277, 0.07889404892921448, -0.03336864709854126, -0.040297649800777435, -0.0030930049251765013, 0.030226370319724083, -0.05643488094210625, 0.028312262147665024, 0.018192637711763382, 0.012365401722490788, 0.02587689645588398, 0.01043387409299612, 0.07562235742807388, -0.026502229273319244, -0.027701005339622498, -0.01635042577981949, 0.0024778025690466166, -0.015899507328867912, -0.032908231019973755, -0.007159041240811348, -0.0010658688843250275, 0.05267304182052612, -0.03361893072724342, 0.055275723338127136, -0.03666050359606743, -0.004153588321059942, -0.03874650225043297, 0.07408232241868973, 0.02256452850997448, 0.021754547953605652, -0.019539766013622284, 0.026799753308296204, 0.018574964255094528, -0.03165153041481972, -0.04094618931412697, -0.004967549815773964, 0.06854896992444992, -0.04940849170088768, 0.04991684854030609, -0.011432506144046783, -0.02977939508855343, 0.02032594010233879, -0.02198462188243866, 0.02766965888440609, -0.05809658393263817, -0.03720211610198021, -0.031177468597888947, -0.013514630496501923, -0.028334902599453926, 0.0642319768667221, 0.041012153029441833, 0.05021132901310921, -0.045239582657814026, -0.040256816893815994, 0.005503685213625431, -0.08669383823871613, 0.034749820828437805, 0.01374784391373396, -0.0756702795624733, 0.05125683173537254, -0.037763647735118866, -0.028153296560049057, -0.03116879053413868, -0.05723504349589348, -0.018758123740553856, -0.011044307611882687, 0.0031520535703748465, -0.03227084502577782, 0.020471451804041862, -0.03354282304644585, -0.07865765690803528, 0.0007906488608568907, -0.012803823687136173, -0.08892159909009933, 0.01839579828083515, -0.010066154412925243, 0.007104951422661543, 0.016464805230498314, -0.11003761738538742, -0.03373746946454048, 0.0019084217492491007, -0.039060432463884354, 0.005554710980504751, -0.012736424803733826, 0.08085959404706955, -0.0820145532488823, -0.05041435360908508, -0.04240645095705986, -0.010468434542417526, -0.03087567538022995, -0.021794121712446213, 0.10283207148313522, -0.002748388098552823, -0.007209863513708115, -0.061564940959215164, -0.0004045050882268697, 0.019075831398367882, 0.04347826540470123, 0.00256711314432323, 0.03131234273314476, -0.02272806316614151, 0.06033115088939667, -0.03447367623448372, 0.0007724791066721082, 0.04416681081056595, -0.005358609836548567, -0.027748586609959602, -0.035620223730802536, -0.028843816369771957, -0.01970944181084633, 0.017449460923671722, -0.011557599529623985, 0.012017267756164074, 0.015381339937448502, -0.02506338618695736, -0.11504285037517548, -0.11586925387382507, -0.004138534888625145, -0.03762424364686012, 0.026290327310562134, 0.007929077371954918, -0.004792377818375826, 0.03240815922617912, -0.006986419204622507, -0.04827429726719856, -0.04955197498202324, 0.0018573119305074215, 0.009374589659273624, -0.03961196541786194, 0.008296623826026917, 0.0004359274171292782, 0.014453960582613945, -0.007350983563810587, 0.0328008197247982, -0.02702750824391842, -0.01493505947291851, 0.03054395504295826, -0.013920736499130726, 0.037120528519153595, -0.06422371417284012, -0.025456145405769348, -0.027850253507494926, -0.03032282181084156, 0.013461524620652199, -0.05648564174771309, -0.012999974191188812, -0.014148927293717861, 0.024103764444589615, -0.010178659111261368, -0.0176334697753191, -0.0004168414161540568, -0.003375401021912694, -0.03115585446357727, -0.06836650520563126, -0.016652802005410194, 0.045062948018312454, 0.0223658736795187, 0.0652463436126709, 0.003191919531673193, 0.013402635231614113, -0.02122677117586136, 0.01308691967278719, 0.016126617789268494, -0.02603626810014248, -0.02142157591879368, 0.019400672987103462, -0.017893977463245392, 0.01569593884050846, -0.012885162606835365, -0.0010653145145624876, 0.09742489457130432, 0.039604976773262024, -0.055121686309576035, -0.02714991569519043, 0.048166900873184204, 0.00251779449172318, 0.024770768359303474, -0.0008890418102964759, -0.016164889559149742, -0.027177806943655014, -0.03358069807291031, -0.022750215604901314, 0.01388048380613327, -0.028379950672388077, -0.0031472279224544764, 5.004902050131932e-05, -0.028173048049211502, -0.0001752159878378734, 0.008867448195815086, -0.051374632865190506, -0.0874214917421341, 0.013994358479976654, 0.06530328094959259, 0.007833175361156464, 0.07359921187162399, 0.007815733551979065, -0.021855318918824196, -0.009421383030712605, 0.014445967972278595, -0.0033846572041511536, -0.005608039442449808, 0.03407567739486694, -0.003520083846524358, 0.020766355097293854, -0.031323883682489395, 0.03448867425322533, 0.06592650711536407, 0.010308055207133293, -0.05512150749564171, -0.021004868671298027, -0.04721403867006302, -0.039651304483413696, 0.02501276507973671, -0.02429153211414814, 0.07431435585021973, -0.003482483560219407, -0.025756705552339554, -0.06461190432310104, -0.03492432460188866, 0.03973478078842163, 0.04181821271777153, 0.05109270289540291, 0.0029623082373291254, 0.03155101090669632, 0.03775754198431969, 0.0571206770837307, -0.016423262655735016, -0.013966957107186317, -0.000772472470998764, -0.046572886407375336, -0.004406891297549009, 0.0021149904932826757, -8.043107037150416e-33, 0.00836100336164236, -0.025708846747875214, -0.015937920659780502, -0.02865706942975521, -0.013671785593032837, 0.012457536533474922, 0.006579043343663216, 0.01626533642411232, -0.04524178057909012, 0.014152226969599724, 0.0027913947124034166, 0.038053419440984726, 0.017688879743218422, -0.019091498106718063, 0.03127119317650795, 0.011015933938324451, 0.010907440446317196, 0.008193298242986202, -0.011750909499824047, -0.0036205919459462166, 0.09576842933893204, -0.011409252882003784, 0.006168900523334742, -0.049626849591732025, 0.05271302908658981, -0.01656496897339821, -0.04124784842133522, -0.025951707735657692, 0.010699356906116009, 0.01207722257822752, 0.007058134768158197, 0.020574698224663734, 0.013569825328886509, -0.014305769465863705, 0.0007826406508684158, -0.005832474213093519, -0.05884530767798424, -0.05804302543401718, 0.02143578790128231, -0.0240302886813879, 0.041810959577560425, 0.01816464401781559, 0.019666139036417007, -0.010153909213840961, 0.031411658972501755, -0.0003805933229159564, 0.02388080023229122, -0.01333149429410696, 0.0005279991892166436, -0.036430854350328445, -0.009385252371430397, 0.019911563023924828, -0.019900647923350334, 0.09681551903486252, 0.008367346599698067, -0.006990519817918539, -0.020786674693226814, -0.0029785705264657736, -0.08378823846578598, 0.05013673007488251, 0.013817758299410343, 0.039576206356287, 0.0012478024000301957, -0.052167098969221115, 0.009205654263496399, 0.008005031384527683, -0.05039646103978157, -0.029496535658836365, -0.02389027737081051, -0.011927253566682339, -0.032104041427373886, 0.06062103435397148, 0.026830457150936127, 0.037104710936546326, 0.019879447296261787, -0.07165010273456573, -0.06275252252817154, 0.01956062763929367, -0.013881507329642773, -0.014920780435204506, -0.0140269435942173, 0.006521397270262241, -0.037747982889413834, -0.01052563264966011, 0.06195519492030144, 0.012701158411800861, -0.03182634711265564, 0.007532812189310789, -0.005239328369498253, 0.004089489113539457, -0.005899984389543533, 0.062272269278764725, -0.03921575844287872, -0.05128227546811104, -0.02199077606201172, 0.058116212487220764, 0.02305126003921032, 0.03305304795503616, 0.008501765318214893, -0.06481648236513138, -0.040178295224905014, 0.029607100412249565, -0.03779543191194534, 0.0603736974298954, -0.022701995447278023, -0.00965602695941925, 0.029649654403328896, -0.0012553120031952858, -0.06539439409971237, -0.0024509301874786615, -0.0023259108420461416, -0.016058431938290596, 0.02034306339919567, -0.04447649419307709, -0.016128381714224815, 0.010147069580852985, 0.016266725957393646, 0.02891012467443943, 0.04037325084209442, 0.03533950448036194, -0.009924515150487423, -0.0374256856739521, -0.029152503237128258, 0.002445512218400836, 0.015435205772519112, -0.0031838642898947, -0.04224509373307228, 0.04209107160568237, 0.028376184403896332, -0.05464553460478783, -0.020846739411354065, 0.00862392969429493, 3.391418488263298e-07, 0.02739112079143524, 0.006678035017102957, -0.00017119084077421576, 0.03686898201704025, 0.036473676562309265, -0.03333253040909767, 0.034307703375816345, 0.007054269779473543, -0.07790409028530121, -0.00921280961483717, 0.008996465243399143, -0.01556466519832611, 0.023130090907216072, 0.06887047737836838, -0.0208724495023489, -0.08034864813089371, -0.01228139828890562, -0.060221489518880844, -0.05226950719952583, -0.031411826610565186, 0.09916891157627106, 0.00448501855134964, 0.07533278316259384, 0.009912945330142975, 0.01187516376376152, 0.03537462651729584, -0.001690869452431798, -0.02396489679813385, 0.05145172402262688, 0.03417225182056427, 0.008312923833727837, -0.011330932378768921, -0.032694198191165924, 0.014297460205852985, -0.05679326131939888, -0.057992927730083466, -0.03725973516702652, 0.010517611168324947, 0.01835687831044197, 0.08191577345132828, 0.01880350522696972, -0.06813786178827286, 0.006661998573690653, -0.04019226133823395, 0.0534675195813179, 0.020409440621733665, -0.034824252128601074, 0.05813688039779663, -0.047409988939762115, -0.0015970197273418307, 0.03595800697803497, 0.010683493688702583, -0.05358387157320976, -0.006856719497591257, -0.03972997888922691, 0.0043693967163562775, -0.005598976742476225, -0.03236996382474899, 0.040355533361434937, 0.047899868339300156, -0.005157799925655127, -0.024218490347266197, -0.001995108090341091, -0.042245738208293915, 0.05150187388062477, -0.034092504531145096, 0.026811882853507996, 3.541114513303494e-34, 0.013418332673609257, 0.015808071941137314, -0.001215452211908996, -0.03394148126244545, 0.016469327732920647, 0.0062222108244895935, -0.02906777895987034, -0.033011168241500854, -0.02139544114470482, -0.0006497537833638489, 0.009529784321784973]

['Vitaly Feldman']

0909.2927v1

We consider the problem of boosting the accuracy of weak learning algorithms in the agnostic learning framework of Haussler (1992) and Kearns et al. (1992). Known algorithms for this problem (Ben-David et al., 2001; Gavinsky, 2002; Kalai et al., 2008) follow the same strategy as boosting algorithms in the PAC model: the weak learner is executed on the same target function but over different distributions on the domain. We demonstrate boosting algorithms for the agnostic learning framework that only modify the distribution on the labels of the points (or, equivalently, modify the target function). This allows boosting a distribution-specific weak agnostic learner to a strong agnostic learner with respect to the same distribution. When applied to the weak agnostic parity learning algorithm of Goldreich and Levin (1989) our algorithm yields a simple PAC learning algorithm for DNF and an agnostic learning algorithm for decision trees over the uniform distribution using membership queries. These results substantially simplify Jackson's famous DNF learning algorithm (1994) and the recent result of Gopalan et al. (2008). We also strengthen the connection to hard-core set constructions discovered by Klivans and Servedio (1999) by demonstrating that hard-core set constructions that achieve the optimal hard-core set size (given by Holenstein (2005) and Barak et al. (2009)) imply distribution-specific agnostic boosting algorithms. Conversely, our boosting algorithm gives a simple hard-core set construction with an (almost) optimal hard-core set size.

Distribution-Specific Agnostic Boosting

http://arxiv.org/pdf/0909.2927v1

Title DistributionSpecific Agnostic Boosting Summary consider problem boosting accuracy weak learning algorithm agnostic learning framework Haussler 1992 Kearns et al 1992 Known algorithm problem BenDavid et al 2001 Gavinsky 2002 Kalai et al 2008 follow strategy boosting algorithm PAC model weak learner executed target function different distribution domain demonstrate boosting algorithm agnostic learning framework modify distribution label point equivalently modify target function allows boosting distributionspecific weak agnostic learner strong agnostic learner respect distribution applied weak agnostic parity learning algorithm Goldreich Levin 1989 algorithm yield simple PAC learning algorithm DNF agnostic learning algorithm decision tree uniform distribution using membership query result substantially simplify Jacksons famous DNF learning algorithm 1994 recent result Gopalan et al 2008 also strengthen connection hardcore set construction discovered Klivans Servedio 1999 demonstrating hardcore set construction achieve optimal hardcore set size given Holenstein 2005 Barak et al 2009 imply distributionspecific agnostic boosting algorithm Conversely boosting algorithm give simple hardcore set construction almost optimal hardcore set size Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.05243123322725296, 0.05108794942498207, 0.0026477654464542866, -0.002771994797512889, -0.009207441471517086, -0.048029303550720215, -0.00439096475020051, 0.02857935056090355, -0.06683926284313202, -0.006493738386780024, 0.029804393649101257, 0.011956808157265186, 0.0057716709561645985, 0.07013380527496338, 0.00959957018494606, -0.03390870988368988, -0.005704029463231564, 0.03430890291929245, -0.04567307233810425, -0.019188083708286285, -0.02531661093235016, -0.048819106072187424, -0.012248346582055092, 0.01792534627020359, -0.05128604546189308, -0.01488723885267973, -0.018483789637684822, 0.01143517717719078, -0.006439608056098223, -0.02594166249036789, 0.0672660619020462, 0.003626239253208041, -0.03012581542134285, 0.029757795855402946, 2.4659848349983804e-06, -0.0156398918479681, -0.02462424896657467, -0.016017509624361992, 0.011653361842036247, -0.007456417195498943, -0.038902852684259415, 0.008453678339719772, -0.005171232856810093, 0.01187810953706503, -0.028396479785442352, -0.03082471340894699, 0.04614314064383507, 0.0740494653582573, 0.014818661846220493, 0.031085075810551643, 0.0036801169626414776, -0.02747858315706253, 0.024052195250988007, -0.04276909679174423, 0.03384383022785187, -0.013834905810654163, 0.01753833331167698, -0.030726484954357147, -0.02460356615483761, -0.0148055674508214, -0.028869234025478363, 0.007032714784145355, 0.033899929374456406, 0.01274734828621149, 0.07726035267114639, 0.013899064622819424, -0.07066643238067627, 0.025846874341368675, -0.01019828300923109, 0.03569663316011429, -0.06674136966466904, -0.02250637859106064, -0.038497935980558395, -0.022973185405135155, -0.017189113423228264, 0.028185255825519562, -0.04006423428654671, -0.0008489821339026093, -0.06240460276603699, 0.03407365828752518, -0.0137496842071414, 0.06565386801958084, 0.018859680742025375, -0.007362651638686657, -0.0005764384404756129, 0.07578761875629425, -0.014432670548558235, 0.03304709494113922, 0.008663421496748924, 0.000738651433493942, -0.05287947878241539, -0.027241859585046768, -0.0051985327154397964, -0.006013949867337942, -0.012629977427423, -0.037202585488557816, -0.016004087403416634, 0.02828727290034294, 0.05716735124588013, -0.00856931321322918, 0.06079908087849617, -0.029720008373260498, -0.0487460196018219, -0.0005172452074475586, -0.006199716590344906, -0.04614808037877083, -0.010987512767314911, 0.01799507439136505, -0.0010730924550443888, 0.033852990716695786, -0.03771945834159851, 0.012249668128788471, -0.0036645985674113035, 0.062155112624168396, -0.01019564364105463, -0.007463788613677025, -0.0948488861322403, 0.005759681109338999, -0.018263567239046097, -0.03709308058023453, 0.04200335219502449, 0.036372918635606766, 0.0032884327229112387, 0.053801529109478, 0.019158096984028816, 0.023464534431695938, -0.07133721560239792, 0.03616977855563164, -0.015678495168685913, -0.0070216418243944645, 0.025155792012810707, 0.010213273577392101, -0.010170497931540012, 0.011110466904938221, 0.03213253989815712, 0.05120421200990677, 0.01371032278984785, -0.030341140925884247, -0.030821718275547028, 0.014910932630300522, 0.008647670038044453, -0.014285231940448284, -0.06179551035165787, -0.08157768845558167, -0.017690256237983704, -0.0178766418248415, -0.00011757142783608288, 0.021975990384817123, 0.011034924536943436, -0.025009499862790108, -0.01196406688541174, 0.044679369777441025, -0.005772324278950691, 0.021873805671930313, 0.07262305915355682, 0.004565727431327105, -0.038611993193626404, 0.07074980437755585, -0.018471403047442436, 0.028447775170207024, 0.03803307190537453, 0.008822986856102943, -0.00876377522945404, -0.01772044226527214, -0.006785417441278696, -0.01572282798588276, -0.008406554348766804, -0.05594002082943916, -0.08461091667413712, -0.03554286062717438, -0.044854506850242615, -0.03426169604063034, -0.007650370243936777, -0.07410319894552231, 0.02409341000020504, -0.016936030238866806, 0.04134036973118782, -0.0034411319065839052, -0.0554840974509716, -0.0002110337227350101, 0.0019967160187661648, -0.02624444104731083, -0.015590106137096882, 0.02966204099357128, -0.05914061516523361, -0.04057743400335312, -0.09080441296100616, 0.024771591648459435, -0.05694616213440895, -0.03988046571612358, 0.015832724049687386, -0.03979504853487015, -0.06466946750879288, -0.011298872530460358, 0.06357273459434509, 0.007115175481885672, 0.0006164229125715792, -0.016226382926106453, 0.03246798366308212, -0.0035969922319054604, -0.06199086084961891, -0.0561693012714386, 0.022206712514162064, -0.06946384161710739, -0.018107250332832336, -0.06174603849649429, -0.02570236101746559, -0.008954712189733982, 0.022882947698235512, -0.05119573697447777, -0.02613266557455063, -0.003534071845933795, 0.027113329619169235, -0.01893860474228859, -0.020414985716342926, 0.00821137148886919, 0.0393875353038311, 0.0070374878123402596, -0.00031437617144547403, 0.00040711965993978083, -0.02449781820178032, -0.013035138137638569, 0.004070389550179243, 0.023716552183032036, 0.08051957190036774, 0.01378820650279522, 0.08732207119464874, 0.04480172321200371, 0.02608541212975979, 0.03380518779158592, 0.019351501017808914, -0.022697556763887405, 0.04427246376872063, -0.05906069651246071, -0.05568917840719223, -0.0012063868343830109, 0.011325212195515633, -0.020880049094557762, 0.012396962381899357, -0.02861705794930458, 0.03674476966261864, 0.04034716635942459, -0.025916891172528267, -0.047412481158971786, -0.014369511976838112, -0.019546858966350555, -0.003942012786865234, -0.0428067110478878, 0.04568721354007721, -0.004172169137746096, 0.04430873319506645, -0.03329549357295036, 0.07285118848085403, -0.0007167645380832255, 0.020084120333194733, -0.054771874099969864, 0.033541128039360046, 0.08641903847455978, 0.001724167843349278, 0.0013278332771733403, 0.019194943830370903, -0.054511405527591705, -0.0007040228229016066, 0.041272956877946854, -0.0024432281497865915, 0.02469385787844658, 0.02759401686489582, 0.02594909258186817, 0.008526608347892761, -0.003691123565658927, 0.007129862438887358, -0.010792145505547523, 0.00967795867472887, 0.007138870656490326, -0.011948463506996632, -0.05636032298207283, 0.04631105810403824, 0.0014770289417356253, -0.03535664826631546, 0.021808292716741562, 0.01625274121761322, -0.00877778884023428, 0.02862253226339817, -0.034605637192726135, 0.012767205014824867, 0.019004257395863533, 0.031146593391895294, -0.07954981178045273, -0.015715893357992172, 0.0050114961341023445, -0.0031585635151714087, 0.0008780939970165491, -0.02397388219833374, -0.023682838305830956, -0.02444179356098175, 0.010413452051579952, -0.01967792771756649, 0.05677465721964836, 0.0323936827480793, -0.012580870650708675, -0.009571763686835766, 0.06903663277626038, -0.028646638616919518, -0.0061468747444450855, -0.02440301887691021, -0.0448196604847908, 0.07470068335533142, -0.00018948002252727747, 0.014326888136565685, 0.042994532734155655, 0.01909611001610756, -0.002447569975629449, -0.01749054715037346, -0.018601972609758377, 0.016358215361833572, -0.005657742731273174, -0.06617309153079987, 0.02512936107814312, 0.004272630903869867, -0.019600940868258476, -0.0027991710230708122, -0.07708249241113663, 0.052244026213884354, 0.0401136539876461, 0.012333391234278679, -0.013219436630606651, -0.0704273208975792, -0.03397512063384056, -0.05843759700655937, 0.02002016268670559, 0.018731705844402313, -0.00823616236448288, -0.03861027956008911, -0.018553996458649635, 0.010979590937495232, 0.01741422340273857, -0.044848181307315826, 0.030388392508029938, 0.03931242227554321, -0.008086426183581352, -0.008301406167447567, -0.050628576427698135, -0.04087749496102333, -0.03344384953379631, 0.07132402807474136, 0.007772028911858797, -0.0012970841489732265, -0.036309387534856796, -0.015158262103796005, 0.036439791321754456, -0.029468998312950134, 0.03930846229195595, -0.07323196530342102, -0.01025472953915596, 0.03688666597008705, 0.010174982249736786, 0.010839193128049374, -0.06436048448085785, -0.03254297748208046, -0.05225544795393944, -0.014078459702432156, 0.027532927691936493, 0.027456335723400116, 0.049289871007204056, -0.03434211388230324, 0.022512679919600487, -0.005092808976769447, 0.009330513887107372, -0.02926083654165268, -0.002722423290833831, 0.061330024152994156, 0.010790103115141392, 0.042748693376779556, 0.010988828726112843, 0.019023366272449493, -0.051250092685222626, 0.012871676124632359, -0.0131536228582263, 0.026885824277997017, 0.030041879042983055, -0.026174139231443405, -0.0641775131225586, -0.003347676247358322, -0.027628934010863304, 0.0656280443072319, -0.036784589290618896, -0.06887277215719223, 0.0407402403652668, -0.07220624387264252, 0.00835892278701067, 0.02355496771633625, -0.07998012006282806, -0.0023642457090318203, -0.02674405463039875, 0.038419369608163834, -0.03943967819213867, -0.06331846117973328, -0.02420992963016033, 0.02607693336904049, -0.0377030111849308, 0.06881071627140045, -0.0010913551086559892, -0.031667158007621765, -0.006549855228513479, -0.10172812640666962, -0.03558314964175224, 0.010096023790538311, 0.03990499675273895, -0.040616121143102646, -0.008955549448728561, 0.008128060959279537, 3.823804945568554e-06, 0.004245473071932793, -0.006349184084683657, 0.069999098777771, 0.011296266689896584, 0.005171727854758501, 0.019443118944764137, 0.04552489146590233, -0.02862362004816532, 0.039266496896743774, 0.06461790204048157, 0.037037160247564316, -0.024693051353096962, 0.02008621208369732, -0.035379134118556976, -0.025047950446605682, 0.04892811179161072, 0.011151331476867199, -0.03618035465478897, -0.011901063844561577, 0.0016128619899973273, -0.021966559812426567, 0.019216032698750496, 0.03201818838715553, 0.021624520421028137, 0.07929277420043945, -0.015568639151751995, -0.0761481374502182, -0.08412668853998184, 0.0206319447606802, -0.002776164561510086, 0.07685176283121109, -0.013000397011637688, 0.05115601420402527, -0.07150290906429291, 0.013029731810092926, -0.05547058954834938, -0.01929023303091526, 0.05310473591089249, 0.07088251411914825, -0.03528277575969696, -0.05508312210440636, 0.024299373850226402, 3.739680323633365e-05, -0.006919302977621555, -0.0486377477645874, 0.005732457619160414, -0.026478765532374382, -0.0029091513715684414, 0.06208697333931923, 0.018978029489517212, -0.047877974808216095, -0.053984928876161575, -0.0014729881659150124, 0.02088133431971073, 0.16028881072998047, 0.029158955439925194, -0.0016205835854634643, 0.030661363154649734, -0.07092642039060593, -0.023884328082203865, 0.0019784336909651756, -0.0028446773067116737, 0.08592452108860016, 0.006940921302884817, -0.021047990769147873, -0.018932830542325974, 0.005091995932161808, 0.004393862094730139, 0.04060979187488556, 0.024498309940099716, -0.00989722553640604, -0.03682424873113632, 0.0022258784156292677, 0.05078820139169693, 0.01931927166879177, 0.017044033855199814, -0.011515775695443153, 0.02076825685799122, 0.05340127274394035, 0.017212608829140663, -0.004713102709501982, -0.022008242085576057, 0.04711924493312836, 0.05275072529911995, -0.04939799755811691, 0.06159050017595291, 0.00023755802249070257, 0.06076991185545921, -0.0179721899330616, 0.01672065258026123, 0.028505967929959297, -0.04883371666073799, 0.0762839987874031, 0.03246124088764191, 0.00884449016302824, 0.037452779710292816, 0.019595446065068245, 0.030457613989710808, -0.051817264407873154, 0.0038633772637695074, -0.013898261822760105, -0.013806985691189766, -0.04346809536218643, 0.02883104793727398, 0.03684001788496971, -0.016122503206133842, -0.024398289620876312, -0.021753353998064995, -0.003948362078517675, -0.033742643892765045, 0.017539087682962418, -0.01704441010951996, 0.011030137538909912, 0.042295582592487335, 0.014323869720101357, -0.012747577391564846, -0.006238067522644997, 0.044473689049482346, 0.036686044186353683, 0.011966604739427567, -0.058042459189891815, -0.011002196930348873, -0.034511685371398926, 0.0552779920399189, 0.06034242361783981, 0.06097716465592384, 0.013180462643504143, 0.01732013374567032, -0.04037242755293846, -0.020099854096770287, -0.0021926602348685265, -0.006061391904950142, 0.10596273094415665, 0.020443055778741837, 0.008516342379152775, 0.022148460149765015, -0.03249979764223099, -0.019435610622167587, -0.04776772856712341, -0.0012348718009889126, 0.028175057843327522, 0.03665320202708244, -0.014059864915907383, -6.319178450112297e-33, 0.00369458575733006, -0.017438700422644615, -0.05571945756673813, 0.010356196202337742, -0.020709408447146416, 0.03372424095869064, -0.0012661450309678912, -0.01001972146332264, 0.03760949894785881, -0.02565319836139679, -0.036744434386491776, 0.019165966659784317, 0.015382167883217335, 0.009243417531251907, -0.008368058130145073, -0.0034827166236937046, 0.01095963828265667, 0.001977117033675313, -0.026943359524011612, 0.0008803550736047328, 0.024658894166350365, 0.022374404594302177, 0.009525240398943424, -0.08710885792970657, -0.0634462758898735, 0.03373520076274872, -0.02787848562002182, 0.014570018276572227, -0.009759737178683281, 0.023314176127314568, 0.054734669625759125, 0.046949632465839386, 0.0221856776624918, 0.0030143659096211195, 0.011393105611205101, -0.04251544922590256, -0.03584418073296547, -0.007789779454469681, -0.038747746497392654, 0.004657055251300335, -0.003961545415222645, 0.06920914351940155, 0.04795508086681366, -0.009561236016452312, 0.01763288863003254, 0.018710210919380188, 0.02691521868109703, -0.0843420997262001, -0.01784052699804306, -0.01963910460472107, 0.019183212891221046, 0.03535095602273941, 0.034381765872240067, 0.03557879850268364, -0.022555530071258545, -0.018868526443839073, -0.011722459457814693, -0.0037300281692296267, 0.048269469290971756, 0.03028721734881401, 0.03708671033382416, 0.03366268053650856, -0.007826283574104309, 0.030239984393119812, 0.021774444729089737, 0.031461942940950394, 0.053401827812194824, -0.015592200681567192, 0.007708946708589792, -0.028154607862234116, 0.00893485825508833, 0.06165961176156998, 0.02511105127632618, 0.05946747586131096, 0.11472286283969879, -0.06086019426584244, -0.07169721275568008, 0.08294747024774551, 0.04952185973525047, -0.033571112900972366, -0.018948698416352272, 0.026126092299818993, -0.06595068424940109, -0.014503094367682934, 0.041524603962898254, -0.018359415233135223, -0.0055471244268119335, -0.04464682191610336, 0.008254692889750004, 0.03227320313453674, -0.048190638422966, 0.08176103234291077, -0.010171194560825825, -0.03438941761851311, -0.0031800996512174606, 0.053182363510131836, 0.005734468810260296, 0.0187839362770319, -0.005625531077384949, -0.06325366348028183, -0.02247469313442707, -0.02739301323890686, -0.02558046579360962, -0.02430199645459652, 0.011804413981735706, 0.01146153174340725, 0.03838473930954933, 0.033239349722862244, -0.02851208671927452, -0.013568420894443989, -0.008675753138959408, -0.020169390365481377, 0.025619441643357277, 0.07485078275203705, 0.029373040422797203, -0.05762989819049835, 0.00041761001921258867, 0.020367328077554703, 0.008257079869508743, 0.006008684169501066, -0.03246234357357025, 0.003509792499244213, -0.023217491805553436, 0.027972685173153877, -0.02675691433250904, 0.020344886928796768, 0.003677795408293605, -0.0334085114300251, 0.04591221734881401, -0.11817961186170578, -0.008532228879630566, -0.044508010149002075, 3.0431559139287856e-07, 0.009546283632516861, -0.0036258602049201727, -0.03360535949468613, -0.023945661261677742, -0.03140822425484657, 0.005175688304007053, -0.039832212030887604, 0.02003048174083233, -0.024870654568076134, -0.026390722021460533, 0.0009585646912455559, -0.032193757593631744, 0.01587541773915291, 0.023268865421414375, -0.06269802153110504, 9.043665158969816e-06, -0.0029505789279937744, 0.026218341663479805, -0.021763252094388008, -0.0024216403253376484, -0.0014959766995161772, 0.09631423652172089, 0.049746956676244736, -0.069237619638443, 0.05713217332959175, 0.005497131496667862, -0.001271502347663045, 0.003904273733496666, 0.01573094166815281, 0.02528277225792408, 0.018895264714956284, -0.060713592916727066, 0.025749703869223595, 0.04417038708925247, -0.028037462383508682, 0.03594985976815224, 0.05373024567961693, 0.012082957662642002, -0.050525981932878494, 0.03766806423664093, -0.006373670883476734, 0.008293974213302135, 0.024588728323578835, -0.008583420887589455, 0.0424937829375267, -0.023658543825149536, -0.0368429534137249, -0.03867686167359352, -0.03961189091205597, 0.006299849599599838, 0.037670645862817764, 0.003354992251843214, -0.026617106050252914, 0.039296116679906845, -0.019159480929374695, -0.026488540694117546, 0.042818833142519, -0.021487625315785408, -0.008940385654568672, 0.03723680227994919, -0.010627473704516888, -0.0035573425702750683, -0.009177622385323048, 0.05566057190299034, -0.002508615143597126, 0.012141176499426365, -0.04668841511011124, 3.480016128120842e-34, 0.00998533982783556, -0.02150142937898636, 0.009491276927292347, -0.009994134306907654, -0.027855968102812767, -0.010613184422254562, 0.048194386065006256, -0.006851853337138891, 0.0024462700821459293, 0.03624366223812103, -0.007354561239480972]

['Prahladh Harsha', 'Adam Klivans', 'Raghu Meka']

0909.5175v4

We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of polynomial threshold functions. More specifically, for a Boolean function f on n variables equal to the sign of a real, multivariate polynomial of total degree d we prove 1) The average sensitivity of f is at most O(n^{1-1/(4d+6)}) (we also give a combinatorial proof of the bound O(n^{1-1/2^d}). 2) The noise sensitivity of f with noise rate \delta is at most O(\delta^{1/(4d+6)}). Previously, only bounds for the linear case were known. Along the way we show new structural theorems about random restrictions of polynomial threshold functions obtained via hypercontractivity. These structural results may be of independent interest as they provide a generic template for transforming problems related to polynomial threshold functions defined on the Boolean hypercube to polynomial threshold functions defined in Gaussian space.

Bounding the Sensitivity of Polynomial Threshold Functions

http://arxiv.org/pdf/0909.5175v4

Title Bounding Sensitivity Polynomial Threshold Functions Summary give first nontrivial upper bound average sensitivity noise sensitivity polynomial threshold function specifically Boolean function f n variable equal sign real multivariate polynomial total degree prove 1 average sensitivity f On114d6 also give combinatorial proof bound On112d 2 noise sensitivity f noise rate delta Odelta14d6 Previously bound linear case known Along way show new structural theorem random restriction polynomial threshold function obtained via hypercontractivity structural result may independent interest provide generic template transforming problem related polynomial threshold function defined Boolean hypercube polynomial threshold function defined Gaussian space Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0954098254442215, 0.007409115321934223, -0.02328428626060486, 0.03325900807976723, 0.0005668032681569457, -0.026422793045639992, 0.0239508505910635, -0.014700226485729218, 0.016340024769306183, -0.0098295072093606, 0.026747964322566986, 0.04693956300616264, -0.02410968951880932, 0.06598447263240814, -0.026375308632850647, 0.0065853106789290905, -0.019100138917565346, -0.03413061797618866, 0.003447499591857195, -0.05254783108830452, 0.0039308937266469, -0.026107123121619225, -0.015358785167336464, -0.010021528229117393, -0.04525787755846977, -0.02928456850349903, 0.058497339487075806, -0.03816813603043556, -0.02198229543864727, 0.007296134252101183, -0.01621871255338192, 0.03861235827207565, -0.03014187142252922, -0.049291059374809265, 1.6926642274484038e-06, -0.04146246239542961, -0.0014812886947765946, -0.0014872465981170535, 0.0221436507999897, 0.026089828461408615, -0.028207357972860336, 0.030709106475114822, 0.002760254545137286, -0.012124921195209026, 0.024962587282061577, -0.018786398693919182, -0.018706515431404114, 0.04523438587784767, -0.03911188244819641, -0.0040647294372320175, -0.01870083436369896, 0.06589850038290024, 0.06045427918434143, 0.01541114691644907, 0.03302723541855812, -0.08297350257635117, -0.012871102429926395, -0.0296691432595253, -0.018932342529296875, -0.03345637023448944, -0.026154035702347755, 0.02248084917664528, 0.005582255776971579, -0.021503135561943054, 0.039821915328502655, -0.0030470199417322874, -0.009218927472829819, 0.04742050915956497, -0.03267620876431465, 0.008112139999866486, -0.09000777453184128, -0.0026433118619024754, -0.004504062235355377, -0.01338453684002161, 0.004406028892844915, 0.025160562247037888, -0.03858096897602081, -0.013504520058631897, -0.01286880113184452, -0.03997670114040375, -0.052562303841114044, 0.035815007984638214, -0.03704102337360382, 0.05230918526649475, 0.06652224808931351, 0.050514839589595795, 0.033951807767152786, 0.022018222138285637, 0.021246924996376038, -0.04672864079475403, -0.012170377187430859, 0.005626349244266748, -0.004760192707180977, -0.003461538814008236, -0.04534372314810753, -0.040743276476860046, -0.03388132154941559, 0.012835935689508915, 0.009238222613930702, -0.039718978106975555, 0.01852855645120144, -0.029655683785676956, 0.049748193472623825, 0.016083966940641403, -0.012318000197410583, 0.01625114493072033, -0.0698932409286499, 0.017241908237338066, 0.011581797152757645, 0.024466505274176598, 0.020955713465809822, 0.035814277827739716, -0.0023235161788761616, 0.08052971959114075, -0.013047484681010246, 0.020583974197506905, -0.03387327864766121, 0.07247906178236008, 0.0010557615896686912, 0.008860234171152115, -0.03668111935257912, 0.0008362431544810534, -0.031616028398275375, -0.05390213429927826, 0.05030202493071556, 0.0023794120643287897, 0.00012183994840597734, 0.046028465032577515, -0.02549765817821026, -0.015038718469440937, -0.009171590209007263, 0.045380428433418274, 0.01337499264627695, -0.005664922297000885, -0.02366728149354458, 0.01922973431646824, -0.01538209430873394, -0.038275811821222305, 0.06303556263446808, -0.019249852746725082, -0.05174795538187027, 0.029095852747559547, -0.03739720582962036, -0.045150235295295715, -0.05583340674638748, -0.0011317685712128878, 0.005805053748190403, 0.012635400518774986, 0.014379091560840607, -0.06289152055978775, 0.021173175424337387, 0.050592031329870224, 0.06980421394109726, -0.06877568364143372, 0.07913347333669662, -0.007620623335242271, -0.03758968040347099, 0.04748047515749931, 0.014547931030392647, 0.039501387625932693, 0.007960828952491283, 0.008690972812473774, 0.030161313712596893, -0.05380681902170181, -0.011584785766899586, 0.00035268798819743097, 0.003521809820085764, -0.013584990054368973, 0.04374505952000618, -0.014172538183629513, 0.009155809879302979, 0.018732719123363495, -0.012838578782975674, -0.06050359830260277, 0.03454307094216347, 0.03835613280534744, -0.022511551156640053, -0.018682053312659264, -0.07808931916952133, 0.013069750741124153, -0.018997885286808014, 0.021286161616444588, -0.013263413682579994, 0.03870173171162605, -0.11484518647193909, -0.004107198677957058, 0.02259780839085579, -0.019922902807593346, -0.0005427010473795235, -0.03178062662482262, -0.011231680400669575, 0.018938187509775162, -0.01682116650044918, -0.035959839820861816, 0.031012464314699173, -0.01607988029718399, -0.005756925325840712, -0.017050737515091896, -0.021226271986961365, -0.025757748633623123, -0.010015377774834633, -0.055961426347494125, 0.010847257450222969, -0.09941644221544266, -0.021972788497805595, -0.05261802300810814, 0.058274514973163605, 0.002471323823556304, -0.009441441856324673, -0.020789848640561104, 0.04638461396098137, 0.0008719463949091733, 0.04630616307258606, 0.01840250752866268, 0.03662134334445, 0.023998508229851723, 0.043822817504405975, -0.000872631324455142, -0.01158029306679964, -0.00956788845360279, -0.03309810161590576, 0.036191176623106, -0.012372179888188839, -0.028135064989328384, 0.029427967965602875, -0.011573557741940022, 0.043879177421331406, 0.012754031457006931, 0.0065232072956860065, 0.012241827324032784, -0.011861459352076054, -0.002702802885323763, 0.010545319877564907, -0.0619530975818634, -0.006621376611292362, -0.03077635169029236, 0.047412533313035965, -0.010645792819559574, 0.0074858409352600574, -0.04582671821117401, 0.04077998548746109, 0.030953237786889076, 0.015290561132133007, 0.0341283418238163, 0.06792287528514862, -0.006508212070912123, -0.015913331881165504, -0.03971998766064644, -0.039999768137931824, -0.01893284171819687, 0.04160599038004875, 0.010204178281128407, -0.026649532839655876, -0.006404155399650335, 0.08535496890544891, -0.026936963200569153, -0.03327200189232826, 0.03658594563603401, -0.01805322989821434, -0.0023135626688599586, 0.0025986351538449526, -0.0346812903881073, 0.007986016571521759, 0.001178302220068872, 0.004136570263653994, 0.05542517825961113, -0.005675408523529768, 0.03947603330016136, -0.02721806801855564, 0.02411172352731228, 0.0008949849288910627, 2.9473090762621723e-05, -0.007460154592990875, 0.03748448193073273, -0.01740957796573639, 0.01957775093615055, 0.04757639765739441, -0.026846805587410927, -0.04225299879908562, 0.07005929201841354, -0.026058882474899292, -0.02497907727956772, -0.007788983639329672, 0.0008648977382108569, 0.014723568223416805, 0.006359435152262449, 0.015704521909356117, -0.0621674619615078, 0.05895017087459564, 0.06377574801445007, 0.02870696410536766, 0.03190432861447334, 0.01459629088640213, -0.035309433937072754, -0.0010774253169074655, -0.02480405755341053, 0.006752118468284607, 0.05025852471590042, 0.015735168009996414, 0.0014861070085316896, -0.007859560661017895, 0.09100030362606049, 0.0168423131108284, 0.005806604865938425, -0.03274518623948097, -0.0438992977142334, 0.022889748215675354, 0.030066296458244324, 0.04867761209607124, 0.014912458136677742, -0.01075618714094162, -0.09026457369327545, -0.027629714459180832, -0.033255912363529205, 0.026033712550997734, -0.024639200419187546, -0.047960326075553894, 0.03135038539767265, -0.010850632563233376, 0.04249022901058197, -0.021918345242738724, -0.009652165696024895, -0.03279006481170654, -0.0042005074210464954, 0.046325501054525375, 0.00314916274510324, -0.019540216773748398, 0.03522111475467682, -0.039762210100889206, 0.029443126171827316, 0.03589984029531479, -0.04685360938310623, -0.01881101354956627, -0.022845009341835976, -0.04006561264395714, 0.016652172431349754, -0.0838056430220604, -0.031089048832654953, 0.014379851520061493, -0.01621590368449688, -0.01632450893521309, -0.00813968013972044, 0.0463048480451107, -0.013600467704236507, 0.07077369838953018, 0.007621333003044128, 0.012828095816075802, -0.020836878567934036, 0.023067457601428032, -0.009234746918082237, -0.020671825855970383, 0.041187457740306854, 0.0021687904372811317, -0.05318591743707657, -0.0007565167616121471, 0.028572125360369682, -0.01478095818310976, 0.006607732269912958, 0.021958976984024048, 0.027066156268119812, -0.013086755760014057, 0.025582728907465935, -0.02193368412554264, 0.11179141700267792, 0.023838145658373833, 0.01297878846526146, 0.004930841736495495, -0.011428149417042732, 0.027905823662877083, 0.03590426594018936, 0.014297215268015862, 0.03383519873023033, 0.032302375882864, -0.017964426428079605, -0.006346605252474546, 0.0004752026579808444, 0.009299837052822113, 0.0015434939414262772, 0.010746936313807964, 0.05412086844444275, -0.0014486854197457433, 0.027728158980607986, 0.031873658299446106, -0.003259442513808608, 0.009311609901487827, -0.017866570502519608, -0.024005545303225517, 0.014001509174704552, -0.0680660530924797, -0.027975032106041908, -0.03685145452618599, 0.008687355555593967, -0.08272086083889008, 0.005372955929487944, 0.03991448134183884, -0.04829505831003189, 0.016514532268047333, -0.027311643585562706, 0.031151391565799713, -0.04731776565313339, 0.039729900658130646, 0.013924045488238335, -0.06109657511115074, 0.0013840018073096871, -0.06733223050832748, 0.005415872670710087, -0.05337080359458923, 0.012393036857247353, -0.0452352799475193, -0.03811027109622955, -0.016021111980080605, 0.03667664900422096, -0.005226314999163151, -0.012583227828145027, 0.024864263832569122, 0.022926408797502518, -0.0034300321713089943, 0.03171210363507271, 0.0011239773593842983, 0.021036885678768158, 0.005464165471494198, -0.006985137704759836, 0.03559301421046257, 0.07300511747598648, 0.014666687697172165, 0.015811737626791, 0.0036682356148958206, -0.0014229376101866364, -0.0025772450026124716, -0.001647024299018085, -0.002899624640122056, -0.012978415004909039, -0.03880074992775917, 0.03629566356539726, -0.011709682643413544, 0.013043739832937717, 0.026476332917809486, -0.014582257717847824, -0.04548689350485802, -0.0853363648056984, 0.11397620290517807, -0.00842980295419693, 0.06980355829000473, -0.008878455497324467, -0.02616853639483452, -0.004559492692351341, -0.027385063469409943, 0.027728738263249397, -0.015645133331418037, 0.034945376217365265, -0.006712388712912798, 0.025243394076824188, 0.06168822944164276, 0.004656810313463211, -0.01776546984910965, -0.030383184552192688, -0.02500917576253414, -0.04129977151751518, -0.014988794922828674, 0.019245384261012077, -0.004554209299385548, 0.0191205907613039, -0.06464515626430511, 0.001973350765183568, -0.025381404906511307, 0.018865667283535004, 0.010980796068906784, 0.0026093206834048033, 0.05704201012849808, 0.06626828014850616, -0.027606109157204628, -0.02201133407652378, 0.0377323217689991, -0.008323469199240208, 0.03166361153125763, 0.02223431132733822, -0.01081919763237238, -0.05134514719247818, -0.0661175474524498, 0.0192502960562706, 0.0028414158150553703, 0.02907324768602848, 0.09377903491258621, -0.014456038363277912, -0.03502301126718521, 0.09134078770875931, 0.03713377192616463, 0.007733596488833427, -0.015804771333932877, 0.006309520918875933, 0.05017119646072388, -0.04365771636366844, -0.030986160039901733, -0.0700559914112091, 0.06230314448475838, 0.021988844498991966, -0.00134158821310848, -0.007292840164154768, -0.014697331935167313, -0.0162451583892107, 0.014564122073352337, 0.001275524846278131, -0.03636293113231659, 0.015200918540358543, 0.035923659801483154, -0.009250796400010586, 0.011370331980288029, -0.008456369861960411, -0.017199460417032242, -0.02259029820561409, -0.008464884012937546, -0.025690661743283272, -0.06604290008544922, -0.0019766585901379585, -0.017506258562207222, -0.01624501869082451, -0.0111555689945817, 0.053712692111730576, -0.0029655424878001213, -0.06425623595714569, -0.06138662248849869, -0.03287942707538605, 0.01790527068078518, 0.037658922374248505, 0.06309609115123749, 0.011716951616108418, -0.0077492413111031055, -0.0011202202877029777, 0.019548466429114342, 0.002824366558343172, -0.0071596489287912846, -0.00020634234533645213, -0.030726442113518715, 0.008991575799882412, -0.018083473667502403, 0.0308779738843441, -0.00711043132469058, 0.08097933977842331, 0.05020912364125252, 0.061824653297662735, -0.010741963982582092, -0.0055275349877774715, 0.034152258187532425, -0.004204219207167625, 0.05193980038166046, 0.017386550083756447, -0.053328417241573334, -0.04350066930055618, 0.001418980653397739, -0.00493346294388175, 0.025873269885778427, -0.004868052899837494, 0.016548186540603638, -0.004108757711946964, -0.06670132279396057, -5.5803376389502723e-33, -0.06695176661014557, -0.021252475678920746, -0.11191655695438385, 0.02156948484480381, 0.020678376778960228, 0.03421051427721977, 0.06847087293863297, 0.010199563577771187, 0.0010610537137836218, -0.004478433635085821, 0.016807354986667633, 0.016871778294444084, 0.006432488095015287, 0.021280812099575996, -0.011281185783445835, -0.001437614788301289, -0.004477883689105511, -0.027755074203014374, -3.103971948803519e-06, 0.00209930632263422, 0.02895394153892994, -0.038157254457473755, 0.006423876620829105, -0.017727497965097427, -0.041200246661901474, 0.0433051623404026, -0.06913012266159058, 0.009094358421862125, -0.050913840532302856, 0.033736638724803925, 0.0327899195253849, 0.028909925371408463, -0.005346017889678478, -0.02737588807940483, 0.022358974441885948, 0.01067956630140543, -0.01316816546022892, -0.03478146344423294, -0.018902931362390518, -0.048890747129917145, 0.0575295016169548, -0.016545370221138, 0.045085906982421875, -0.02159809321165085, -0.03441097214818001, -0.050519075244665146, 0.030167873948812485, -0.02719787508249283, -0.03303186222910881, -0.08541708439588547, 0.029720935970544815, 0.005790598224848509, -0.03215847536921501, 0.05613309517502785, -0.047634877264499664, -0.02324029617011547, -0.017772145569324493, -0.026983143761754036, 0.01936051808297634, 0.02001095563173294, 0.05003778263926506, 0.07016119360923767, -0.042366545647382736, -0.008975189179182053, 0.0005413891631178558, -0.037048544734716415, 0.0826776996254921, 0.03702725097537041, 0.06090979278087616, -0.05772162973880768, 0.01431493740528822, -0.0726630762219429, 0.007586897816509008, 0.097058966755867, 0.0744861289858818, -0.05378439649939537, -0.07796140760183334, -0.019911903887987137, -0.06613675504922867, 0.035213030874729156, 0.04223579540848732, -0.02408994734287262, -0.039925988763570786, -0.011425218544900417, -0.00638360483571887, 0.0292002335190773, -0.010005485266447067, 0.034248195588588715, -0.02094731107354164, 0.0036650625988841057, -0.012672667391598225, -0.021387562155723572, -0.02311048097908497, 0.008050895296037197, 0.006413970608264208, -0.020580321550369263, 0.04521234706044197, 0.05134798586368561, -0.015558041632175446, 0.011885382235050201, 0.048801716417074203, 0.009309101849794388, -0.02356444112956524, -0.023189812898635864, 0.01744781993329525, 0.012866812758147717, 0.002524473937228322, 0.021363666281104088, -0.07659713178873062, -0.017655108124017715, 0.01565796695649624, -0.005914495792239904, 0.05368770286440849, 0.1254952847957611, 0.010354932397603989, -0.1260215938091278, -0.04717467725276947, 0.017037509009242058, 0.011524842120707035, 0.022286493331193924, 0.0064868866465985775, 0.055811334401369095, -0.05112835019826889, 0.03489818796515465, -0.021603185683488846, 0.004970652516931295, -0.005828606430441141, -0.05306768789887428, 0.014563904143869877, -0.00022560599609278142, -0.017448745667934418, -0.012704608030617237, 2.483335492797778e-07, 0.006528811529278755, 0.01573931984603405, -0.06832695752382278, 0.04085936397314072, 0.03741806373000145, -0.0320090726017952, -0.002551282988861203, 0.06410570442676544, -0.01949411630630493, 0.02283596806228161, -0.03836937993764877, -0.032742518931627274, 0.003775231773033738, -0.025005266070365906, 0.04376600310206413, -0.08325257152318954, 0.05374067276716232, 0.11326497793197632, 0.006487561389803886, 0.07706153392791748, 0.0535542331635952, 0.008635570295155048, 0.0030687442049384117, 0.032827578485012054, 0.014630964957177639, -0.019905151799321175, -0.010625596158206463, -0.07569417357444763, 0.015568706206977367, 0.011824693530797958, 0.042941104620695114, -0.048810843378305435, -0.0035951328463852406, 0.05772029235959053, 0.014554683119058609, 0.03165561705827713, -0.02903536707162857, 0.02881031110882759, 0.026768922805786133, -0.013687140308320522, 6.079969898564741e-05, -0.03261649236083031, 0.04465483874082565, -0.03317444026470184, 0.033182062208652496, 0.014509251341223717, -0.0207352451980114, -0.008319473825395107, 0.006995399482548237, 0.02769973874092102, 0.05167800188064575, -0.03326838091015816, -0.018502434715628624, -0.066131591796875, -0.03390612453222275, 0.026826806366443634, 0.05725839361548424, 0.04301796853542328, 0.06499817222356796, 0.041507788002491, -0.009554990567266941, -0.08452077209949493, 0.06225235387682915, -0.03092191182076931, 0.03538693115115166, 0.025530915707349777, 0.009729446843266487, 2.7106369379971638e-34, -0.007983553223311901, 0.02708120457828045, 0.03371362015604973, -0.04563657194375992, -0.020826062187552452, 0.0004144749545957893, 0.0026633539237082005, -0.07284574210643768, 0.04850677028298378, -0.02691642940044403, 0.015442213974893093]

['Natalia B. Janson', 'Christopher J. Marsden']

1107.0674v3

We propose an alternative approach to construct an artificial learning system, which naturally learns in an unsupervised manner. Its mathematical prototype is a dynamical system, which automatically shapes its vector field in response to the input signal. The vector field converges to a gradient of a multi-dimensional probability density distribution of the input process, taken with negative sign. The most probable patterns are represented by the stable fixed points, whose basins of attraction are formed automatically. The performance of this system is illustrated with musical signals.

"Memory foam" approach to unsupervised learning

http://arxiv.org/pdf/1107.0674v3

Title Memory foam approach unsupervised learning Summary propose alternative approach construct artificial learning system naturally learns unsupervised manner mathematical prototype dynamical system automatically shape vector field response input signal vector field converges gradient multidimensional probability density distribution input process taken negative sign probable pattern represented stable fixed point whose basin attraction formed automatically performance system illustrated musical signal Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04835788905620575, -0.0039457413367927074, -0.035873204469680786, -7.620686665177345e-05, -0.008316803723573685, -0.04124770313501358, 0.01951499655842781, -0.008734975010156631, -0.03990660235285759, 0.04339568316936493, -0.006893483456224203, 0.007636201102286577, -0.006929332390427589, 0.04931671917438507, 0.026973510161042213, -0.07995342463254929, -0.02433633990585804, -0.008955181576311588, -0.02526722103357315, -0.030926942825317383, 0.006957986392080784, -0.05477866530418396, -0.028907617554068565, 0.014349090866744518, -0.04127170518040657, 0.021603157743811607, -0.0709393247961998, -0.028791140764951706, -0.002503596944734454, -0.05705427750945091, -0.0031020306050777435, -0.010938526131212711, 0.015676533803343773, 0.07562613487243652, 2.1293274130584905e-06, -0.016563385725021362, -0.013556997291743755, -0.03147680312395096, 0.07213978469371796, -0.021229229867458344, -0.012504864484071732, 0.014390331692993641, -0.04947184771299362, -0.033354729413986206, -0.03382149338722229, -0.0018244052771478891, -0.006066564004868269, -0.00890753511339426, 0.07555850595235825, 0.03956625238060951, -0.002679782919585705, -0.08838137239217758, -0.008416618220508099, 0.005925111006945372, 0.0014857520582154393, 0.030944418162107468, 0.006122604012489319, 0.0037775191012769938, 0.004029847681522369, -0.05531167984008789, -0.051627036184072495, 0.04745817184448242, 0.005140942521393299, -0.015549699775874615, 0.0843871608376503, 0.02960832603275776, -0.016931388527154922, -0.02447091042995453, -0.005970606114715338, 0.047642894089221954, -0.042638473212718964, -0.03674037754535675, 0.03555097430944443, 0.0005148840136826038, 0.009955096058547497, 0.01759207807481289, -0.059374336153268814, -0.012538997456431389, -0.02343275211751461, -0.030170945450663567, -0.06604025512933731, -0.0030916675459593534, 0.0009090417879633605, -0.045809824019670486, 0.02707577496767044, 0.0029466014821082354, -0.009688115678727627, -0.004744606092572212, -0.0010750785004347563, -0.06710071861743927, 0.024235939607024193, 0.011687388643622398, 0.029148554429411888, 0.05637319013476372, 0.0019430821994319558, -0.009567417204380035, -0.006113439332693815, -0.07768256962299347, 0.005810040980577469, -0.005980886053293943, 0.1043698787689209, -0.016928082332015038, 0.045878082513809204, 0.014072638936340809, -0.03964763134717941, 0.0011807719711214304, -0.09537995606660843, -0.0022403765469789505, -0.003662274219095707, 0.058280471712350845, -0.05699113756418228, 0.010289681144058704, -0.013361557386815548, 0.06730841100215912, 0.043377652764320374, 0.007829859852790833, -0.04699309915304184, -0.028963221237063408, -0.021266231313347816, -0.009258881211280823, 0.006302217952907085, 0.030750051140785217, 0.006666778586804867, -0.027035798877477646, -0.016370201483368874, 0.04500347375869751, -0.028331516310572624, 0.026168091222643852, -0.017720337957143784, 0.053960900753736496, 0.02762514166533947, 0.02807784639298916, -0.010609087534248829, 0.0690101906657219, 0.044514402747154236, 0.0718221664428711, 0.024724328890442848, 0.049526315182447433, -0.05381379649043083, -0.03345715254545212, 0.04319978877902031, -0.028660278767347336, -0.00257063377648592, -0.05214320495724678, -0.033128272742033005, -0.05456584319472313, -0.03934092819690704, 0.023313801735639572, 0.010419859550893307, -0.0012622185749933124, 0.008573357947170734, 0.041851580142974854, 0.010816800408065319, 0.027234643697738647, 0.07275071740150452, -0.016468660905957222, -0.010089113377034664, 0.01247179601341486, 0.012861345894634724, -0.00953807681798935, -0.009700462222099304, -0.021129731088876724, 0.03961046412587166, -0.001477859215810895, 0.03605561703443527, -0.03832508996129036, -0.03185003250837326, -0.07383613288402557, -0.03188369795680046, 0.05423590540885925, 0.003306842176243663, -0.025929460301995277, 0.025432439520955086, -0.0029278714209795, 0.02623685449361801, 0.02327476441860199, 0.037409186363220215, 0.050989359617233276, 0.015933653339743614, -0.018765728920698166, 0.009746791794896126, -0.0061307642608881, 0.03504958376288414, 0.07084214687347412, -0.023328350856900215, -0.0015838365070521832, -0.02030237950384617, 0.010830326937139034, -0.030128464102745056, -0.06644826382398605, 0.06096058338880539, -0.048610880970954895, -0.03577926382422447, -0.022465243935585022, 0.026039371266961098, 0.045275356620550156, 0.009908554144203663, 0.003144257701933384, 0.0005959222908131778, 0.03552458435297012, -0.03979731723666191, -0.012051168829202652, 0.06451419740915298, -0.046561531722545624, 0.02087376080453396, -0.09582652896642685, 0.0067209904082119465, -0.06577377766370773, -0.014425731264054775, -0.00047743727918714285, -0.020565683022141457, 0.01125342957675457, -0.0023764795623719692, -0.013321171514689922, -0.035792652517557144, 0.05342860147356987, -0.011262035928666592, 0.008269148878753185, -0.04510827735066414, 0.030797244980931282, -0.01491495780646801, 0.04003356397151947, -0.009716261178255081, 0.003222959116101265, -0.02174673043191433, -0.029815366491675377, 0.04380427673459053, -0.015161601826548576, 0.055820997804403305, 0.010571293532848358, 0.050824686884880066, -0.011919737793505192, 0.015958109870553017, -0.04617650434374809, -0.007442863658070564, -0.006984381470829248, -0.041175488382577896, 0.024155648425221443, 0.004747099708765745, 0.012799779884517193, 0.03021962195634842, -0.014848588034510612, 0.013826001435518265, -0.06390807777643204, 0.07365783303976059, 0.0030452783685177565, 0.016717329621315002, 0.016340184956789017, 0.033043015748262405, -0.001983864465728402, -0.008674489334225655, 0.05287362262606621, 0.020989947021007538, 0.02887389063835144, 0.010300368070602417, -0.042927127331495285, 0.09178343415260315, 0.029795579612255096, -0.05388432368636131, -0.008258096873760223, 0.04429340362548828, -0.034196436405181885, -0.041890691965818405, 0.002824052469804883, -0.014540319330990314, -0.0012965066125616431, 0.03385495766997337, 0.015654630959033966, -0.00858058501034975, -0.007074421271681786, -0.05457921698689461, -0.005580171477049589, -0.02897617407143116, -0.00265869521535933, -0.02149816043674946, -0.015286415815353394, 0.04204300045967102, 0.020614974200725555, -0.06269422918558121, 0.025856727734208107, -0.031525615602731705, -0.03670201078057289, -0.017940638586878777, 0.0015414560912176967, -0.02072262391448021, 0.0034042324405163527, 0.043550536036491394, -0.009154184721410275, -0.02423957921564579, -0.010394240729510784, -0.016715165227651596, 0.0392439067363739, 0.027046767994761467, 0.0029203228186815977, -0.032086849212646484, -0.029710417613387108, 0.04452241584658623, 0.07743936777114868, 0.020069526508450508, -0.02963903732597828, 0.009585813619196415, 0.043348219245672226, -0.03543037548661232, 0.031209100037813187, -0.03388553485274315, 0.052107881754636765, 0.017713638022542, 0.039152517914772034, -0.0019496047170832753, -0.0015348788583651185, 0.1000259518623352, 0.005150325130671263, 0.016761140897870064, 0.042569778859615326, 0.00097892084158957, 0.014607568271458149, -0.03742325305938721, -0.0035252326633781195, -0.001080673304386437, -0.011483386158943176, -0.0017399470089003444, -0.04088738188147545, 0.050538137555122375, 0.06832938641309738, -0.015057944692671299, -0.012618317268788815, -0.019988909363746643, 0.020641406998038292, -0.003934402484446764, -0.008363388478755951, 0.016588853672146797, 0.004514755215495825, -0.011041931807994843, 0.02165800891816616, 0.01825854368507862, 0.023855959996581078, -0.06798877567052841, -0.06061578914523125, -0.03489508107304573, -0.014958218671381474, 0.015327147208154202, 0.01396249420940876, -0.07462026923894882, 0.022160710766911507, 0.03346865996718407, 0.013337536714971066, -0.04834585264325142, 0.0008249750244431198, 0.026924200356006622, 0.010085845366120338, 0.04556955024600029, 0.011121604591608047, -0.013984511606395245, -0.0033890344202518463, -0.013395213522017002, 0.05814668908715248, 0.02396964654326439, 0.02371419407427311, -0.03207210823893547, 0.005602997727692127, 0.03643965721130371, -0.04090750589966774, 0.036166369915008545, 0.0015360410325229168, -0.08866959810256958, 0.028581319376826286, -0.04453540965914726, 0.007830780930817127, -0.018609395250678062, 0.03211062401533127, -0.014325152151286602, -0.03845765441656113, 0.0028228096198290586, -0.0019139157375320792, -0.005228974856436253, -0.04185495525598526, -0.011900987476110458, 0.020533883944153786, -0.003724531037732959, -0.004401850514113903, -0.009511235170066357, 0.037153907120227814, 0.01945311389863491, -0.01985793001949787, 0.029941728338599205, 0.029378777369856834, 0.00900364387780428, 0.003945761825889349, -0.055828604847192764, 0.032231297343969345, 0.023449912667274475, -0.02175823040306568, -0.01608322188258171, -0.05055391415953636, -0.0446874164044857, -0.015526716597378254, -0.04145517945289612, 0.029622765257954597, 0.021840378642082214, 0.0008419632795266807, 0.04232630133628845, -0.07932013273239136, -0.004357349593192339, -0.031693097203969955, -0.06774905323982239, 0.011600630357861519, 0.0673871785402298, 0.03022146224975586, -0.032503027468919754, -0.048452917486429214, -0.04842240735888481, 0.014130968600511551, 0.05499329790472984, 0.004189065657556057, 0.009812240488827229, 0.07135283201932907, 0.0038571006152778864, 0.02104922942817211, 0.04974963888525963, -0.030017521232366562, 0.0514342375099659, 0.04264751821756363, 0.08784589916467667, -0.027072681114077568, 0.034106530249118805, -0.03332991153001785, -0.0035307947546243668, 0.011508312076330185, -0.024261407554149628, -0.03814782202243805, -0.01314536016434431, 0.001885873731225729, 0.020150335505604744, 0.055697645992040634, 0.019536267966032028, -0.07193771004676819, -0.030893422663211823, 0.04058954119682312, -0.013724204152822495, -0.04494931176304817, 0.02344689890742302, -0.02780243568122387, 0.09271375089883804, 0.07195566594600677, 0.06804624199867249, 0.03943134471774101, 0.0003838658449240029, -0.049757275730371475, -0.03156255558133125, 0.052871961146593094, 0.002830067416653037, -0.014979630708694458, -0.06653990596532822, 0.021355245262384415, -0.03306511789560318, 0.00926309172064066, -0.04975783824920654, -0.003989060875028372, -0.03292383998632431, 0.05439167097210884, 0.06409183144569397, 0.010817884467542171, 0.008213694207370281, -0.03633088618516922, 0.03358406573534012, 0.03735654428601265, -0.0026339213363826275, -0.003316426882520318, -0.014429628849029541, 0.030513424426317215, 0.02180805802345276, 0.006949622184038162, 0.0016762946033850312, 0.007286261301487684, 0.06042518466711044, 0.010807919315993786, -0.01070957351475954, -0.04059212654829025, -0.008403418585658073, 0.027504418045282364, -0.021317917853593826, 0.0892506092786789, 0.02572718635201454, -0.021683556959033012, -0.026892345398664474, 0.020452670753002167, -0.0037386794574558735, 0.005022044293582439, -0.0140857407823205, 0.017272844910621643, 0.031236732378602028, 0.02031293325126171, -0.004150176886469126, -0.028026368468999863, 0.06660556048154831, -0.06617956608533859, 0.02120901644229889, 0.04833303019404411, 0.03437885269522667, -0.0006010840297676623, -0.05616265907883644, -0.010731952264904976, 0.061238598078489304, 0.014431551098823547, -0.007183928973972797, 0.042566850781440735, 0.009661653079092503, 0.03169846907258034, -0.001865594880655408, -0.019656764343380928, -0.029022088274359703, -0.018320506438612938, -0.01888852007687092, -0.03934812918305397, -0.03773719444870949, 0.024475447833538055, 0.08133354038000107, -0.03230811282992363, -0.028708308935165405, 0.021295813843607903, 0.007594224065542221, 0.007262056693434715, 0.016388915479183197, -0.04739196226000786, 0.0209005456417799, 0.017777323722839355, 0.01965547353029251, -0.011524769477546215, -0.001705520204268396, -0.0006151158013381064, -0.041519150137901306, -0.01974198967218399, -0.040625348687171936, 0.04807085916399956, -0.03069632686674595, 0.06996515393257141, 0.0300711989402771, 0.011787891387939453, -0.0168314129114151, 0.01783071458339691, -0.009851851500570774, 0.0014538090908899903, 0.027736281976103783, -0.015593272633850574, 0.04003053158521652, -0.01170008722692728, 0.07478661835193634, -0.026586659252643585, -0.008834073320031166, 0.03539763391017914, -0.0011294609867036343, -0.014951168559491634, -0.04305296018719673, -0.009439168497920036, -0.052771519869565964, -5.4968341936877034e-33, -0.01080534141510725, -0.008830690756440163, -0.02846132405102253, -0.005696274805814028, -0.023734746500849724, -0.02601224184036255, 0.00011378287308616564, -0.011653848923742771, 0.03394016996026039, -0.03570134937763214, -0.02819478139281273, 0.003931418061256409, -0.01564483903348446, 0.004861743655055761, 0.061075128614902496, -0.013106404803693295, 0.03902805596590042, -0.053033795207738876, 0.03522059693932533, 0.021211517974734306, 0.07066690176725388, 0.07573334127664566, 0.004943637177348137, -0.09090645611286163, -0.06615003943443298, -0.017086312174797058, -0.01627081260085106, -0.034720368683338165, -0.02738102339208126, -0.0465962253510952, -0.03217676654458046, 0.00038137464434839785, -0.04293546825647354, 4.6434233809122816e-05, -0.025336559861898422, -0.0248675849288702, -0.02045799419283867, -0.023744219914078712, -0.06873910874128342, 0.019419614225625992, -0.03534069284796715, 0.0019667220767587423, 0.07978156208992004, -0.03857011720538139, -0.06613107770681381, 0.06496290862560272, 0.07335253059864044, -0.04526664316654205, 0.008649613708257675, -0.0871700569987297, -0.03925053030252457, 0.00036249394179321826, -0.013009092770516872, -0.02748287282884121, 0.04306565225124359, -0.009136863052845001, -0.03214510902762413, -0.016383357346057892, -0.037232644855976105, 0.05962726101279259, -0.048990409821271896, 0.042946819216012955, 0.02503157965838909, 0.015554848127067089, 0.06750161200761795, 0.028330020606517792, 0.06081709638237953, -0.052626121789216995, -0.01294493954628706, 0.0011541947023943067, -0.027353985235095024, 0.024708643555641174, 0.05076412484049797, -0.009138480760157108, 0.08239047974348068, -0.05736256390810013, 0.025359246879816055, 0.04781681299209595, 0.024660319089889526, 0.0035126875154674053, -0.02662668190896511, 0.056887563318014145, -0.04531153291463852, 0.012952218763530254, 0.03982175141572952, 0.005485674366354942, -0.008342375978827477, -0.021347347646951675, 0.01874435320496559, -0.04223131388425827, 0.04195741191506386, -0.04327012225985527, -0.04617667570710182, -0.00016465828230138868, 0.054354891180992126, -0.04667678847908974, 0.04693795368075371, 0.013394705951213837, 0.048176880925893784, -0.06395301967859268, -0.025765348225831985, -0.019473789259791374, -0.0029404994565993547, -0.01642446592450142, 0.005129737313836813, -0.0007623539422638714, -0.027881203219294548, 0.06807493418455124, -0.020197631791234016, -0.015759794041514397, 0.024921856820583344, -0.026102446019649506, 0.059801604598760605, -0.04893752187490463, 0.03177900239825249, -0.04730779677629471, -0.02074923738837242, 0.040903639048337936, 0.032160691916942596, 0.02083810232579708, -0.05079254135489464, 0.003408577525988221, -0.04994715377688408, 0.06075061112642288, -0.03604932874441147, 0.005697065033018589, -0.025470692664384842, -0.0072379279881715775, -0.029797593131661415, -0.054277386516332626, -0.002147418912500143, 0.0010167118161916733, 2.8728740630867833e-07, -0.07791806757450104, 0.009293240495026112, -0.0002455157518852502, -0.00908565241843462, 0.04472736641764641, -0.005622255150228739, -0.08006031811237335, -0.0049583143554627895, -0.003379075787961483, -0.011583065614104271, 0.02652573212981224, -0.042096056044101715, 0.02306591160595417, 0.018324803560972214, -0.09915248304605484, -0.013596847653388977, 0.0029154852963984013, 0.014286295510828495, -0.03111896850168705, 0.004657297395169735, 0.00878886878490448, 0.052560098469257355, 0.0522928461432457, -0.019069846719503403, 0.036699067801237106, 0.018454309552907944, 0.020596448332071304, 0.05958036705851555, 0.07857861369848251, -0.07363605499267578, 0.01892765425145626, -0.03152290731668472, -0.055633705109357834, 0.008842773735523224, -0.04162894934415817, 0.042343270033597946, 0.0002752440923359245, -0.018823834136128426, 0.007393238600343466, -0.017466513440012932, 0.04773205518722534, 0.06668896228075027, 0.08292119950056076, 0.00591562082991004, 0.035946525633335114, -0.01519936416298151, -0.01491010095924139, -0.032185547053813934, -0.043391015380620956, 0.029284052550792694, 0.04806393384933472, 0.03874117136001587, -0.05706406384706497, -0.05776059255003929, -0.02660215273499489, -0.02753429114818573, 0.04840885102748871, 0.01722601056098938, -0.008514116518199444, 0.031093109399080276, -0.030428055673837662, 0.009347010403871536, 0.0015728308353573084, 0.010265598073601723, 0.00949106179177761, -0.03658429905772209, -0.02857029065489769, 2.508286146585165e-34, 0.0033533331006765366, -0.06733430922031403, 0.008137360215187073, -0.020066991448402405, -0.05993486940860748, 0.002668517641723156, 0.030917759984731674, 0.01469551119953394, 0.04046473279595375, 0.02825453132390976, -0.036173176020383835]

['Shalev Ben-David', 'Lev Reyzin']

1107.2379v5

We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain efficient algorithms for instances resilient to certain multiplicative perturbations, e.g. on the order of $O(\sqrt{n})$ for max-cut clustering. Awasthi et al. (2010) consider center-based objectives, and Balcan and Liang (2011) analyze the $k$-median and min-sum objectives, giving efficient algorithms for instances resilient to certain constant multiplicative perturbations. Here, we are motivated by the question of to what extent these assumptions can be relaxed while allowing for efficient algorithms. We show there is little room to improve these results by giving NP-hardness lower bounds for both the $k$-median and min-sum objectives. On the other hand, we show that constant multiplicative resilience parameters can be so strong as to make the clustering problem trivial, leaving only a narrow range of resilience parameters for which clustering is interesting. We also consider a model of additive perturbations and give a correspondence between additive and multiplicative notions of stability. Our results provide a close examination of the consequences of assuming stability in data.

Data Stability in Clustering: A Closer Look

http://arxiv.org/pdf/1107.2379v5

Title Data Stability Clustering Closer Look Summary consider model introduced Bilu Linial 2010 study problem optimal clustering change distance perturbed show even problem NPhard sometimes possible obtain efficient algorithm instance resilient certain multiplicative perturbation eg order Osqrtn maxcut clustering Awasthi et al 2010 consider centerbased objective Balcan Liang 2011 analyze kmedian minsum objective giving efficient algorithm instance resilient certain constant multiplicative perturbation motivated question extent assumption relaxed allowing efficient algorithm show little room improve result giving NPhardness lower bound kmedian minsum objective hand show constant multiplicative resilience parameter strong make clustering problem trivial leaving narrow range resilience parameter clustering interesting also consider model additive perturbation give correspondence additive multiplicative notion stability result provide close examination consequence assuming stability data Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.06040188670158386, -0.010612626560032368, -0.033688731491565704, -0.017667856067419052, 0.004086358938366175, -0.03444294258952141, -0.007579537108540535, 0.019404662773013115, -0.01079876534640789, 0.0032477136701345444, 0.025861529633402824, 0.015340637415647507, -0.022591078653931618, 0.01096390001475811, -0.022542497143149376, -0.07165073603391647, 0.0205550380051136, -0.036043211817741394, 0.0028221060056239367, 0.004026805050671101, 0.0314459428191185, -0.0599561482667923, -0.02179701253771782, -0.004392547998577356, -0.020120104774832726, -0.016684599220752716, 0.0037090538535267115, -0.04853247106075287, 0.040073003619909286, -0.007290187291800976, 0.03409652039408684, 0.0551941879093647, -0.0035900138318538666, -0.022804908454418182, 2.289727945026243e-06, -0.036836765706539154, -0.07509766519069672, -0.0038295246195048094, 0.014797689393162727, 0.0010565182892605662, 0.057428404688835144, -0.032718975096940994, -0.0059785074554383755, -0.03448569402098656, 0.0020922585390508175, 0.01830691285431385, -0.027055207639932632, 0.009403562173247337, 0.08502602577209473, 0.0016779422294348478, -0.002485065720975399, -0.02065037563443184, 0.00031020434107631445, 0.007251833565533161, -0.031171301379799843, -0.017424186691641808, 0.003629442071542144, 0.045307692140340805, 0.026327108964323997, 0.01255166344344616, -0.024076169356703758, -0.00989548210054636, -0.0033267829567193985, -0.02499302662909031, -0.004493712447583675, -0.004190410953015089, -0.022427069023251534, 0.005100201349705458, 0.011407486163079739, 0.05401650443673134, -0.0011558982077986002, 0.04318244755268097, -0.01199238933622837, 0.010663773864507675, 0.0032434030435979366, 0.02408689446747303, -0.017774250358343124, 0.001974658574908972, 0.00838194228708744, -0.05868278816342354, 0.00382928061299026, 0.08723820745944977, 0.0077276527881622314, -0.009081274271011353, -0.016011007130146027, 0.042112722992897034, 0.0297248475253582, 0.030788252130150795, -0.07639936357736588, -0.07395025342702866, -0.09584183990955353, 0.020150937139987946, 0.00552088487893343, 0.01849180832505226, -0.038810595870018005, -0.02535441890358925, 0.008514028042554855, -0.0325532928109169, 0.024219844490289688, -0.043213363736867905, -0.023827916011214256, -0.011828521266579628, 0.020474916324019432, -0.003792800474911928, 0.024534011259675026, -0.008434603922069073, -0.011835265904664993, 0.019948279485106468, 0.05199253559112549, 0.06272094696760178, -0.02995641529560089, 0.04205691069364548, 0.013737783767282963, 0.055094849318265915, 0.019380997866392136, 0.04043493792414665, -0.03606226667761803, 0.08460401743650436, -0.031017987057566643, -0.010830055922269821, -0.018363863229751587, -0.02318715490400791, 0.08298593759536743, -0.0018929033540189266, 0.04889019951224327, -0.025076085701584816, -0.04249557480216026, 0.020619498565793037, 0.007121447939425707, -0.005648669321089983, 0.0472588986158371, 0.00799350906163454, -0.005892681889235973, 0.019377093762159348, -0.03332582116127014, 0.03663010522723198, -0.0014811137225478888, 0.023595459759235382, -0.10097339749336243, -0.021760093048214912, -0.046328574419021606, 0.0019673830829560757, -0.1255245804786682, -0.047614872455596924, 0.022111184895038605, -0.03340592980384827, -0.014660313725471497, -0.015746397897601128, -0.02310679852962494, -0.049272939562797546, -0.033890414983034134, 0.07105593383312225, -0.04232437163591385, 0.025473138317465782, 0.03509436920285225, 0.04194517061114311, -0.044086262583732605, -0.0016000198666006327, 0.04200048744678497, -0.04048638045787811, 0.09910985827445984, -0.01800847053527832, 0.0025798350106924772, -0.03138554096221924, -0.031236138194799423, -0.0262345802038908, 0.011151375249028206, -0.0037045381031930447, -0.006938344333320856, -0.043929409235715866, -0.03426844999194145, 0.003848960157483816, -0.02121328003704548, -0.038422808051109314, 0.02205691672861576, 0.024840421974658966, 0.006471619941294193, 0.05195556581020355, -0.11009565740823746, -0.0004758478025905788, -0.05951444432139397, 0.009966130368411541, -0.019511820748448372, 0.028241796419024467, -0.06247797980904579, -0.023865167051553726, 0.02037118561565876, -0.035646673291921616, -0.03255405277013779, -0.0004102727398276329, -0.038865700364112854, 0.006235247477889061, 0.03277279809117317, -0.045737139880657196, 0.016658641397953033, -0.027374347671866417, 0.005380577407777309, 0.013664891943335533, -0.006957004778087139, -0.010865520685911179, 0.012260321527719498, -0.02611822821199894, 0.04000565782189369, -0.07256155461072922, 0.017117518931627274, -0.07948949933052063, -0.059342868626117706, 0.015770282596349716, 0.011492857709527016, -0.11186331510543823, -0.01443946361541748, -0.005770054645836353, 0.003451998345553875, 0.0073916492983698845, 0.01565052755177021, 0.09889981895685196, 0.01983517035841942, -0.06311477720737457, -0.0256962850689888, 0.03620964661240578, -0.0031894438434392214, -0.015434815548360348, 0.005673673935234547, 0.009379024617373943, 0.027022497728466988, 0.08623236417770386, 0.010412751697003841, 0.03618381544947624, 0.029337918385863304, 0.010660567320883274, 0.03185325860977173, -0.05095545947551727, 0.07475941628217697, 0.022219067439436913, 0.018551819026470184, 0.06359749287366867, -0.002350871916860342, -0.003664544317871332, 0.024550097063183784, 0.08006589114665985, 0.013456041924655437, -0.01710054837167263, -0.015058723278343678, -0.03149637207388878, 0.08492863923311234, 0.015961769968271255, 0.002119983546435833, -0.0025132347363978624, 0.054365336894989014, -0.024259580299258232, 0.04623084142804146, -0.01611248590052128, 0.024960914626717567, 0.006585783790796995, 0.011512032710015774, -0.050306182354688644, 0.02999196946620941, 0.018315143883228302, -0.008397271856665611, 0.008102573454380035, -0.016349628567695618, -0.04590633139014244, 0.013238504528999329, 0.009158750995993614, -0.021270066499710083, -0.02020014449954033, -0.0037899587769061327, 0.031458139419555664, -0.05375281721353531, -0.009472611360251904, -0.0025674784556031227, -0.010994740761816502, -0.001510406145825982, 0.01702212169766426, -0.006825309246778488, 0.03299878165125847, 0.031049007549881935, 0.03579730913043022, -0.03699543699622154, 0.06627003848552704, -0.011455833911895752, -0.03976639360189438, -0.013240955770015717, -0.0004936250043101609, 0.010951489210128784, 0.026127029210329056, 0.04811375215649605, -0.017108852043747902, -0.03688174858689308, 0.04311465471982956, -0.04460587352514267, -0.014369985088706017, -0.01328024547547102, -0.014620121568441391, -0.037471894174814224, 0.015712454915046692, 0.006817338988184929, 0.04133416712284088, 0.0321122407913208, -0.021907098591327667, -0.012947618961334229, 0.017580168321728706, 0.05445180460810661, -0.0019503411604091525, -0.02537948079407215, 0.028232429176568985, 0.06005473807454109, 0.019535932689905167, 0.04636070132255554, 0.002233854727819562, 0.02446938306093216, -0.1140352264046669, 0.013461509719491005, -0.031708166003227234, -0.02106979861855507, 0.045355986803770065, -0.054024431854486465, 0.0025024497881531715, 0.004796135704964399, 0.01705523207783699, -0.042732905596494675, -0.039762869477272034, 0.04597977548837662, 0.05747057497501373, 0.044589653611183167, 0.03280921280384064, -0.0684291273355484, -0.02626940794289112, -0.07739163190126419, -0.044037140905857086, 0.00619793776422739, -0.06347741186618805, 0.017994597554206848, 0.0027384969871491194, -0.04678942263126373, -0.003260919591411948, -0.02095361240208149, 0.02740989811718464, 0.009241364896297455, 0.008402818813920021, 0.04663190245628357, -0.02507808804512024, -0.0039565046317875385, 0.05608191713690758, 0.06862231343984604, 0.006062159780412912, 0.05859318748116493, -0.003166886977851391, -0.003964898642152548, 0.07968730479478836, 0.015762001276016235, 0.01593836024403572, -0.026143817231059074, -0.013912729918956757, 0.024212872609496117, 0.02532627061009407, -0.06968463212251663, -0.05669704079627991, -0.012085041962563992, -0.05566767603158951, 0.03442788124084473, 0.06488768011331558, 0.04264119267463684, -0.009481841698288918, -0.042611781507730484, 0.03409213200211525, -0.029578886926174164, -0.031009254977107048, -0.02502129040658474, 0.00294595118612051, 0.02023993618786335, 0.025363612920045853, 0.028165368363261223, 0.041463155299425125, -0.004274747334420681, -0.031580712646245956, 0.012700286693871021, -0.052339863032102585, 0.02828335016965866, 0.02196619100868702, -0.0002360101352678612, 0.058962419629096985, 0.034243203699588776, -0.017291473224759102, 0.032455068081617355, 0.05520674213767052, -0.050905223935842514, 0.036885540932416916, 0.012948870658874512, 0.03596926108002663, 0.015267333947122097, -0.08710318803787231, -0.025210903957486153, -0.058113738894462585, 0.020405501127243042, -0.050022225826978683, 0.006573836784809828, 0.0682743489742279, 0.031383831053972244, -0.009061533957719803, 0.01378396712243557, -0.09128694981336594, -0.011748461984097958, 0.013460074551403522, -0.0873001217842102, 0.028888968750834465, -0.051597580313682556, -0.019649768248200417, -0.00907810591161251, -0.005007435102015734, 0.06264226883649826, 0.05511119216680527, -0.04507086053490639, -0.016239166259765625, 0.005452534183859825, 0.040252186357975006, 0.008751675486564636, -0.013038018718361855, 0.03775670751929283, 0.0065405722707509995, 0.0013917479664087296, 0.033001381903886795, 0.04502614960074425, 0.027368782088160515, 0.030909160152077675, -0.0250979196280241, 0.0071850065141916275, -0.05193096399307251, -0.06198897585272789, -0.0341547355055809, -0.010135657154023647, 0.02622978761792183, -0.001847006264142692, 0.026665901765227318, -0.00040753427310846746, 0.03077586367726326, -0.03494168445467949, -0.006419926881790161, 0.07521946728229523, -0.043882034718990326, 0.06452784687280655, -0.04037000983953476, 0.048292405903339386, -0.006063287146389484, -0.005421188659965992, -0.021784847602248192, -0.013354088179767132, -0.043280646204948425, -0.0425465852022171, 0.02571532316505909, -0.00022702156275045127, -0.05849287658929825, 0.07697362452745438, 0.02947241999208927, 0.009690431877970695, -0.0230703167617321, -0.03849184140563011, -0.020328998565673828, -0.06405947357416153, 0.0011692040134221315, 0.05939900130033493, 0.004310763441026211, 0.02383195050060749, -0.05117100849747658, -0.04389682039618492, 0.038168877363204956, -0.03340192884206772, -0.014221065677702427, 0.02301386184990406, -0.022785067558288574, -0.02238343097269535, -0.05833180993795395, -0.004369254689663649, 0.014338989742100239, 0.023937460035085678, -0.027830561622977257, -0.060848403722047806, -0.05547648295760155, 0.01113204751163721, -0.044506240636110306, 0.059107933193445206, 0.03803536668419838, 0.06683457642793655, -0.011154625564813614, -0.05829489231109619, -0.017735369503498077, -0.001004521851427853, 0.0006914783152751625, 0.02122841216623783, 0.0840226337313652, 0.013682732358574867, 0.003684021532535553, -0.029355285689234734, 0.00928042083978653, 0.06277062743902206, -0.0369490385055542, 0.03833723068237305, 0.02970626763999462, -0.024922240525484085, 0.004613095428794622, -0.013852796517312527, 0.03342793136835098, 0.008247028104960918, -0.015181059949100018, -0.006293090060353279, 0.05597038194537163, -0.0010422031627967954, -0.0182181466370821, 0.029747355729341507, 0.038814447820186615, -0.015863953158259392, 0.058414507657289505, -0.007948818616569042, 0.03459123522043228, -0.03185538575053215, -0.05293981730937958, -0.014857993461191654, 0.02967672608792782, -0.014324779622256756, -0.0009584333747625351, 0.0018098256550729275, -0.03984251245856285, 0.054838281124830246, -0.0014612141530960798, -0.004033216740936041, -0.023803161457180977, 0.022340118885040283, 0.0017365914536640048, 0.08458825945854187, 0.02698204107582569, -0.01819748617708683, -0.069945327937603, -0.013733500614762306, -0.03642364591360092, -0.05720185488462448, 0.07925324141979218, -0.0024238103069365025, 0.015527189709246159, 0.003058358794078231, 0.01516453456133604, -0.003491520881652832, -0.010526268742978573, 0.027995694428682327, 0.009123524650931358, 0.05207531899213791, 0.03565771132707596, -0.01307512167841196, -0.0040401979349553585, 0.01708655059337616, 0.056556522846221924, 0.029370982199907303, -0.05572250857949257, -0.025558829307556152, 0.02013537660241127, 0.029518667608499527, -5.837417886133122e-33, 0.0014331038109958172, -0.0536411814391613, -0.07459590584039688, -0.06678281724452972, -0.04460008442401886, -0.03737165406346321, 0.0025123523082584143, 0.03517582640051842, -0.0009475630358792841, -0.06342227756977081, -0.009029318578541279, 0.01697278954088688, -0.029083337634801865, -0.028804872184991837, -0.006205121520906687, 0.014318514615297318, -0.045044369995594025, 0.012055921368300915, -0.03460099175572395, 0.02264118194580078, 0.03775642812252045, -0.00578736886382103, -0.018279150128364563, -0.036927614361047745, -0.022739175707101822, 0.04963930323719978, -0.020681990310549736, -0.008521554060280323, -0.04453544691205025, 0.02395516075193882, 0.07566628605127335, 0.02794305607676506, 0.005679482594132423, -0.012330231256783009, -0.019183795899152756, -0.0578014962375164, -0.012368242256343365, -0.010566208511590958, -0.04852951318025589, 0.01381616573780775, 0.006193045526742935, -0.00335195055231452, 0.049289554357528687, -0.01714305579662323, -0.03132212907075882, 0.005988114047795534, 0.046615343540906906, -0.015967633575201035, -0.03012481890618801, 0.0625472441315651, 0.08489052951335907, 0.04579918831586838, -0.044303424656391144, 0.04272640869021416, -0.00371104059740901, -0.003556639887392521, 0.0023247189819812775, 0.01424962654709816, -0.019975263625383377, 0.06663227081298828, 0.0016760978614911437, 0.0461861677467823, -0.017302973195910454, 0.023572510108351707, 0.0346914641559124, 0.036119915544986725, -0.01066936831921339, 0.007807199843227863, 0.0008817409980110824, -0.006921628024429083, 0.011913339607417583, 0.029642783105373383, 0.025986941531300545, 0.03960491344332695, -0.008668835274875164, -0.07229731976985931, -0.027188383042812347, 0.04798518493771553, -0.02897235006093979, -0.03367450460791588, -0.012818128801882267, 0.022888217121362686, -0.05217829346656799, -0.028453513979911804, 0.04096270352602005, -0.05487299710512161, -0.03781048208475113, -0.013838203623890877, -0.006960916332900524, 0.007836979813873768, -0.06710070371627808, -0.01277261320501566, -0.048353832215070724, -0.03517093509435654, 0.02767009101808071, -0.0034854027908295393, -0.034978996962308884, 0.02327202819287777, 0.008980534970760345, -0.015585631132125854, 0.034763582050800323, -0.03489344194531441, -0.005125574301928282, -0.03936350345611572, -0.031106188893318176, -0.022430535405874252, 0.007110635284334421, 0.007134031504392624, -0.024889403954148293, -0.007660806179046631, 0.09568323940038681, 0.012236635200679302, 0.033690083771944046, 0.018883300945162773, 0.0069580902345478535, -0.0741073414683342, -0.019109297543764114, 0.08434610068798065, 0.08947808295488358, 0.009423986077308655, 0.0084127988666296, 0.032778460532426834, -0.009015684016048908, 0.016808783635497093, -0.0002945578598883003, 0.009463455528020859, 0.02234349213540554, -0.024445265531539917, -0.011857089586555958, -0.026349561288952827, -0.04536278173327446, -0.07628843933343887, 2.878415443774429e-07, 0.026812540367245674, 0.0300630871206522, 0.03196657821536064, -0.03274942561984062, -0.002860994078218937, -0.009575797244906425, -0.06164117529988289, 0.0019023956265300512, -0.05449527129530907, -0.001641858951188624, -0.0013117232592776418, -0.009543370455503464, 0.010941434651613235, 0.02457413636147976, 0.03260946646332741, 0.0012631373247131705, -0.007719182409346104, 0.10277123749256134, -0.007102993316948414, -0.010203737765550613, 0.013157964684069157, 0.04478541389107704, -0.014451734721660614, 0.009165448136627674, -0.022226961329579353, -0.027365075424313545, 0.006800480652600527, -0.027090879157185555, 0.010962997563183308, 0.011005238629877567, -1.83983393071685e-05, 0.001904910197481513, -0.010378154926002026, -0.04196488484740257, -0.009137923829257488, 0.019600650295615196, -0.030529696494340897, 0.026494411751627922, 0.003172982018440962, -0.006451706867665052, 0.07704360783100128, 0.04066126048564911, 0.02693096175789833, -0.03565075621008873, 0.017289549112319946, -0.005159690510481596, -0.01818743720650673, 0.07167556136846542, 0.0018049001228064299, -0.0063465796411037445, 0.07481641322374344, 0.009545460343360901, -0.02873208187520504, 0.01752849854528904, -0.013836522586643696, 0.010107767768204212, 0.04784371703863144, -0.024062376469373703, -0.009736699052155018, 0.02149217575788498, -0.021237647160887718, -0.019338715821504593, 0.0820695236325264, 0.007999015972018242, 0.06492401659488678, 0.04776144027709961, -0.017781712114810944, 2.830611748532925e-34, 0.042520198971033096, -0.003572555026039481, -0.016703495755791664, -0.006088825408369303, -0.02194027043879032, -0.0298001728951931, -0.015950312837958336, -0.03363088145852089, 0.012390472926199436, -0.0034250158350914717, -0.02842184156179428]

['Moritz Hardt', 'Guy N. Rothblum', 'Rocco A. Servedio']

1107.2444v1

This work considers computationally efficient privacy-preserving data release. We study the task of analyzing a database containing sensitive information about individual participants. Given a set of statistical queries on the data, we want to release approximate answers to the queries while also guaranteeing differential privacy---protecting each participant's sensitive data. Our focus is on computationally efficient data release algorithms; we seek algorithms whose running time is polynomial, or at least sub-exponential, in the data dimensionality. Our primary contribution is a computationally efficient reduction from differentially private data release for a class of counting queries, to learning thresholded sums of predicates from a related class. We instantiate this general reduction with a variety of algorithms for learning thresholds. These instantiations yield several new results for differentially private data release. As two examples, taking {0,1}^d to be the data domain (of dimension d), we obtain differentially private algorithms for: (*) Releasing all k-way conjunctions. For any given k, the resulting data release algorithm has bounded error as long as the database is of size at least d^{O(\sqrt{k\log(k\log d)})}. The running time is polynomial in the database size. (*) Releasing a (1-\gamma)-fraction of all parity queries. For any \gamma \geq \poly(1/d), the algorithm has bounded error as long as the database is of size at least \poly(d). The running time is polynomial in the database size. Several other instantiations yield further results for privacy-preserving data release. Of the two results highlighted above, the first learning algorithm uses techniques for representing thresholded sums of predicates as low-degree polynomial threshold functions. The second learning algorithm is based on Jackson's Harmonic Sieve algorithm [Jackson 1997].

Private Data Release via Learning Thresholds

http://arxiv.org/pdf/1107.2444v1

Title Private Data Release via Learning Thresholds Summary work considers computationally efficient privacypreserving data release study task analyzing database containing sensitive information individual participant Given set statistical query data want release approximate answer query also guaranteeing differential privacyprotecting participant sensitive data focus computationally efficient data release algorithm seek algorithm whose running time polynomial least subexponential data dimensionality primary contribution computationally efficient reduction differentially private data release class counting query learning thresholded sum predicate related class instantiate general reduction variety algorithm learning threshold instantiation yield several new result differentially private data release two example taking 01d data domain dimension obtain differentially private algorithm Releasing kway conjunction given k resulting data release algorithm bounded error long database size least dOsqrtklogklog running time polynomial database size Releasing 1gammafraction parity query gamma geq poly1d algorithm bounded error long database size least polyd running time polynomial database size Several instantiation yield result privacypreserving data release two result highlighted first learning algorithm us technique representing thresholded sum predicate lowdegree polynomial threshold function second learning algorithm based Jacksons Harmonic Sieve algorithm Jackson 1997 Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.02293570153415203, 0.11268457025289536, -0.04038812592625618, 0.03342091292142868, -0.03727922961115837, -0.0418853722512722, 0.05555300787091255, -0.016690997406840324, 0.005520952399820089, 0.05024070292711258, 0.005215880926698446, 0.013172555714845657, -0.020722955465316772, 0.06755504012107849, -0.04937829449772835, -0.007934760302305222, 0.016944603994488716, -0.00873746257275343, -0.024753833189606667, -0.033200703561306, -0.01672019436955452, -0.026792481541633606, 0.009820107370615005, -0.026904797181487083, 0.0050636110827326775, -0.018546337261795998, 0.0019190273014828563, -0.04485885426402092, 0.02770061232149601, -0.03799222782254219, 0.01015747245401144, 0.041860431432724, 0.019525092095136642, -0.013252520002424717, 2.1320313408068614e-06, 0.0003612867440097034, -0.05106557160615921, 0.027375515550374985, -0.04654407501220703, -0.0038555460050702095, -0.03808078542351723, -0.01680474914610386, 0.05197782441973686, -0.007274293340742588, -0.018868103623390198, -0.02777007967233658, -0.002348378300666809, 0.008243146352469921, 0.07980972528457642, -0.0014421014348044991, 0.008912792429327965, -0.0197148360311985, -0.0019751715008169413, -0.016429582610726357, 0.016114145517349243, -0.06630061566829681, 0.015526363626122475, -0.027668548747897148, -0.013835340738296509, -0.018038522452116013, -0.009796489961445332, -0.0039026690647006035, -0.013579029589891434, 0.012570055201649666, 0.015647292137145996, 0.004639627877622843, 0.018141336739063263, -0.027004580944776535, -0.033841509371995926, -0.011384667828679085, 0.027350004762411118, 0.004941632505506277, 0.03687426447868347, 0.03511282056570053, 0.029601555317640305, 0.005970204249024391, -0.0022088815458118916, 0.04358624294400215, -0.05675641819834709, -0.0001015917951008305, -0.027590060606598854, 0.0546705536544323, -0.03583041578531265, 0.0009092966793105006, 0.029771503061056137, 0.00019498854817356914, -0.014174497686326504, 0.025207389146089554, -0.05369546636939049, -0.07398836314678192, 0.003986642230302095, -0.014875818975269794, 0.07026185095310211, -0.015740657225251198, 0.019162174314260483, -0.010056651197373867, -0.038925860077142715, -0.04849929362535477, 0.022878170013427734, -0.018341561779379845, 0.003393033519387245, -0.03732750937342644, 0.08139613270759583, 0.022676587104797363, 0.06672536581754684, 0.015109838917851448, -0.03235182166099548, 0.038279253989458084, 0.027107492089271545, 0.04766175523400307, -0.002213375410065055, 0.03743764013051987, -0.009136245585978031, 0.12424887716770172, -0.023897036910057068, 0.059498146176338196, -0.056797679513692856, 0.05296403542160988, -0.036763351410627365, 0.0378231480717659, -0.01817687228322029, 0.02053779363632202, -0.017670389264822006, 0.003013937035575509, 0.027290383353829384, -0.11786837875843048, -0.03565066307783127, 0.02606315352022648, 0.017203258350491524, -0.018750039860606194, 0.0064085861667990685, -0.055312469601631165, 0.040364257991313934, 0.017031490802764893, -0.045808952301740646, 0.030951768159866333, 0.017605137079954147, 0.03171548247337341, -0.02681623212993145, -0.09204483777284622, 0.01654474064707756, 0.01422378420829773, -0.033512428402900696, -0.03432128578424454, 0.013344244100153446, -0.051830124109983444, -0.03228982910513878, -0.01599937491118908, -0.011647178791463375, 0.025914812460541725, 0.007164135575294495, 0.040050238370895386, 0.052671898156404495, 0.011071106418967247, 0.049373310059309006, 0.055405423045158386, 0.014351861551404, -0.00029565938166342676, 0.016155490651726723, 0.020878462120890617, 0.026513872668147087, -0.014417757280170918, 0.04284840449690819, -0.06741531193256378, 0.05323419347405434, -0.00489440793171525, -0.013789777643978596, 0.030926840379834175, 0.008811135776340961, -0.08108688145875931, -0.05231102555990219, 0.047432124614715576, -0.008378533646464348, -0.07128679752349854, 0.026669466868042946, 0.06769814342260361, 0.0052517917938530445, 0.007029042113572359, -0.10176922380924225, 0.050763025879859924, -0.0479193776845932, 0.013863200321793556, -0.002194109372794628, 0.02715287171304226, -0.012659231200814247, -0.049073170870542526, -0.015776610001921654, -0.040230706334114075, -0.021440749987959862, -0.026632823050022125, 0.016947230324149132, -0.03880526125431061, 0.016583802178502083, 0.019581329077482224, -0.03483562916517258, -0.004047643858939409, 0.08973028510808945, 0.029040636494755745, 0.008336497470736504, -0.04640219360589981, -0.0325220562517643, -0.06787993013858795, -0.0095481863245368, -0.03025544248521328, -0.012970536015927792, -0.035197723656892776, 0.06830896437168121, -0.005113751161843538, -0.008286172524094582, -0.0796194076538086, 0.003882915712893009, 0.010328566655516624, 0.04077973589301109, -0.0033118054270744324, -0.026074180379509926, 0.047715477645397186, 0.03064809925854206, -0.022864654660224915, -0.018605565652251244, -0.0017471940955147147, -0.02218801900744438, 0.014355911873281002, 0.02697567455470562, 0.023226454854011536, -0.015365258790552616, -0.008054428733885288, 0.06841059029102325, 0.02733445167541504, 0.04839299991726875, 0.016034888103604317, 0.01863122545182705, 0.0064065405167639256, 0.03737310320138931, 0.017751863226294518, -0.0020331740379333496, -0.02246597595512867, 0.05098056420683861, -0.007166493684053421, -0.040385279804468155, -0.05324077606201172, 0.06171085312962532, 0.04366092383861542, -0.018589483574032784, 0.009097463451325893, 0.04080982506275177, 0.017099563032388687, -0.05479332059621811, -0.003433952573686838, -0.024870356544852257, -0.02005390264093876, 0.04640067741274834, -0.015320219099521637, -0.014247309416532516, -0.0407172366976738, -0.001100533059798181, -0.09647096693515778, -0.07273758202791214, 0.001994071528315544, -0.021308690309524536, 0.01517562847584486, -0.018762808293104172, -0.04812724143266678, 0.01967397704720497, 0.0026280833408236504, -0.0018704080721363425, 0.0071244132705032825, -0.013733663596212864, 0.027040686458349228, 0.028449801728129387, 0.011684050783514977, 0.03348558023571968, -0.0013890803093090653, 0.03395150229334831, 0.006242901086807251, -0.0479908250272274, -0.03234698250889778, -0.005201553460210562, -0.04214978590607643, -0.020494448021054268, 0.019289199262857437, 0.059567008167505264, -0.010545344091951847, 0.033091772347688675, -0.05958251282572746, 0.011492054909467697, 0.01474505290389061, -0.0012669397983700037, -0.07633469253778458, 0.04118554666638374, 0.03778691589832306, -0.03804779052734375, 0.0190600398927927, 0.008752599358558655, -0.018911104649305344, -0.02413910999894142, -0.013567693531513214, -0.060055412352085114, 0.015418769791722298, 0.020787132903933525, 0.020838679745793343, 0.01740003563463688, 0.0467296838760376, 0.018343396484851837, 0.000706817430909723, -0.024538276717066765, -0.025702932849526405, 0.03863643482327461, 0.013279283419251442, 0.043717801570892334, -0.04858751595020294, 0.051018256694078445, -0.0541018508374691, 0.003277915995568037, 0.0215777400881052, 0.019194673746824265, -0.020594840869307518, -0.02774726040661335, 0.011139529757201672, -0.02042672410607338, 0.027943875640630722, -0.025537898764014244, -0.039598092436790466, 0.02244255505502224, 0.06170463562011719, 0.039433855563402176, -0.0001195233198814094, -0.034457460045814514, -0.01656688004732132, 0.011846169829368591, 0.0028093443252146244, 0.05773329362273216, -0.0017193478997796774, -0.03780781850218773, 0.021511342376470566, -0.005435854662209749, 0.0470789335668087, -0.07903458923101425, -0.0047978186048567295, 0.0004746770719066262, -0.07270928472280502, -0.009904544800519943, -0.030853355303406715, -0.014606443233788013, -0.033370621502399445, 0.0593741275370121, -0.03144163265824318, -0.004156856331974268, 0.023227229714393616, 0.012613045983016491, -0.017149271443486214, 0.001912805368192494, 0.02226834185421467, 0.02977304905653, -0.008201117627322674, 0.019148627296090126, -0.06951117515563965, -0.05097823590040207, -0.04070349037647247, -0.03522944077849388, -0.02489188127219677, 0.029009640216827393, 0.0917281061410904, 0.06317728012800217, 0.04747594892978668, 0.048531100153923035, -0.0008328157709911466, 0.019001048058271408, -0.028194455429911613, -0.021942254155874252, 0.043349914252758026, -0.020227396860718727, -0.02710464969277382, 0.03407064825296402, -0.0010244116419926286, 0.016587641090154648, -0.05203007906675339, -0.01817295327782631, 0.025040732696652412, -0.026348073035478592, 0.005175234749913216, -0.019582640379667282, -0.09653587639331818, 0.05368126183748245, -0.02456537075340748, 0.04252804070711136, -0.03603583946824074, -0.08218551427125931, -0.057574741542339325, -0.06232544779777527, 0.047893866896629333, -0.0022283284924924374, 0.014175542630255222, 0.007875893265008926, -0.06790482997894287, 0.046578776091337204, -0.029464110732078552, -0.057548634707927704, -0.013090405613183975, 0.009373369626700878, -0.029014965519309044, 0.022729139775037766, -0.010361582040786743, 0.00019384257029742002, -0.0010088756680488586, -0.04976306110620499, -0.02010689675807953, -0.03434070944786072, 0.03779464587569237, -0.015813693404197693, -0.030505988746881485, -0.008099041879177094, 0.00852123647928238, -0.04421107470989227, -0.010519223287701607, 0.0726597011089325, 0.01250976137816906, 0.0036121439188718796, 0.006024481728672981, 0.06778023391962051, 0.030745944008231163, 0.03849854692816734, 0.02610146813094616, 0.041283346712589264, 0.0010018307948485017, -0.012736019678413868, 0.006960445549339056, 0.013389264233410358, 0.006580139510333538, 0.0060569532215595245, -0.03376875817775726, 0.008208757266402245, 0.02484174259006977, -0.00286798644810915, 0.07353940606117249, -0.0014636097475886345, 0.05677654594182968, 0.029513124376535416, -0.004253649618476629, -0.0649191290140152, -0.032552994787693024, 0.051676224917173386, -0.03280279412865639, 0.042534470558166504, -0.012951136566698551, 0.007879274897277355, 0.026064379140734673, -0.009583874605596066, -0.052927032113075256, -0.05705859884619713, -0.004902937449514866, -0.025783222168684006, -0.023619314655661583, 0.04365680739283562, -0.01232859492301941, 0.002072165720164776, -0.03295009955763817, -0.06595760583877563, -0.014721996150910854, -0.06236642226576805, 0.046141836792230606, 0.015472312457859516, 0.015609972178936005, -0.038422051817178726, -0.02143947407603264, -0.03852365165948868, 0.03155341371893883, 0.04064720496535301, -0.039651207625865936, -0.0076311021111905575, 0.016139324754476547, -0.03706403821706772, -0.004836749751120806, 0.0035381210036575794, 0.018284589052200317, 0.023157211020588875, 0.0536593459546566, -0.07760478556156158, -0.0562458336353302, -0.0072407191619277, -0.02168967016041279, 0.05492530018091202, 0.019947053864598274, 0.09270461648702621, -0.0011494357604533434, -0.027596725150942802, 0.07946987450122833, -0.009307915344834328, -0.01619734987616539, -0.0244434904307127, -0.003198496997356415, 0.023269515484571457, 0.0057320063933730125, 0.029436370357871056, -0.028256146237254143, 0.08640466630458832, -0.049100685864686966, -0.036781299859285355, 0.03339158743619919, 0.034170497208833694, 0.016258124262094498, -0.023745566606521606, 0.017416220158338547, -0.030550125986337662, 0.007946922443807125, 0.05171193182468414, 0.03591139614582062, 0.006930503994226456, -0.011964622884988785, -0.016275934875011444, 0.025644365698099136, -0.023116933181881905, 0.0266208965331316, -0.03736356645822525, -0.03357365354895592, 0.035918328911066055, 0.006363832391798496, -0.03496326133608818, 0.07936686277389526, -0.05498986691236496, -0.00021264645329210907, -0.0016994670731946826, -0.030867259949445724, 0.04077010974287987, -0.03511516749858856, -0.001991230295971036, -0.006930166389793158, -0.018177881836891174, -0.007356935180723667, 0.02062392607331276, 0.028215816244482994, 0.015440466813743114, -0.02846524305641651, -0.04295060783624649, -0.0627799704670906, -0.03923529386520386, 0.029432708397507668, -0.0075033968314528465, 0.03620551899075508, 0.0345405638217926, 0.004392778035253286, -0.021680373698472977, -0.007530491333454847, 0.03530445322394371, 0.005627191159874201, 0.03904348611831665, 0.014007564634084702, 0.0006675546756014228, -0.042613543570041656, 0.014202923513948917, -0.031024139374494553, -0.06709612160921097, -0.06236813962459564, 0.004484920762479305, -0.00823455024510622, -0.014252669177949429, -5.1377507915542343e-33, -0.013820159249007702, -0.020877663046121597, -0.06910260021686554, 0.04728254675865173, 0.022820327430963516, 0.028688976541161537, 0.015202042646706104, -0.03175573796033859, 0.00845638383179903, -0.024261590093374252, -0.01886008307337761, 0.015177692286670208, 0.020979605615139008, -0.017672821879386902, -0.005475126206874847, -0.01655171439051628, 0.015596034936606884, -0.05315606668591499, -0.027046609669923782, 0.018493106588721275, 0.05937453731894493, 0.019114987924695015, 0.012763863429427147, -0.016159702092409134, 0.002172573935240507, 0.03960314020514488, -0.05580681934952736, 0.028607791289687157, -0.055058445781469345, 0.018871191889047623, 0.023403925821185112, -0.033555980771780014, -0.0012324259150773287, -0.006795890163630247, -0.01794266328215599, 0.03779449686408043, -0.08154790848493576, -0.02598375454545021, -0.0379517637193203, -0.017503591254353523, 0.05140288174152374, -0.016695991158485413, 0.04671790823340416, -0.011051627807319164, -0.010028830729424953, -0.03423069790005684, -0.006889394950121641, -0.018682247027754784, -0.0032582904677838087, -0.06214294955134392, 0.09246457368135452, 0.010394146665930748, -0.02224544622004032, 0.05833465978503227, 0.05443554371595383, -0.015428902581334114, -0.02940993942320347, -0.06310886889696121, 0.010074473917484283, 0.04640043154358864, 0.063359834253788, 0.004386530723422766, -0.04437466710805893, 0.013724537566304207, 0.0408899150788784, -0.014507469721138477, 0.0747036561369896, 0.0419035404920578, 0.04847535863518715, -0.013058684766292572, -0.019764766097068787, 0.019604654982686043, -0.0054428293369710445, 0.03783692792057991, 0.061730388551950455, -0.048531848937273026, -0.06871797144412994, 0.028719862923026085, -0.08762473613023758, 0.00037135821185074747, 0.018481241539120674, -0.0027034638915210962, -0.07385885715484619, -0.02536603808403015, -0.026888318359851837, 0.059497855603694916, -0.03151498734951019, 0.05066497623920441, -0.042802080512046814, 0.016849463805556297, -0.05047804117202759, -0.00044051476288586855, -0.003321899799630046, -0.03096781298518181, -0.024201171472668648, 0.008428111672401428, 0.09844837337732315, -0.009950160048902035, -0.01882113888859749, -0.035249609500169754, -0.016868099570274353, 0.03175625205039978, -0.014260551892220974, -0.0418425016105175, -0.0028204990085214376, 0.027793724089860916, 0.015876255929470062, -0.005585122853517532, -0.039260827004909515, -0.005942591931670904, 0.019205104559659958, 0.023265305906534195, 0.02554258145391941, 0.045063622295856476, 0.008347916416823864, -0.054940979927778244, -0.0011417533969506621, 0.03979755565524101, 0.023200344294309616, 0.014174148440361023, -0.061192017048597336, 0.06317883729934692, -0.017971741035580635, 0.009950412437319756, 0.03527276962995529, -0.014294941909611225, 0.024298787117004395, -0.034492895007133484, 0.07918555289506912, 0.03099420666694641, -0.0018690417055040598, -0.014532893896102905, 2.733569601787167e-07, -0.01537947729229927, -0.047490574419498444, -0.011324676685035229, 0.033181313425302505, 0.0142137436196208, -0.0013717074180021882, 0.02652602456510067, 0.09554722160100937, 0.02109130285680294, 0.013257207348942757, -0.010043379850685596, -0.004487757571041584, 0.027944089844822884, 0.031463172286748886, 0.025133183225989342, -0.07717008143663406, 0.03641526773571968, 0.0025256325025111437, 0.0024847204331308603, 0.009097099304199219, 0.03002190589904785, 0.0033991725649684668, 0.05245623737573624, 0.0055445777252316475, -5.238140875007957e-05, -0.033280860632658005, 0.010499401018023491, -0.04572181776165962, -0.016199342906475067, 0.021724259480834007, 0.05058844015002251, 0.02824314683675766, 0.009103870019316673, 0.02109578251838684, -0.035650402307510376, -0.003200716571882367, -0.047920458018779755, 0.1041034534573555, 0.05264492332935333, 0.02152743935585022, 0.04319196939468384, -0.03551619499921799, -0.01956520788371563, 0.018498901277780533, 0.035599302500486374, 0.015232834033668041, -0.04607057571411133, 0.027673544362187386, 0.03826456889510155, -0.049511536955833435, 0.06099459528923035, -0.010013635270297527, 0.008875659666955471, -0.015046421438455582, 0.0026101062539964914, 0.034229815006256104, 0.03707105293869972, -0.002554328879341483, -0.04280039668083191, -0.022002210840582848, -0.026837609708309174, -0.0010192668996751308, 0.07300779223442078, 0.0033626114018261433, -0.02247893065214157, 0.007405194453895092, 0.053138475865125656, 3.0988317791529833e-34, -0.042294688522815704, -0.012809350155293941, -0.024370580911636353, -0.040851764380931854, -0.0017695066053420305, -0.009178416803479195, 0.06829439103603363, -0.019895855337381363, 0.05301215127110481, 0.005266123916953802, -0.026748737320303917]

['Cem Tekin', 'Mingyan Liu']

1107.4042v3

In this paper we consider the problem of learning the optimal policy for uncontrolled restless bandit problems. In an uncontrolled restless bandit problem, there is a finite set of arms, each of which when pulled yields a positive reward. There is a player who sequentially selects one of the arms at each time step. The goal of the player is to maximize its undiscounted reward over a time horizon T. The reward process of each arm is a finite state Markov chain, whose transition probabilities are unknown by the player. State transitions of each arm is independent of the selection of the player. We propose a learning algorithm with logarithmic regret uniformly over time with respect to the optimal finite horizon policy. Our results extend the optimal adaptive learning of MDPs to POMDPs.

Optimal Adaptive Learning in Uncontrolled Restless Bandit Problems

http://arxiv.org/pdf/1107.4042v3

Title Optimal Adaptive Learning Uncontrolled Restless Bandit Problems Summary paper consider problem learning optimal policy uncontrolled restless bandit problem uncontrolled restless bandit problem finite set arm pulled yield positive reward player sequentially selects one arm time step goal player maximize undiscounted reward time horizon reward process arm finite state Markov chain whose transition probability unknown player State transition arm independent selection player propose learning algorithm logarithmic regret uniformly time respect optimal finite horizon policy result extend optimal adaptive learning MDPs POMDPs Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.018138518556952477, 0.01950143836438656, -0.00023229478392750025, -0.04689545929431915, 0.009580551646649837, 0.00302061066031456, -0.02586354687809944, 0.030193006619811058, -0.024679509922862053, -0.01024720724672079, 0.009138932451605797, 0.040470190346241, -0.06576757878065109, -0.0034520747140049934, 0.003291134024038911, -0.007381906732916832, 0.011735864914953709, -0.041705746203660965, 0.06348328292369843, -0.0042069172486662865, 0.0008675826247781515, -0.06592988967895508, -0.03636883571743965, 0.0089952377602458, 0.017602423205971718, 0.028036363422870636, -0.02786330133676529, -0.019745348021388054, 0.016748270019888878, -0.11002218723297119, 0.02048901841044426, -0.052130863070487976, 0.020176107063889503, 0.07772893458604813, 2.2382716906577116e-06, -0.047139812260866165, -0.04696228355169296, -0.0559433251619339, 0.01853487640619278, -0.06538039445877075, 0.039659347385168076, 0.07784198969602585, 0.004624541383236647, 0.04345293343067169, -0.031736381351947784, -0.042310114949941635, 0.020442316308617592, 0.0776551365852356, -0.0005460505490191281, 0.03579943627119064, 0.027605656534433365, -0.0054996986873447895, -0.020632026717066765, -0.045411158353090286, 0.01775190979242325, -0.06399575620889664, 0.04918638616800308, -0.018443472683429718, 0.0070240250788629055, -0.0739513635635376, 0.008244840428233147, -0.023124506697058678, -0.028429251164197922, 0.0024862485006451607, 0.04082690179347992, -0.008730892091989517, -0.01355805341154337, 0.011999989859759808, 0.008613497950136662, -0.010113229975104332, -0.030799372121691704, 0.013295716606080532, 0.006404983811080456, -0.017637355253100395, 0.014437106437981129, 0.012650118209421635, -0.011833862401545048, 0.04159789904952049, -0.0651218593120575, 0.041600052267313004, -0.003971450496464968, 0.03436335548758507, 0.0018946826457977295, 0.02425857074558735, -0.023766789585351944, 0.06331021338701248, -0.05322550982236862, -0.027433054521679878, 0.06989684700965881, 0.028662709519267082, -0.016536802053451538, -0.004914623219519854, 0.014375058934092522, 0.02317240834236145, -0.08375399559736252, 0.02462780848145485, 0.019596852362155914, 0.009393919259309769, 0.02024546079337597, 0.04428447410464287, 0.08843004703521729, -0.028902072459459305, 0.03538114205002785, 0.011206800118088722, -0.02327016554772854, 0.019875418394804, -0.0459018349647522, 0.0361100472509861, 0.011739524081349373, 0.04799720272421837, -0.06068042665719986, 0.022158926352858543, -0.01915104128420353, 0.0559164434671402, 0.07344888150691986, 0.0005201007006689906, -0.04179677739739418, 0.01628953218460083, -0.003141534747555852, 0.008517996408045292, -0.015758400782942772, 0.02119530737400055, -0.029793472960591316, 0.019022516906261444, -0.08883655816316605, -0.032623499631881714, -0.026876071467995644, 0.028012968599796295, 0.019047975540161133, 0.048791173845529556, 0.020295187830924988, -0.0010144991101697087, -0.04505375772714615, -0.013231649994850159, 0.0073150768876075745, 0.06720708310604095, 0.024241887032985687, 0.0266750268638134, -0.0950196385383606, 0.005397972650825977, 0.030796561390161514, 0.01234725583344698, -0.002292437246069312, -0.0233765821903944, -0.038907114416360855, -0.05908852070569992, -0.011333187110722065, 0.006844037212431431, 0.005176306236535311, -0.013480701483786106, -0.04340488091111183, -0.004807708784937859, -0.001045504817739129, -0.006220377050340176, 0.03968338668346405, -0.028220906853675842, 0.02357707917690277, 0.01844402775168419, 0.018862474709749222, 0.05967213585972786, 0.017373424023389816, 0.0049387081526219845, 0.01575317420065403, -0.011777757667005062, -0.0045431372709572315, -0.02256411500275135, 0.02600719779729843, -0.03484121337532997, 0.024191301316022873, 0.07875672727823257, 0.010582211427390575, -0.024636613205075264, -0.0385991707444191, 0.0045736609026789665, 0.018061695620417595, -0.015386585146188736, 0.04106735810637474, -0.030667880550026894, 0.010122827254235744, 0.011742832139134407, -0.023441368713974953, -0.024512620642781258, 0.019389482215046883, 0.03554369881749153, -0.017304571345448494, -0.02789754420518875, -1.7136033420683816e-05, -0.020921949297189713, -0.02825366146862507, -0.04409275949001312, 0.017808198928833008, -0.005420387256890535, -0.07389982789754868, 0.04343635216355324, 0.03943983092904091, 0.003293809713795781, -0.05905211716890335, -0.11574313789606094, 0.033246494829654694, 0.08886709809303284, -0.050691477954387665, -0.025377318263053894, 0.033393632620573044, -0.0660095140337944, 0.009245825000107288, -0.037006925791502, -0.0102424006909132, -0.06316211074590683, -0.020445186644792557, -0.045091066509485245, 0.03400412201881409, -0.0453706718981266, 0.03323955833911896, -0.013767611235380173, -0.062935970723629, 0.023886876180768013, -0.003289590124040842, 0.045754898339509964, -0.005349705461412668, 0.001300764619372785, -0.05159486457705498, 0.028317661955952644, -0.007222292013466358, 0.012022017501294613, -0.026632210239768028, -0.09576327353715897, 0.08887872099876404, -0.015585348941385746, 0.059063076972961426, -0.04736141487956047, 0.00992429070174694, 0.0052628712728619576, 0.0015432598302140832, 0.0031337053515017033, -0.060269199311733246, -0.013077898882329464, -0.04336131364107132, -0.00877770222723484, 0.02615509368479252, -0.016542455181479454, 0.05177340283989906, 0.023949364200234413, -0.011373275890946388, -0.04799969866871834, -0.0016709663905203342, -0.023772986605763435, 0.017802074551582336, 0.00566613906994462, 0.035041939467191696, -0.003095077583566308, -0.008860208094120026, -0.07260094583034515, 0.04623273387551308, 0.02498730458319187, 0.00574969919398427, -0.030906107276678085, -0.04331526532769203, 0.0262006763368845, -0.09999413043260574, 0.027015307918190956, -0.0025746736209839582, -0.035230230540037155, -0.04188583418726921, 0.03908179700374603, 0.048342473804950714, 0.0057391817681491375, 0.022239727899432182, 0.03512904420495033, 0.008033648133277893, -0.004469343926757574, 0.011478069238364697, -0.015813687816262245, -0.024544285610318184, 0.0014176071854308248, -0.050279196351766586, -0.005747711751610041, 0.028619946911931038, 0.0023337462916970253, -0.026737965643405914, 0.03282850608229637, 0.0355367511510849, 0.03806727007031441, -0.03176995366811752, -0.014939804561436176, 0.014302922412753105, -0.010049141012132168, 0.016867438331246376, 0.005185588262975216, -0.011469259858131409, -0.047874175012111664, 0.012516303919255733, 0.026667945086956024, 0.003990065306425095, 0.017330991104245186, -0.00623280368745327, -0.02540004812180996, -0.060136448591947556, 0.04421519860625267, 0.018238449469208717, 0.06393741816282272, 0.0301506444811821, 0.059175048023462296, -0.017969798296689987, 0.027617724612355232, 0.0014781897189095616, -0.06945987045764923, -0.003296616720035672, -0.022105606272816658, 0.08901673555374146, 0.07525110244750977, 0.009881152771413326, 0.04101409763097763, 0.007332955952733755, -0.025602733716368675, 0.040238115936517715, -0.04245453327894211, -0.04517297074198723, 0.0457528792321682, -0.012421130202710629, -0.03012758493423462, 0.007423554081469774, -0.00518386485055089, 0.07044623792171478, 0.058040495961904526, -0.011233636178076267, -0.024340827018022537, -0.04733775183558464, 0.019177956506609917, -0.04830673336982727, 0.02273661457002163, 0.027149753645062447, 0.014606460928916931, -0.02090575359761715, -0.027013659477233887, -0.08142832666635513, 0.04276274889707565, -0.023620644584298134, -0.0668831467628479, 0.01206094492226839, -0.004295114427804947, -0.0003916917194146663, -0.04128895699977875, -0.016661515459418297, -0.027751445770263672, 0.008693316020071507, -0.029153790324926376, -0.012472836300730705, 0.004584791604429483, -0.052814558148384094, -0.047598082572221756, 0.04601888731122017, 0.024398699402809143, -0.030216896906495094, -0.048011649399995804, 0.018132580444216728, 0.03834749013185501, 0.07029049098491669, -0.04191184043884277, 0.029362214729189873, -0.052429214119911194, 0.05895611643791199, 0.023072006180882454, 0.06447351723909378, -0.00040749783511273563, -0.03093629702925682, 0.030133038759231567, 0.019780853763222694, -0.07194514572620392, -0.01377305667847395, 0.055660806596279144, -0.018132409080863, 0.007033459842205048, -0.0029821123462170362, -0.0004907537950202823, 0.029723061248660088, -0.042015232145786285, 0.0032109057065099478, -0.04027382656931877, 0.047508224844932556, 0.012112189084291458, 0.057917140424251556, 0.008265030570328236, -0.030784856528043747, -0.01866781897842884, 0.09908919036388397, -0.04468230530619621, -0.07972545921802521, 0.02932429499924183, -0.08303265273571014, 0.00866516400128603, 0.005644180811941624, -0.05385981872677803, 0.03158712014555931, -0.03315966576337814, -0.02077357843518257, -0.08863619714975357, -0.04358840733766556, 0.04876622557640076, -0.035186003893613815, 0.028753425925970078, 0.057973235845565796, 0.01243616919964552, 0.07513710111379623, -0.012298366986215115, -0.0302655640989542, 0.0195469968020916, 0.04414502903819084, 0.002024488290771842, -0.0025222983676940203, 0.02633684128522873, -0.04398677125573158, -0.017854588106274605, 0.006356189958751202, -0.0052641830407083035, 0.017677925527095795, 0.01693454012274742, 0.010285821743309498, -0.007664176635444164, 0.023724475875496864, 0.026418909430503845, 0.031080935150384903, 0.06708983331918716, 0.0473315566778183, -0.043877728283405304, 0.004183682147413492, -0.007154044229537249, -0.013844167813658714, 0.04529345780611038, -0.021066278219223022, -0.06697611510753632, 0.009255068376660347, -0.07048241049051285, -0.0036902541760355234, 0.0031704094726592302, -0.05544663220643997, 0.0379619300365448, 0.025646746158599854, -0.03338789567351341, 0.017234455794095993, -0.06476414203643799, -0.004122348036617041, -0.006445252802222967, 0.1013864204287529, -0.0018790338654071093, 0.02264978364109993, -0.019633246585726738, 0.039493411779403687, -0.023390160873532295, -0.04003264755010605, -0.004316117148846388, -0.02528989687561989, -0.047088850289583206, 0.019826723262667656, 0.00027402120758779347, -0.0356585830450058, 0.013303284533321857, -0.05382853001356125, -0.028890762478113174, -0.02098146080970764, 0.011110503226518631, 0.051210179924964905, 0.0100975651293993, -0.006008525379002094, -0.0016651340993121266, -0.023510020226240158, 0.014973499812185764, -0.05174053832888603, 0.038016967475414276, -0.004597667139023542, 0.018666213378310204, 0.023209454491734505, -0.02497524581849575, 0.018138479441404343, -0.033673904836177826, -0.014828786253929138, 0.0019582046661525965, -0.0065275258384644985, -0.03418980538845062, 0.03137704357504845, 0.0198028814047575, -0.0007646549493074417, 0.026195460930466652, 0.02112942561507225, -0.029009507969021797, 0.0269773006439209, 0.007107808720320463, 0.06314114481210709, -0.005273016635328531, -0.016665035858750343, 0.0481170117855072, 0.04015569016337395, 0.012686159461736679, 0.01902925595641136, -0.04473312571644783, 0.029717864468693733, -0.023761345073580742, -0.002991829067468643, 0.009851335547864437, 0.034929972141981125, 0.05065906047821045, -0.0337996669113636, 0.02528064139187336, 0.01032951008528471, 0.034439802169799805, 0.044890400022268295, 0.05636012554168701, 0.020992480218410492, 0.061946794390678406, 0.005372951272875071, 0.034554220736026764, -0.005113872699439526, -0.04860030487179756, -0.023162538185715675, -0.04157198593020439, -0.00496716471388936, 0.024408426135778427, 0.06381256878376007, -0.0382513664662838, -0.02057039551436901, -0.015624189749360085, 0.03140350431203842, -0.0015441414434462786, -0.012419418431818485, -0.06790821254253387, 0.0015884505119174719, 0.0392523929476738, 0.037289801985025406, -0.00609456654638052, 0.06812171638011932, 0.05056363716721535, 0.06694617867469788, 0.03877019137144089, -0.025859205052256584, -0.005607502534985542, -0.025537483394145966, 0.009882728569209576, 0.10803259164094925, 0.04519782215356827, -0.015286366455256939, -0.016454428434371948, 0.02878458984196186, 0.034592386335134506, -0.011340511031448841, 0.015228605829179287, 0.059524934738874435, -0.04453525319695473, 0.030788319185376167, -0.043289583176374435, -0.019111638888716698, 0.04816621169447899, -0.07634826004505157, -0.006184910424053669, -0.03137964382767677, 0.008327011950314045, -0.05489581450819969, -5.585904339385385e-33, 0.004549697507172823, -0.03612406179308891, 0.007975752465426922, -0.07592832297086716, -0.04208933934569359, -0.0551304891705513, -0.0001646581367822364, 0.013836218975484371, 0.023634472861886024, -0.000846794864628464, -0.02396978996694088, -0.032108597457408905, 0.011730823665857315, 0.00977888610213995, 0.021958278492093086, -0.016166869550943375, -0.015726594254374504, 0.0150983901694417, -0.013576755300164223, 0.0005670760874636471, 0.04260323569178581, 0.027653981000185013, -0.015749366953969002, -0.02673514373600483, -0.04180964082479477, 0.02840648591518402, -0.021536577492952347, -0.0019615550991147757, -0.021675890311598778, 0.01076449267566204, 0.016952790319919586, -0.024627087637782097, -0.01754242740571499, -0.0541096031665802, 0.012547026388347149, -0.0798795148730278, 0.004905371461063623, -0.05778667703270912, -0.07573055475950241, 0.018605075776576996, 0.00723830284550786, 0.00805399939417839, 0.013737701810896397, -0.019749101251363754, -0.030637038871645927, 0.013891219161450863, 0.031185602769255638, -0.002300715772435069, -0.051936496049165726, 0.004493281245231628, 0.02868591621518135, 0.0006853097002021968, -0.005729194264858961, 0.006923148408532143, 0.0021054884418845177, 0.051034774631261826, -0.03728443384170532, -0.03021734021604061, 0.010135010816156864, 0.014036161825060844, 0.002606774214655161, 0.011137407273054123, -0.029719598591327667, 0.03453594073653221, 0.03885139897465706, 0.021738853305578232, -0.02169688791036606, -0.0038955167401582003, 0.06180568411946297, -0.00814512837678194, -0.06766822189092636, 0.002764761680737138, -0.01243152841925621, 0.0011031815083697438, 0.054669272154569626, -0.009723542258143425, 0.011601983569562435, 0.07905984669923782, 0.05934811383485794, 0.050159383565187454, -0.03061710111796856, 0.03463785722851753, -0.012740712612867355, 0.01992393098771572, 0.011712196283042431, 0.013309608213603497, 0.016115766018629074, -0.018154287710785866, 0.027444684877991676, 0.01536222081631422, 0.03783939406275749, -0.01762673445045948, 0.002644384279847145, -0.00012587656965479255, 0.030360857024788857, -0.046730004251003265, 0.01456913910806179, 0.03199184685945511, -0.018899045884609222, -0.029193557798862457, -0.05412076413631439, -0.04959244281053543, -0.011614944785833359, -0.017620636150240898, 0.013810662552714348, 0.0015176727902144194, -0.003030865453183651, 0.015960505232214928, -0.02433144487440586, 0.011196961626410484, 0.024165824055671692, -0.0012977917212992907, 0.036611732095479965, 0.0007502064690925181, 0.03335652872920036, -0.05335615575313568, 0.007718613371253014, 0.05954508110880852, 0.0003453923563938588, -0.08994917571544647, -0.0074996924959123135, 0.0022242553532123566, -0.024889947846531868, -0.004165175370872021, -0.02736922912299633, 0.0390712209045887, -0.04949769005179405, 0.03380715847015381, -0.06915900111198425, -0.05394706130027771, 0.005135107785463333, -0.014575863257050514, 2.8733174417538976e-07, -0.06847956031560898, 0.003422836773097515, -0.009996023960411549, -0.05215100571513176, -0.00989825464785099, 0.050035275518894196, -0.040662556886672974, -0.01367015391588211, -0.03206094354391098, 0.07602173835039139, 0.06022469699382782, -0.04953641816973686, 0.01689894124865532, -0.017522132024168968, -0.015225386247038841, -0.04601145163178444, -0.001300508389249444, 0.06861013919115067, -0.024196719750761986, -0.01733469031751156, -0.03524298965930939, 0.021006615832448006, 0.02720559388399124, -0.03499762713909149, 0.04149919003248215, -0.046627506613731384, 0.019726987928152084, 0.016284052282571793, 0.02410583198070526, -0.02159309946000576, 0.019101878628134727, 0.018372351303696632, -0.04900219663977623, -0.05645690858364105, -0.0073772151954472065, 0.04137912765145302, -0.021163269877433777, 0.031411971896886826, 0.013186836615204811, 0.0018569210078567266, 0.019546866416931152, 0.03381992131471634, 0.06427675485610962, 0.017490293830633163, 0.017523594200611115, -0.04404224827885628, -0.02984984777867794, -0.017196020111441612, 0.027284404262900352, 0.007413793355226517, 0.006018601357936859, -0.00837698020040989, 0.009390566498041153, -0.026461878791451454, -0.005666289012879133, 0.029804248362779617, -0.02138226479291916, 0.0051319473423063755, 0.016526630148291588, 0.07832974195480347, 0.0074459705501794815, 0.022700481116771698, -0.019812364131212234, 0.1003478541970253, 0.019953425973653793, -0.122858427464962, 0.002842172747477889, 2.534424595090393e-34, -0.007189412601292133, -0.02971676178276539, -0.011082812212407589, -0.007765826303511858, 0.00599499000236392, 0.007255012635141611, 0.012030395679175854, 0.009019656106829643, 0.055376648902893066, 0.01645842008292675, -0.010799652896821499]

['Cem Tekin', 'Mingyan Liu']

1107.4153v1

We study the problem of allocating multiple users to a set of wireless channels in a decentralized manner when the channel quali- ties are time-varying and unknown to the users, and accessing the same channel by multiple users leads to reduced quality due to interference. In such a setting the users not only need to learn the inherent channel quality and at the same time the best allocations of users to channels so as to maximize the social welfare. Assuming that the users adopt a certain online learning algorithm, we investigate under what conditions the socially optimal allocation is achievable. In particular we examine the effect of different levels of knowledge the users may have and the amount of communications and cooperation. The general conclusion is that when the cooperation of users decreases and the uncertainty about channel payoffs increases it becomes harder to achieve the socially opti- mal allocation.

Performance and Convergence of Multi-user Online Learning

http://arxiv.org/pdf/1107.4153v1

Title Performance Convergence Multiuser Online Learning Summary study problem allocating multiple user set wireless channel decentralized manner channel quali tie timevarying unknown user accessing channel multiple user lead reduced quality due interference setting user need learn inherent channel quality time best allocation user channel maximize social welfare Assuming user adopt certain online learning algorithm investigate condition socially optimal allocation achievable particular examine effect different level knowledge user may amount communication cooperation general conclusion cooperation user decrease uncertainty channel payoff increase becomes harder achieve socially opti mal allocation Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.006412604358047247, -0.00685839680954814, -0.018063856288790703, -0.05273253470659256, -0.02940223552286625, -0.027210433036088943, 0.052487507462501526, -0.031595148146152496, -0.03633590415120125, -0.018512319773435593, -0.0009975646389648318, 0.02545742690563202, -0.023026078939437866, 0.0005301390192471445, -0.043359555304050446, -0.031011497601866722, -0.010064290836453438, -0.01847275160253048, -0.010829116217792034, -0.018725261092185974, 0.021636582911014557, -0.02130287140607834, -0.012463761493563652, -0.008318614214658737, -0.03831527382135391, -0.017711110413074493, 0.0014055464416742325, -0.025950979441404343, -0.002907771384343505, 0.0012525621568784118, 0.03177308663725853, -0.008025329560041428, 0.006593030411750078, 0.021368982270359993, 2.038245838775765e-06, -0.009772449731826782, -0.061631377786397934, 0.005694093182682991, 0.01431355345994234, 0.031521670520305634, -0.005899740848690271, 0.002153053181245923, -0.0036619629245251417, 0.03435255214571953, -0.016130540519952774, 0.0553676076233387, 0.039534781128168106, -0.017443157732486725, 0.05594899505376816, 0.006809957325458527, 0.004018611740320921, -0.038635943084955215, -0.016060177236795425, 0.021646589040756226, 5.402213355409913e-05, -0.047996848821640015, 0.03420179337263107, 0.027685385197401047, -0.04289974644780159, -0.07020901888608932, 0.004983751103281975, 0.03919973224401474, 0.022398589178919792, -0.004312986042350531, 0.0925663635134697, -0.041032060980796814, -0.010634571313858032, -0.032798849046230316, -0.05433250963687897, -0.016390852630138397, -0.0004334563564043492, 0.021336060017347336, 0.008412146009504795, 0.009271089918911457, -0.024812763556838036, 0.05293837562203407, -0.03524942323565483, 0.011922790668904781, -0.07429315149784088, 0.009167694486677647, -0.03567136451601982, 0.05777273699641228, -0.027729827910661697, 0.03449955955147743, -0.015409326180815697, 0.11272923648357391, -0.06450396776199341, -0.02054752968251705, 0.0006113209528848529, 0.024856528267264366, -0.01998496986925602, 0.019974296912550926, 0.05365315079689026, 0.010353527963161469, -0.047169409692287445, -0.0036761697847396135, -0.00813924428075552, -0.025530897080898285, -0.017201924696564674, -0.06232811510562897, 0.0623573362827301, -0.06504899263381958, 0.1007416695356369, 0.009399842470884323, 0.03256595507264137, -0.06642784178256989, -0.019405154511332512, 0.006670388393104076, 0.009456959553062916, 0.021339666098356247, -0.054904669523239136, -0.0029775435104966164, -0.007723877672106028, 0.07533130794763565, 0.043078240007162094, -0.03986663743853569, -0.061693236231803894, 0.043399520218372345, -0.023015135899186134, -0.01258830912411213, -0.0005954811349511147, -0.003597737057134509, 0.0037631310988217592, 0.03865564614534378, -0.002246873453259468, -0.016800660640001297, -0.008919770829379559, 0.07029233127832413, -0.03722488135099411, -0.036284685134887695, 0.0413624607026577, 0.027761291712522507, -0.03274872899055481, 0.016773302108049393, -0.05239209905266762, 0.07059719413518906, -0.018809601664543152, 0.03067309409379959, 0.0019405379425734282, -0.06672101467847824, 0.0790693387389183, 0.005314727313816547, -0.035434186458587646, -0.030295344069600105, -0.03840380534529686, 0.004359864164143801, -0.018293792381882668, 0.019419383257627487, -0.034141648560762405, -0.05598369985818863, -0.0224906075745821, 0.01065787672996521, -0.012326215393841267, 0.03858407214283943, 0.1314086616039276, 0.026850206777453423, -0.02547561004757881, 0.042035747319459915, 0.014421166852116585, 0.006182483863085508, 0.03602125495672226, -0.05401322618126869, -0.016849519684910774, -0.022844642400741577, 0.06717919558286667, 0.014921505935490131, 0.08132810890674591, -0.03975808620452881, 0.006985511630773544, 0.05322372913360596, -0.029235223308205605, 0.04663700982928276, -0.03845678269863129, 0.03313996642827988, 0.02409221976995468, 0.04399116337299347, 0.1020766943693161, 0.011655602604150772, -0.09204571694135666, 0.12330182641744614, 0.0015024924650788307, -0.04379938170313835, 0.006948893424123526, 0.044349320232868195, -0.02433020807802677, -0.038104962557554245, 0.028934311121702194, 0.004190746694803238, -0.008665340952575207, 0.006552185397595167, 0.005901355762034655, -0.04658346250653267, -0.01968284137547016, 0.027103768661618233, 0.031138217076659203, -0.0614740364253521, -0.003113578772172332, -0.03297033533453941, 0.03731156140565872, -0.004597429186105728, -0.011715737171471119, -0.07385598868131638, 0.032928019762039185, -0.04006185010075569, -0.008628442883491516, 0.0032269866205751896, 0.009916707873344421, -0.028743090108036995, 0.0021835332736372948, -0.043526407331228256, 0.035833459347486496, -0.01549261249601841, 0.028472162783145905, 0.011334207840263844, -0.01774050109088421, 0.0832863375544548, -0.0137091763317585, 0.006413402501493692, 0.010557934641838074, 0.022418349981307983, -0.037089720368385315, 0.053135454654693604, -0.01929369941353798, 0.030631136149168015, 0.021366003900766373, 0.029705794528126717, 0.009425857104361057, 0.035233549773693085, 0.05157553032040596, -0.01774030365049839, 0.045900456607341766, -0.03444782644510269, 0.011935449205338955, 0.0006572935963049531, -0.06017865240573883, -0.041816823184490204, -0.03186725080013275, 0.033506203442811966, 0.0020507327280938625, -0.04324183240532875, 0.05097212642431259, 0.0011812291340902448, 0.015705782920122147, -0.0049588847905397415, 0.02914866805076599, 0.0007956061162985861, 0.04540826752781868, -0.012274674139916897, -0.00026554480427876115, -0.007990353740751743, 0.022863809019327164, 0.009798344224691391, 0.030270779505372047, 0.03302042558789253, -0.02613317035138607, -0.04805478826165199, -0.02998913638293743, 0.03207096457481384, -0.003458519233390689, 0.05238400772213936, -0.06228237226605415, -0.029262689873576164, 0.02281402423977852, -0.022416459396481514, 0.032539188861846924, 0.03119978867471218, 0.008160949684679508, 0.05710478127002716, -0.02630412019789219, -0.04256289452314377, 0.03149805963039398, 0.005751625634729862, -0.03626125305891037, 0.032032087445259094, -0.03577377647161484, 0.004163142293691635, 0.025457818061113358, 0.004002563655376434, -0.01244663167744875, 0.009518353268504143, 0.028026554733514786, 0.014350080862641335, 0.008141492493450642, -0.01241689920425415, 0.008757192641496658, -0.007486083544790745, 0.060303814709186554, -0.07350452244281769, -0.04868622496724129, -0.03177915886044502, -0.01976625993847847, -0.016276663169264793, 0.010740778408944607, -0.009420955553650856, 0.022490642964839935, 0.04832693189382553, -0.05235983058810234, 0.02665712684392929, 0.019131606444716454, 0.05535799637436867, -0.0032293985132128, 0.04653230309486389, -0.06640498340129852, -0.010632319375872612, 0.022207660600543022, -0.04940074682235718, 0.002064804546535015, 0.044556230306625366, 0.04449554532766342, 0.024749990552663803, -0.009362231008708477, 0.014392352662980556, -0.014049823395907879, 0.0195513516664505, -0.02125844918191433, -0.08385317027568817, -0.06384513527154922, -0.0003010096261277795, 0.00768722128123045, -0.013487040065228939, 0.0587783083319664, -0.008508550003170967, 0.07365809381008148, 0.06483667343854904, 0.006680138409137726, -0.027470555156469345, -0.07223160564899445, 0.005099700763821602, -0.015927055850625038, -0.014907227829098701, 0.05010632425546646, -0.05059215426445007, -0.0331965796649456, -0.007171289063990116, -0.015796709805727005, 0.08733908832073212, -0.048789121210575104, -0.053732842206954956, -0.006423220504075289, -0.010270745493471622, -0.04924172908067703, -0.029135307297110558, 0.012957426719367504, 0.0007297636475414038, 0.04176421836018562, -0.03453681617975235, -0.006341959815472364, 0.02171434462070465, 0.03891913220286369, 0.012855838984251022, 0.0027728634886443615, -0.03858110308647156, -0.02554532140493393, -0.0005322227370925248, 0.024673836305737495, -0.007530570030212402, -0.004867257084697485, 0.002697334624826908, -0.0521983802318573, -0.028823819011449814, 0.013241603970527649, 0.0028907395899295807, 0.02978135272860527, 0.0034851960372179747, 0.03005526214838028, 0.005540237296372652, 0.03735164552927017, -0.07203134149312973, -0.0013756725238636136, 0.04338103532791138, 0.06406821310520172, -0.006350110284984112, 0.05147566273808479, 0.01578165963292122, 0.029414229094982147, -0.10646987706422806, -0.043604083359241486, -0.05711561068892479, 0.0021015899255871773, 0.0028817225247621536, 0.017666632309556007, -0.05652237311005592, -0.00779196061193943, -0.027621455490589142, 0.05449237301945686, 0.0019273437792435288, -0.050045423209667206, -0.03120206855237484, -0.022364385426044464, -0.030945632606744766, 0.010002023540437222, -0.06936796754598618, 0.015307770110666752, -0.031511321663856506, -0.028777340427041054, -0.03959979489445686, 0.02016216330230236, -0.012334144674241543, 0.023717178031802177, -0.0036392908077687025, 0.062338631600141525, -0.06256737560033798, -0.0055089653469622135, -0.04598812758922577, -0.06727162003517151, 0.052165817469358444, 0.01705288328230381, 0.013650604523718357, 0.00289167370647192, -0.058470193296670914, 0.0042421226389706135, -0.0059632048942148685, -0.00706184608861804, -0.027959095314145088, 0.0017387873958796263, -0.033013273030519485, 0.028020091354846954, -0.016891630366444588, 0.04006003215909004, 0.03354700654745102, 0.03551846742630005, 0.055557940155267715, 0.004827121272683144, -0.004924918059259653, -0.008077070116996765, -0.0033359904773533344, 0.024194901809096336, 0.051871974021196365, -0.011154483072459698, -0.04712453857064247, -0.021954312920570374, -0.021688014268875122, 0.0053097400814294815, 0.01591063290834427, 0.016099654138088226, 0.016312630847096443, 0.024200478568673134, -0.027275225147604942, -0.03693872317671776, -0.052373915910720825, 0.06514256447553635, -0.002859533531591296, 0.040007732808589935, -0.006698906887322664, 0.05597672611474991, 0.060246940702199936, 0.04693762958049774, 0.0032422549556940794, -0.07079174369573593, 0.052594609558582306, 0.02430807612836361, -0.017200199887156487, 0.014448008500039577, -0.016798224300146103, -0.02014022134244442, 0.03676248714327812, -0.029874682426452637, -0.045376669615507126, -0.04083343595266342, 0.02735064923763275, 0.011001602746546268, 0.021662335842847824, 0.007064915727823973, -0.00047670365893281996, -0.03630483150482178, -0.014095992781221867, 0.017185300588607788, -0.046315182000398636, 0.0016597877256572247, 0.05544457957148552, 0.044394396245479584, 0.012116760015487671, 0.061427172273397446, -0.004093674942851067, 0.01358441635966301, 0.0019744273740798235, -0.07941652089357376, -0.067936010658741, 0.02042107842862606, -0.024261275306344032, -0.009726118296384811, 0.014470306225121021, 0.029406657442450523, -0.0740494430065155, 0.029131220653653145, 0.03959251195192337, 0.028534742072224617, 0.01305161602795124, -0.022475959733128548, -0.0036952218506485224, 0.016599563881754875, 0.01604229398071766, 0.03621957451105118, -0.012688801623880863, 0.11501624435186386, -0.04259682819247246, 0.036169108003377914, 0.04081423208117485, -0.011639809235930443, -0.03845638409256935, -0.017800867557525635, 0.06396494805812836, -0.0053441873751580715, -0.002745651872828603, 0.0357840396463871, 0.037979982793331146, -0.03547826036810875, 0.00792135763913393, -0.0162167027592659, 0.048249710351228714, 0.04871159419417381, 0.007586325518786907, 0.03058026172220707, -0.06726334989070892, 0.027510549873113632, 0.041778743267059326, -0.02860032580792904, 0.08052333444356918, 0.026874378323554993, -0.030310170724987984, 0.03396572917699814, 0.002685606013983488, 0.042857762426137924, -0.12837618589401245, 0.003822788828983903, 0.015353092923760414, -0.01305136177688837, -0.009415189735591412, 0.03626984357833862, 0.00891205295920372, 0.0062800063751637936, -0.029191209003329277, -0.09451090544462204, -0.050276778638362885, -0.028722016140818596, 0.048918288201093674, 0.043618954718112946, 0.025084545835852623, -0.03882439061999321, 0.013870581984519958, 0.024472128599882126, 0.03463122621178627, -0.0465935543179512, -0.019626103341579437, 0.057921089231967926, -0.0064576733857393265, 0.025878431275486946, -0.0055875396355986595, -0.042804718017578125, 0.007015706971287727, -0.04410016909241676, -0.028109390288591385, -0.0007549255387857556, 0.015618661418557167, 0.04565194994211197, -6.036623036295221e-33, -0.01488399039953947, -0.006341553758829832, -0.04429082199931145, 0.0008252370171248913, -0.028838135302066803, -0.03547808155417442, 0.039642855525016785, 0.0018600351177155972, 0.003547786269336939, -0.050639521330595016, -0.01095697470009327, 0.027875211089849472, 0.040511082857847214, 0.008541383780539036, 0.006207503378391266, 0.009852380491793156, 0.005976769607514143, -0.015607766807079315, -0.01746763288974762, 0.002302690176293254, -0.00431909691542387, 0.026348423212766647, -0.01503703836351633, 0.027100766077637672, -0.03192635253071785, 0.002271640347316861, -0.012931634671986103, -0.017018092796206474, -0.0533783882856369, -0.0016763380263000727, 0.002536775777116418, -0.0038189857732504606, 0.015017444267868996, -0.009707294404506683, 0.020880000665783882, -0.004767934326082468, -0.0008011020836420357, 0.012563218362629414, -0.07074317336082458, 0.03941447660326958, -0.04605140909552574, 0.016628997400403023, 0.039844948798418045, 0.013258556835353374, -0.0710107758641243, 0.0012415716191753745, 0.057051751762628555, 0.056235820055007935, -0.06548423320055008, -0.013274687342345715, 0.03190234303474426, -0.0007295127143152058, 0.01783422939479351, 0.015810532495379448, -0.007708949968218803, -0.06042461469769478, -0.041584406048059464, -0.07766906172037125, -0.0567208006978035, 0.036143869161605835, -0.07260172814130783, 0.013893547467887402, -0.0077743446454405785, -0.014610713347792625, 0.008581753820180893, 0.024539383128285408, -0.03323027864098549, -0.021436750888824463, -0.012198265641927719, -0.04263909161090851, -0.002355125267058611, -0.018071673810482025, -0.026336444541811943, -0.011564888060092926, -0.009127589873969555, -0.06131492182612419, 0.0015011554351076484, -0.009481670334935188, 0.07043961435556412, -0.01185908168554306, -0.030300656333565712, 0.0029430428985506296, 0.0005346322432160378, -0.016773629933595657, 0.005800697952508926, -0.032064586877822876, 0.0215021800249815, -0.021877478808164597, -0.01522559579461813, -0.00578952906653285, 0.0007197188097052276, 0.0014237015275284648, 0.007941674441099167, -0.06987934559583664, -0.017628895118832588, -0.027233002707362175, 0.03664327412843704, 0.061558835208415985, 0.0008852833998389542, -0.017028825357556343, -0.10716038942337036, -0.037143900990486145, -0.04171772673726082, 0.0036435462534427643, 0.006391867995262146, -0.008119942620396614, 0.023513101041316986, 0.046827126294374466, -0.03062073513865471, 0.022953607141971588, 0.026503996923565865, 0.00935772992670536, 0.06990683823823929, 0.027743851765990257, 0.05634331330657005, -0.09234285354614258, -0.0008810343570075929, 0.028247475624084473, -0.015841776505112648, -0.03112669289112091, -0.02490457333624363, -0.07327574491500854, -0.023255251348018646, -0.03204444423317909, -0.04132140055298805, 0.047419898211956024, -0.07219891995191574, 0.014754357747733593, 0.00690283952280879, -0.03047463297843933, -0.016474878415465355, -0.0678463876247406, 2.74859473847755e-07, -0.013401784002780914, 0.06726739555597305, -0.014758272096514702, -0.022572744637727737, -0.028734412044286728, -0.012602737173438072, -0.01571628451347351, 0.03625881299376488, -0.02468448132276535, 0.05676541104912758, -0.012809710577130318, -0.006113331764936447, 0.05500207096338272, 0.006132741924375296, -0.0292084738612175, -0.05448693782091141, -0.05317050218582153, 0.08069849759340286, -0.02374946139752865, 0.014844630844891071, 0.029349004849791527, -0.005158391315490007, 0.021159956231713295, -0.031388942152261734, 0.04354912415146828, 0.0025795905385166407, 0.00252893497236073, 0.03039492480456829, -0.004590735770761967, 0.010725926607847214, 0.038573794066905975, -0.017812678590416908, -0.03418206050992012, 0.004579834174364805, 3.760857362067327e-05, 0.0008726119995117188, -0.017944728955626488, 0.022539816796779633, 0.027862228453159332, 0.016051700338721275, -0.009828346781432629, -0.023376919329166412, 0.03347305580973625, 0.005977587774395943, 0.023492779582738876, -0.03924060985445976, -0.04194732755422592, 0.007978848181664944, 0.07117096334695816, -0.04423046112060547, 0.03113187849521637, 0.009386012330651283, 0.024727629497647285, -0.020196394994854927, -0.00027251860592514277, 0.018597135320305824, 0.004755948670208454, 0.009772982448339462, 0.03545285388827324, 0.01611347310245037, 0.013557692989706993, -0.07043009996414185, 0.012185540050268173, 0.05563279986381531, 0.0675194039940834, 0.008726662024855614, 0.02986229956150055, 2.0184973694496063e-34, -0.011615779250860214, 0.00031571488943882287, 0.03619782626628876, 0.009974672459065914, -0.02946396730840206, -0.018644439056515694, 0.016624875366687775, -0.011847525835037231, 0.035549625754356384, 0.028559735044836998, 0.027546804398298264]

['Bin Yang', 'Manohar Kaul', 'Christian S. Jensen']

1308.0484v2

We are witnessing increasing interests in the effective use of road networks. For example, to enable effective vehicle routing, weighted-graph models of transportation networks are used, where the weight of an edge captures some cost associated with traversing the edge, e.g., greenhouse gas (GHG) emissions or travel time. It is a precondition to using a graph model for routing that all edges have weights. Weights that capture travel times and GHG emissions can be extracted from GPS trajectory data collected from the network. However, GPS trajectory data typically lack the coverage needed to assign weights to all edges. This paper formulates and addresses the problem of annotating all edges in a road network with travel cost based weights from a set of trips in the network that cover only a small fraction of the edges, each with an associated ground-truth travel cost. A general framework is proposed to solve the problem. Specifically, the problem is modeled as a regression problem and solved by minimizing a judiciously designed objective function that takes into account the topology of the road network. In particular, the use of weighted PageRank values of edges is explored for assigning appropriate weights to all edges, and the property of directional adjacency of edges is also taken into account to assign weights. Empirical studies with weights capturing travel time and GHG emissions on two road networks (Skagen, Denmark, and North Jutland, Denmark) offer insight into the design properties of the proposed techniques and offer evidence that the techniques are effective.

Using Incomplete Information for Complete Weight Annotation of Road Networks -- Extended Version

http://arxiv.org/pdf/1308.0484v2

Title Using Incomplete Information Complete Weight Annotation Road Networks Extended Version Summary witnessing increasing interest effective use road network example enable effective vehicle routing weightedgraph model transportation network used weight edge capture cost associated traversing edge eg greenhouse gas GHG emission travel time precondition using graph model routing edge weight Weights capture travel time GHG emission extracted GPS trajectory data collected network However GPS trajectory data typically lack coverage needed assign weight edge paper formulates address problem annotating edge road network travel cost based weight set trip network cover small fraction edge associated groundtruth travel cost general framework proposed solve problem Specifically problem modeled regression problem solved minimizing judiciously designed objective function take account topology road network particular use weighted PageRank value edge explored assigning appropriate weight edge property directional adjacency edge also taken account assign weight Empirical study weight capturing travel time GHG emission two road network Skagen Denmark North Jutland Denmark offer insight design property proposed technique offer evidence technique effective Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.000518434215337038, 0.07075861841440201, -0.027200251817703247, 0.006896170321851969, -0.020292436704039574, -0.027530454099178314, 0.03619689494371414, 0.0022630393505096436, -0.02496631257236004, -0.04408511519432068, 0.10394570231437683, 0.04095079377293587, -0.008358469232916832, 0.057944077998399734, 0.028931155800819397, -0.08266657590866089, -0.0031226803548634052, -0.021706538274884224, -0.0483301505446434, 0.03491387888789177, 0.01153368316590786, -0.011166091077029705, 0.04005500301718712, 0.00547566544264555, -0.023713478818535805, 0.018171217292547226, -0.02665260061621666, 0.010590201243758202, 0.0423334464430809, -0.0945965126156807, 0.04920193552970886, 0.028287867084145546, 0.053971100598573685, 0.038418274372816086, 2.1245509742584545e-06, 0.017199169844388962, -0.054669857025146484, 0.01849547028541565, 0.034048233181238174, 0.003539825091138482, 0.04632789269089699, 0.021243955940008163, 0.029269207268953323, -0.012971200980246067, 0.01299859769642353, -0.03797925263643265, 0.02257756143808365, -0.023538323119282722, 0.010989561676979065, -0.018833551555871964, -0.021768882870674133, -0.0272793211042881, -0.08395605534315109, 0.001066880184225738, 0.03620285913348198, 0.02671470120549202, -0.003171896329149604, 0.07624654471874237, 0.011243059299886227, 0.0025670852046459913, -0.04769830405712128, 0.010813535191118717, -0.002933577401563525, 0.009235034696757793, 0.08414962887763977, 0.0203802939504385, -0.009098531678318977, -0.0015933040995150805, -0.0032433883752673864, 0.05382990464568138, 0.04678003862500191, -0.021116962656378746, 0.05004190653562546, 0.016266683116555214, -0.05973329767584801, -0.02405514009296894, -0.016346655786037445, -0.05899374559521675, 0.006001053377985954, 0.01755937561392784, -0.05508149415254593, 0.061079561710357666, -0.00027884566225111485, 0.029931707307696342, -0.029246686026453972, 0.023102451115846634, -0.028120525181293488, -0.028786228969693184, 0.008013303391635418, 0.031413931399583817, -0.028671104460954666, -0.02529764734208584, 0.02863972820341587, -0.04242357239127159, 0.008540390990674496, -0.042666930705308914, 0.12645937502384186, -0.016791539266705513, 0.0667705237865448, -0.019031429663300514, 0.05971638858318329, -0.0085010239854455, 0.03888959810137749, -0.006394342985004187, 0.0007086278055794537, 0.005893878173083067, -0.036344289779663086, 0.007803524378687143, -0.015318022109568119, 0.02380555123090744, -0.046697333455085754, -0.03656337037682533, -0.0381113663315773, 0.019421128556132317, -0.011681127361953259, 0.0745798796415329, 0.014617484994232655, 0.01597581058740616, -0.012568392790853977, -0.04157485067844391, -0.007738130167126656, 0.03208290785551071, 0.0573650486767292, -0.025723613798618317, 0.03474107012152672, 0.007139924447983503, -0.044839534908533096, 0.05213212966918945, 0.02953311614692211, 0.08812898397445679, 0.04145084694027901, 0.010967971757054329, 0.041702233254909515, 0.015164614655077457, -0.012315903790295124, 0.0744294673204422, 0.02880273200571537, -0.032008618116378784, -0.07355022430419922, -0.039597827941179276, 0.018807806074619293, -0.02561897598206997, -0.06520670652389526, -0.0695652887225151, 0.004283531568944454, -0.0167480930685997, -0.04969937354326248, 0.042712412774562836, -0.015042796730995178, 0.00439424067735672, -0.06618916988372803, -0.014186450280249119, -0.009673500433564186, 0.01954331062734127, 0.036796554923057556, 0.00873965211212635, 0.05280623212456703, -0.010669924318790436, 0.026422642171382904, 0.03335857763886452, -0.005385744385421276, 0.018212825059890747, -0.044961366802453995, -0.03988969326019287, 0.02745230495929718, 0.029546018689870834, 0.021458083763718605, -0.00944304745644331, -0.04053948074579239, 0.0035939242225140333, -0.007817225530743599, 0.020275849848985672, -0.06533651053905487, 0.09002881497144699, 0.03295763209462166, -0.01890190690755844, 0.03684297949075699, 0.007272771093994379, -0.05440520495176315, 0.06944868713617325, -0.06474866718053818, -0.046420853585004807, 0.0018995440332219005, -0.01448152121156454, -0.09216862916946411, -0.005919578950852156, 0.028583163395524025, 0.016008976846933365, -0.008909737691283226, -0.025662267580628395, 0.02821490727365017, 0.0012655715690925717, 0.07053645700216293, -0.039080262184143066, 0.036722708493471146, -0.07308254390954971, -0.008363263681530952, -0.0355067104101181, -0.014831320382654667, 0.006547529716044664, -0.025835687294602394, 0.008892946876585484, -0.018176067620515823, -0.062128305435180664, -0.008596046827733517, 0.033747218549251556, -0.025374116376042366, -0.015369473956525326, -0.02454792894423008, -0.10390643030405045, 0.018178138881921768, 0.031248608604073524, -0.020985260605812073, -0.018944503739476204, 0.006279638037085533, 0.05478568747639656, 0.04015537351369858, -0.0796452984213829, -0.02655334770679474, 0.058882493525743484, 0.04058682918548584, -0.041711658239364624, -0.020587483420968056, 0.02678835764527321, 0.04055655375123024, 0.06729237735271454, -0.017446618527173996, 0.032199013978242874, -0.013592766597867012, -0.0013305271277204156, 0.00012565177166834474, -0.006941149476915598, 0.028740355744957924, 0.027547534555196762, -0.026958003640174866, 0.059116899967193604, 0.08010595291852951, 0.08951964229345322, -0.022093908861279488, -0.04590298607945442, -0.019817985594272614, 0.0672239288687706, 0.011979753151535988, -0.030607618391513824, -0.06468033045530319, -0.013093709014356136, -0.030592860653996468, 0.006724425125867128, 0.011215241625905037, 0.02967189811170101, -0.019640237092971802, -0.029683923348784447, 0.012994605116546154, 0.05384395271539688, 0.028665263205766678, -0.013249771669507027, -0.022774336859583855, 0.05013187229633331, 0.016428539529442787, 0.06179821118712425, -0.03990756347775459, -0.029578477144241333, -0.02673557959496975, -0.018565060570836067, -0.009937970899045467, 0.008813710883259773, 0.008241998963057995, -0.022143790498375893, 0.01929379440844059, -0.009233808144927025, 0.016024919226765633, 0.004071612376719713, -0.02646918222308159, -0.00116477080155164, 0.0012500174343585968, 0.04234686493873596, 0.037223346531391144, 0.0180877186357975, -0.05524159222841263, 0.04411591589450836, -0.03278426080942154, -0.0196393933147192, -0.026980994269251823, -0.023064034059643745, -0.045820724219083786, 0.047602999955415726, 0.056870508939027786, -0.10731512308120728, -0.03448177129030228, -0.007901748642325401, -0.018335260450839996, -0.009122960269451141, 0.004302992019802332, -0.06044105440378189, -0.06063900515437126, 0.04226084053516388, -0.005553977098315954, -0.04454706981778145, 0.032291706651449203, -0.08129767328500748, 0.015588563866913319, -0.05846434086561203, -0.033941566944122314, 0.02856035716831684, -0.024733202531933784, 0.04405542090535164, 0.006036956328898668, -0.07385876774787903, -0.014569947496056557, -0.023475101217627525, 0.011828710325062275, -0.0011280738981440663, 0.062300775200128555, -0.016833879053592682, -0.01380175817757845, 0.013190031982958317, -0.03666931018233299, 0.013055051676928997, 0.04881735518574715, 0.08524882793426514, 0.02336004003882408, -0.012522418051958084, 0.006111845374107361, -0.0013789169024676085, 0.0005674311541952193, 0.009770487435162067, 0.005115556996315718, 0.019502023234963417, 0.013791493140161037, 0.042579274624586105, 0.01856674998998642, 0.013375425711274147, 0.05075342208147049, 0.031209582462906837, -0.015080442652106285, -0.03599391505122185, 0.029989460483193398, -0.029027847573161125, 0.005262767896056175, 0.018736829981207848, -0.007444869726896286, -0.049729663878679276, 0.004499248694628477, 0.019473141059279442, 0.02213885448873043, -0.032272517681121826, 0.008542385883629322, -0.06048787385225296, 0.05017876625061035, 0.04693063721060753, 0.015244003385305405, 0.03217850252985954, 0.008308237418532372, 0.0017599002458155155, 0.005677813198417425, 0.017382757738232613, 0.010330816730856895, 0.004331690724939108, 0.03523663431406021, 0.02809709683060646, -0.00853854138404131, -0.003066167701035738, -0.020690834149718285, 0.045706890523433685, -0.03745296224951744, 0.060121119022369385, -0.017283344641327858, 0.01437029242515564, -0.02005063183605671, 0.010068204253911972, 0.025046836584806442, -0.03854510188102722, 0.002590693300589919, -0.011745644733309746, 0.0013605437707155943, -0.037703197449445724, 0.023804837837815285, 0.004760667681694031, 0.014161617495119572, -0.02933669462800026, 0.05608546733856201, -0.047992072999477386, 0.05942326784133911, -0.006417735945433378, -0.028845762833952904, -0.05265320837497711, -0.02968016266822815, 0.005255160387605429, -0.02474072389304638, 0.07059094309806824, 0.01169099286198616, -0.0033808238804340363, 0.022428283467888832, -0.10667738318443298, -0.027480091899633408, -0.04415062814950943, -0.07436070591211319, -0.026218919083476067, 0.02469741366803646, -0.02248276397585869, 0.029607851058244705, -0.11007259786128998, 0.006891115102916956, -0.00814493466168642, -0.012368589639663696, 0.03954806178808212, -0.024992691352963448, 0.030459435656666756, -0.05448394641280174, -0.02434205636382103, 0.054116856306791306, 0.0274507999420166, -0.013844113796949387, -0.01717258431017399, 0.03753434121608734, 0.029943937435746193, 0.0049849809147417545, -0.03782057762145996, 0.001186338602565229, -0.03658542409539223, -0.008344713598489761, 0.03805186226963997, 0.06729424744844437, -0.007237025070935488, 0.011742479167878628, -0.019048132002353668, 0.04260579124093056, 0.025562241673469543, -0.04278040677309036, -0.04857410863041878, 0.006916833575814962, -0.0707913339138031, -0.08527564257383347, -0.02725493535399437, -0.053913600742816925, -0.020796408876776695, 0.028116103261709213, -0.003687927732244134, -0.011260888539254665, 0.0028695594519376755, -0.02825414389371872, -0.0048967329785227776, 0.03876003995537758, -0.04626154899597168, 0.03154923394322395, 0.03385217487812042, -0.06548654288053513, -0.036908600479364395, -0.03615107387304306, 0.037492766976356506, 0.048035770654678345, -0.01966775581240654, 0.03759820759296417, -0.002787190955132246, 0.04486899822950363, -0.04535171762108803, -0.03621862828731537, -0.0539998933672905, -0.08102339506149292, 0.023283008486032486, 0.03490656241774559, 0.031140105798840523, -0.014288955368101597, -0.020991763100028038, 0.010278611443936825, -0.0013063594233244658, -0.0015529433730989695, 0.04037651792168617, -0.03384280949831009, -0.0007362521719187498, -0.013695789501070976, 0.01548848394304514, 0.002903424436226487, 0.03599504381418228, 0.03283842280507088, 0.011530312709510326, 0.005949453916400671, -0.040018822997808456, 0.031565628945827484, 0.006827034987509251, 0.0253682192414999, 0.05816878005862236, 0.04967669025063515, 0.041554104536771774, -0.02840098924934864, 0.012190035544335842, 0.0018920399015769362, 0.0043638963252305984, -0.03406934067606926, -0.022814299911260605, -0.013668520376086235, 0.04958745837211609, -0.025679247453808784, -0.00868357252329588, 0.0318479984998703, -0.04677071049809456, -0.015932288020849228, 0.03512609750032425, -0.013608960434794426, -0.011725188232958317, -0.037181612104177475, 0.03693719953298569, 0.01818498596549034, -0.10397854447364807, 0.016316810622811317, 0.03514394909143448, 0.03676717355847359, -0.030620167031884193, 0.019169285893440247, 0.01563488319516182, -0.07695038616657257, 0.0013602470280602574, 0.011824773624539375, -0.0001697871630312875, -0.03501547500491142, 0.029660100117325783, -0.009358602575957775, 0.051794495433568954, -0.020683251321315765, -0.025736430659890175, 0.007954795844852924, 0.03239822015166283, 0.0223354734480381, 0.0019564901012927294, 0.04592771828174591, 0.022782057523727417, -0.02176940068602562, -0.03273386508226395, 0.012245467863976955, 0.038554847240448, 0.07094451040029526, -0.008027097210288048, -0.03959076479077339, -0.00877742562443018, -0.017703337594866753, 0.05965414643287659, 0.021372869610786438, -0.03573344275355339, -0.014296310022473335, 0.00405884999781847, 0.006274233106523752, -0.03174027055501938, 0.032191306352615356, 0.015920177102088928, 0.07216405868530273, -0.0010549823055043817, -0.01745547726750374, -0.0849209800362587, 0.008959203027188778, -0.04228249564766884, 0.04508768394589424, -0.06676612794399261, -0.09540143609046936, 0.04081805795431137, 0.007893760688602924, -6.605184307191022e-33, 0.000692978675942868, -0.07358542829751968, 0.003215144155547023, -0.015772918239235878, -0.07501048594713211, 0.01145479641854763, -0.022700628265738487, 0.013595103286206722, -0.03809613734483719, -0.005711114965379238, -0.014728873036801815, -0.025256453081965446, 0.0076774125918745995, 0.015643112361431122, 0.03847777843475342, 0.06399638950824738, -0.020905062556266785, 0.05907558649778366, -0.014688489027321339, -0.04282146319746971, 0.0003357905661687255, 0.008459636941552162, -0.003838977077975869, 0.017925184220075607, 0.004998341202735901, -0.0280488021671772, -0.030699361115694046, 0.018727608025074005, -0.03209684044122696, 0.03803357854485512, 0.025844618678092957, 0.021191881969571114, 0.013427162542939186, 0.014500830322504044, -0.06959953904151917, 0.04556049779057503, -0.005272441077977419, -0.039394885301589966, -0.003218799363821745, 0.007898890413343906, -0.054993368685245514, -0.017976876348257065, 0.044622696936130524, 0.010249861516058445, 0.007955430075526237, 0.03021797351539135, 0.03367173299193382, -0.020585808902978897, 0.00838153064250946, 0.06219080090522766, 0.0073286364786326885, -0.03695831820368767, -0.03947710245847702, 0.09054603427648544, 0.02897166833281517, 0.04241892322897911, -0.0351066030561924, 0.012726493179798126, -0.032067231833934784, -0.016300376504659653, -0.0231151320040226, 0.035653237253427505, -0.02762194164097309, 0.007089222781360149, 0.0661710575222969, 0.03900241106748581, -0.09614937007427216, -0.03165074810385704, -0.06905177235603333, -0.03927145153284073, 0.00994483008980751, 0.003089634468778968, -0.021487947553396225, -0.04050983488559723, -0.016088655218482018, -0.07524547725915909, -0.07068085670471191, -0.031827107071876526, -0.029624491930007935, -0.021078525111079216, -0.021933795884251595, 0.0017209351062774658, 0.024594608694314957, 0.0004460573836695403, -0.002866948489099741, -0.041236843913793564, -0.0029689099173992872, -0.0510270781815052, -0.032554395496845245, 0.012455631047487259, -0.028079217299818993, 0.03340816870331764, 0.01462568249553442, -0.032708749175071716, -0.02345263585448265, -0.0023005104158073664, 0.0009045222541317344, 0.020421957597136497, 0.008920878171920776, 0.03795071318745613, -0.047587305307388306, -0.01001568604260683, -0.06655032187700272, 0.05534110590815544, 0.01836390048265457, 0.014405614696443081, 0.01450292393565178, -0.017598120495676994, -0.012702963314950466, 0.016040146350860596, -0.011946560814976692, -0.032392606139183044, 0.012598332948982716, -0.03871314972639084, -0.023809602484107018, -0.0136543745175004, 0.009691375307738781, 0.02173309586942196, 0.005676779896020889, 0.01125794742256403, -0.014204311184585094, 0.03061404637992382, -0.046902988106012344, -0.005994442384690046, -0.016071897000074387, -0.012245560996234417, -0.014877168461680412, -0.030575385317206383, 0.0008205382036976516, -0.0012191258138045669, -0.01464027352631092, -0.007336009293794632, 2.8100399163122347e-07, 0.02327069267630577, 0.02729119174182415, -0.021024571731686592, 0.052560534328222275, -0.003961826674640179, -0.023807616904377937, 0.00217239698395133, -0.01525566540658474, -0.019495656713843346, 0.016058137640357018, 0.03276887536048889, -0.004877904430031776, -0.021520201116800308, 0.013114393688738346, -0.011249079369008541, 0.05169746279716492, -0.004995543975383043, -0.03328273445367813, -0.05288464576005936, 0.03223803639411926, 0.06232134625315666, 0.04462843015789986, 0.02577798068523407, 0.023013833910226822, -0.007465559523552656, 0.03364897891879082, -0.011673797853291035, -0.0633942186832428, -0.01189741212874651, -0.012584066949784756, 0.028810476884245872, 0.03673509508371353, -0.005388244986534119, 0.008116185665130615, -0.011053129099309444, -0.025340626016259193, -0.020467113703489304, 0.02157222293317318, 0.001515077194198966, 0.011468867771327496, 0.02939263917505741, -0.07602453231811523, 0.008941744454205036, -0.032312873750925064, -0.011346520856022835, 0.0014820300275459886, 0.010437753982841969, 0.033474553376436234, -0.0053033079020679, -0.005696592386811972, 0.04093838110566139, 0.04238390177488327, 0.02925063483417034, -0.005030028987675905, -0.022217126563191414, -0.005469534546136856, 0.02679777517914772, 0.045270007103681564, 0.04650261253118515, 0.0602206327021122, 0.030577590689063072, -0.00557021563872695, 0.013219368644058704, 0.08492904901504517, 0.07192440330982208, 0.03165358677506447, -0.013505331240594387, 2.5322386806930924e-34, 0.019482241943478584, 0.019589677453041077, -0.009479189291596413, -0.05647344887256622, 0.0067748199217021465, 0.009575147181749344, 0.01907842606306076, -0.027063140645623207, -0.035044457763433456, -0.03253897652029991, -0.04735591635107994]

['Ibrahim Sabek', 'Moustafa Youssef']

1308.0768v1

Device-free (DF) localization is an emerging technology that allows the detection and tracking of entities that do not carry any devices nor participate actively in the localization process. Typically, DF systems require a large number of transmitters and receivers to achieve acceptable accuracy, which is not available in many scenarios such as homes and small businesses. In this paper, we introduce MonoStream as an accurate single-stream DF localization system that leverages the rich Channel State Information (CSI) as well as MIMO information from the physical layer to provide accurate DF localization with only one stream. To boost its accuracy and attain low computational requirements, MonoStream models the DF localization problem as an object recognition problem and uses a novel set of CSI-context features and techniques with proven accuracy and efficiency. Experimental evaluation in two typical testbeds, with a side-by-side comparison with the state-of-the-art, shows that MonoStream can achieve an accuracy of 0.95m with at least 26% enhancement in median distance error using a single stream only. This enhancement in accuracy comes with an efficient execution of less than 23ms per location update on a typical laptop. This highlights the potential of MonoStream usage for real-time DF tracking applications.

MonoStream: A Minimal-Hardware High Accuracy Device-free WLAN Localization System

http://arxiv.org/pdf/1308.0768v1

Title MonoStream MinimalHardware High Accuracy Devicefree WLAN Localization System Summary Devicefree DF localization emerging technology allows detection tracking entity carry device participate actively localization process Typically DF system require large number transmitter receiver achieve acceptable accuracy available many scenario home small business paper introduce MonoStream accurate singlestream DF localization system leverage rich Channel State Information CSI well MIMO information physical layer provide accurate DF localization one stream boost accuracy attain low computational requirement MonoStream model DF localization problem object recognition problem us novel set CSIcontext feature technique proven accuracy efficiency Experimental evaluation two typical testbeds sidebyside comparison stateoftheart show MonoStream achieve accuracy 095m least 26 enhancement median distance error using single stream enhancement accuracy come efficient execution le 23ms per location update typical laptop highlight potential MonoStream usage realtime DF tracking application Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.01658228039741516, -0.03223137557506561, 0.02454759180545807, -0.05127699300646782, -0.04538963362574577, 0.0006878644344396889, 0.06296417862176895, -0.02067403867840767, -0.00982116349041462, -0.027491485700011253, 0.04349096119403839, 0.019006837159395218, 0.0335182324051857, 0.0243130624294281, 0.005873844958841801, -0.02775912545621395, -0.007689948193728924, 0.009780594147741795, -0.0704227015376091, 0.0368698425590992, 0.048770930618047714, -0.009626982733607292, -0.0013406232465058565, -0.013569621369242668, -0.0014538426185026765, 0.027034560218453407, -0.03296190872788429, 0.03161248564720154, -0.013476093299686909, -0.048294831067323685, 0.04291864484548569, 0.027618050575256348, 0.062190502882003784, 0.02997412532567978, 1.8672122905627475e-06, 0.014453005976974964, -0.019034123048186302, -0.022907249629497528, -0.006235986016690731, -0.030966371297836304, -0.05672599747776985, -0.01707157865166664, 0.016357986256480217, 0.014362208545207977, 0.07062601298093796, 0.016498226672410965, 0.014079076237976551, 0.012571590021252632, -0.011915301904082298, 0.036774732172489166, 0.013331713154911995, -0.009646274149417877, -0.03294467553496361, -0.011850749142467976, 0.024055257439613342, -0.013890646398067474, -0.03618382290005684, 0.0015941924648359418, -0.0022260614205151796, 0.04215824231505394, 0.0036189581733196974, 0.03476335480809212, 0.00017962249694392085, 0.04054441303014755, 0.028758591040968895, 0.022420212626457214, -0.055630769580602646, 0.03625136613845825, -0.0058145890943706036, -0.012286691926419735, -0.023690106347203255, -0.029081296175718307, 0.03984340280294418, 0.02159087546169758, -0.01314445212483406, -0.055501505732536316, -0.04516943171620369, -0.040119368582963943, -0.014154590666294098, 0.0009431040962226689, -0.05157866328954697, 0.00795834232121706, -0.024368975311517715, -0.014541932381689548, -0.01929197832942009, 0.014340220019221306, -0.026682695373892784, 0.03513344004750252, -0.05712934583425522, 0.0318412259221077, 0.005108064506202936, -0.01541992463171482, 0.05884579196572304, -0.032051969319581985, -0.01729685626924038, -0.02333207055926323, -0.05208402872085571, 0.03360305726528168, -0.05275677517056465, -0.12278295308351517, -0.022353002801537514, 0.009433337487280369, 0.011598601005971432, 0.026217179372906685, -0.022838350385427475, 0.01221440453082323, -0.058725833892822266, -0.042090486735105515, -0.0629814863204956, 0.018863264471292496, -0.024489521980285645, -0.06027771905064583, -0.03045000694692135, 0.040223464369773865, -0.010009249672293663, -0.008592769503593445, -0.03202913701534271, -0.03228806331753731, 0.02180701680481434, -0.05969122797250748, -0.05800890922546387, 0.04916062206029892, 0.013548439368605614, -0.06039608642458916, 0.056196436285972595, 0.030796077102422714, -0.019634971395134926, 0.018817532807588577, -0.011921976692974567, -0.012973020784556866, -0.023329291492700577, 0.03376508504152298, 0.039501819759607315, 0.012609533965587616, -0.015149245969951153, -0.025218864902853966, 0.018444523215293884, -0.0630456805229187, -0.002224345225840807, 0.034993112087249756, 0.028600506484508514, 0.004762464668601751, -0.006771394982933998, -0.08760234713554382, -0.028627753257751465, 0.04289444908499718, 0.02438630349934101, -0.006220126990228891, 0.016721516847610474, 0.015168187208473682, 0.017239458858966827, 0.030577177181839943, -0.02632230333983898, 0.04808318242430687, 0.035757359117269516, -0.02118130400776863, -0.00887210387736559, -0.018695972859859467, -0.01912022940814495, 0.006741760298609734, 0.031336791813373566, 0.005867521278560162, -0.00843743048608303, 0.008529054932296276, -0.06116398423910141, -0.01080050878226757, 0.012270106934010983, 0.010067541152238846, 0.00028539609047584236, -0.023903880268335342, -0.022081973031163216, -0.03771377354860306, 0.06475310772657394, 0.020312944427132607, 0.0028421112801879644, 0.041823022067546844, 0.04807731881737709, -0.05674608051776886, -0.024880168959498405, 0.06173763796687126, -0.045031845569610596, -0.03437933698296547, 0.014016342349350452, 0.042157720774412155, -0.03422124683856964, -0.06449033319950104, 0.017543377354741096, 0.008212544023990631, -0.02883588895201683, 0.005376975983381271, -0.029792102053761482, -0.0493113175034523, -0.0014426704728975892, 0.019348379224538803, 0.020760830491781235, -0.07283437252044678, 0.03697500005364418, 0.01817473955452442, 0.012773064896464348, 0.026879046112298965, -0.031441979110240936, -0.021766209974884987, 0.010549018159508705, -0.007911225780844688, 0.001535526243969798, 0.0020255385898053646, -0.027183454483747482, 0.008243393152952194, 0.02595171146094799, -0.036667995154857635, 0.02703205682337284, 0.00290656671859324, -0.003665067721158266, 0.04363653063774109, -0.020253218710422516, 0.056626804172992706, 0.008515972644090652, 0.019455328583717346, 0.012845193967223167, 0.06968964636325836, 0.02903386950492859, 0.0016091888537630439, 0.06280236691236496, 0.009252350777387619, 0.06840739399194717, 0.00022590563457924873, -0.02068307437002659, 0.02628416195511818, -0.023054717108607292, -0.001594386762008071, 0.0694907084107399, -0.0002394579933024943, 0.0021873940713703632, -0.026614578440785408, 0.03224076330661774, 0.029762445017695427, 0.021015243604779243, 0.008873667567968369, 0.021848654374480247, 0.025522826239466667, 0.04352705180644989, 0.07621145993471146, 0.014026511460542679, -0.03328579664230347, -0.043396372348070145, -0.03448373079299927, -0.03978646919131279, 0.04530303552746773, 0.043799687176942825, -0.004624961409717798, 0.02450786903500557, -0.007984397932887077, 0.012221910990774632, 0.03529796749353409, 0.04040875285863876, -0.0356767475605011, -0.013099655508995056, 0.07743323594331741, 0.020793529227375984, 0.004838298540562391, -0.058917079120874405, -0.02808181755244732, 0.02420024387538433, 0.03576864302158356, 0.021592332050204277, -0.004467414226382971, 0.0028574843890964985, 0.040607526898384094, 0.056371722370386124, -0.06299751251935959, 0.009246543981134892, 0.018074048683047295, 0.035089634358882904, 0.015141364187002182, -0.05300746485590935, -0.039820194244384766, -0.03154553100466728, 0.04011216387152672, -0.03386708348989487, -0.031778182834386826, -0.05660063028335571, -0.06356094777584076, 0.003418275387957692, 0.0066922553814947605, 0.03312592953443527, -0.03465496748685837, 0.007543422747403383, -0.04720807820558548, -0.023892680183053017, -0.06574513018131256, -0.00561907235532999, -0.005959274247288704, 0.029133599251508713, 0.04283730313181877, 0.03485707938671112, 0.0026705057825893164, -0.03429465740919113, -0.003009436884894967, -0.03172164037823677, -0.011022228747606277, -0.012489783577620983, -0.008448807522654533, -0.03124692104756832, 0.0022742755245417356, 0.004733116365969181, 0.044502221047878265, -0.005467005539685488, 0.03248908370733261, -0.03608131781220436, -0.02586292289197445, -0.05014178156852722, 0.0227019302546978, 0.04331815242767334, -0.03487547114491463, 0.003813604824244976, -0.03107358328998089, -0.06597883254289627, 0.01818639226257801, -0.030610371381044388, -0.004117028322070837, 0.03475179150700569, -0.029101470485329628, -0.053682249039411545, -0.003999811597168446, -0.018922612071037292, 0.058494750410318375, -0.04294562339782715, 0.012567446567118168, -0.012385205365717411, 0.006908533163368702, 0.017317956313490868, -0.05873236060142517, -0.024301856756210327, 0.058246910572052, -0.011934546753764153, -0.02569708414375782, -0.0236204843968153, -0.030052425339818, 0.023651152849197388, 0.003974853549152613, -0.043924570083618164, -0.00600274745374918, -0.014514649286866188, 0.040493447333574295, 0.02185819111764431, -0.05229635536670685, -0.01705566607415676, -0.00310378335416317, 0.015797685831785202, 0.05650737136602402, 0.015893762931227684, 0.05753960832953453, 0.013872739858925343, 0.031079918146133423, -0.02024560607969761, 0.007463559042662382, 0.009384512901306152, 0.011370894499123096, -0.009223014116287231, 0.051701076328754425, -0.044704120606184006, 0.0279073566198349, 0.013903285376727581, 0.02891351841390133, -0.06904405355453491, 0.045345596969127655, 0.025147533044219017, -0.014986048452556133, -0.06099634990096092, 0.008878753520548344, 0.09659501165151596, -0.03957778587937355, -0.0350179485976696, 0.04217681661248207, 0.02991894632577896, -0.02691580168902874, -0.05196209251880646, 0.022145068272948265, -0.039024364203214645, 0.05820540711283684, 0.0005029463791288435, 0.031025266274809837, -0.009790079668164253, 0.00020756282901857048, 0.03413042053580284, 0.03443985804915428, -0.002822187729179859, 0.04908917844295502, 0.03148270398378372, -0.005499015096575022, 0.021186597645282745, 0.006198329385370016, -0.0654807835817337, 0.002634740434587002, 0.012809590436518192, 0.034130316227674484, -0.0026419651694595814, -0.014929869212210178, 0.007619861047714949, 0.0034962755162268877, 0.041204217821359634, -0.1087854728102684, 0.017241906374692917, -0.020548367872834206, -0.07532203197479248, 0.039255592972040176, 0.0318896658718586, 0.034159377217292786, 0.051696572452783585, 0.003750899340957403, -0.022328753024339676, 0.021312229335308075, -0.051790326833724976, 0.01702098548412323, -0.021859541535377502, 0.013153104111552238, 0.029305757954716682, -0.011888749897480011, 0.043937116861343384, -0.008750393986701965, -0.004195135086774826, -0.014658906497061253, -0.02390160784125328, -0.013615435920655727, 0.05577312037348747, -0.0482206866145134, -0.003589851316064596, -0.006431777961552143, -0.02469947189092636, -0.013824810273945332, -0.011212065815925598, 0.003111143596470356, -0.025025416165590286, -0.01741977222263813, 0.07328648865222931, 0.00621043099090457, 0.0245742779225111, -0.004371353425085545, -0.07577838003635406, -0.04453064128756523, 0.014578028582036495, 0.04052387550473213, 0.0433758944272995, 0.00458341371268034, 0.07638681679964066, -0.010914365760982037, 0.025696851313114166, -0.008826004341244698, -0.03421357646584511, 0.037813447415828705, 0.0036389401648193598, 0.007409509737044573, 0.10434118658304214, 0.025740621611475945, -0.022064533084630966, -0.008121499791741371, 0.053469978272914886, -0.07350556552410126, -0.02227693982422352, 0.028332136571407318, 0.0162938442081213, 0.015621588565409184, -0.02491210401058197, -0.07139992713928223, 0.03955904766917229, -0.06250561028718948, -0.02834354154765606, 0.03496035560965538, 0.006807154975831509, -0.003947421442717314, 0.015321421436965466, -0.007675013039261103, 0.023064378648996353, -0.019922303035855293, 0.016391754150390625, -0.015981025993824005, -0.018219633027911186, -0.031623177230358124, 0.013167561031877995, 0.019486917182803154, -0.006673796568065882, 0.01730833388864994, 0.03610021620988846, 0.015776734799146652, 0.017446594312787056, -0.0025430049281567335, -0.02148662507534027, 0.0010394107084721327, -0.058357056230306625, 0.020434018224477768, 0.00409508915618062, 0.0044647762551903725, 0.03589800372719765, -0.005868909414857626, 0.0478673093020916, -0.033161696046590805, 0.02139861322939396, -0.026041414588689804, -0.023592982441186905, -0.00825476460158825, -0.06269669532775879, 0.009658897295594215, 0.00489084841683507, -0.0036088572815060616, 0.05665094777941704, 0.036250077188014984, -0.09851057082414627, -0.01699472963809967, 0.014674699865281582, -0.0017601896543055773, -0.03930533677339554, -0.0016641519032418728, 0.03828353062272072, 0.031039588153362274, 0.053803443908691406, 0.08255927264690399, 0.0613379068672657, 0.026542989537119865, 0.025551792234182358, -0.002727781655266881, 0.001000646618194878, -0.024147165939211845, 0.042185354977846146, -0.016860339790582657, -0.020428603515028954, -0.008603398688137531, 0.031772445887327194, -0.039622269570827484, 0.03641665354371071, -0.08143410086631775, 0.024578601121902466, -0.020440896973013878, 0.0015890325885266066, -0.11931740492582321, -0.005045345984399319, 0.0373184010386467, 0.0077490187250077724, 0.02521670050919056, -0.030077464878559113, 0.05023033916950226, 0.01324789971113205, -0.004891910124570131, -0.0014681860338896513, -0.04174903780221939, -0.001205120119266212, -0.03407583013176918, 0.01288654562085867, -0.007251455448567867, -0.01640731282532215, -0.06433658301830292, 0.0056880381889641285, -0.03655104711651802, -0.043856583535671234, 0.05358909070491791, -0.028422795236110687, -4.848994277694586e-33, -0.05399395152926445, -0.0250429417937994, -0.07533160597085953, -0.061551108956336975, 0.006112633738666773, -0.019304851070046425, 0.05912211164832115, 0.053399015218019485, -0.024088848382234573, -0.05039810761809349, -0.04165542125701904, 0.027102064341306686, 0.016815291717648506, -0.00907117035239935, -0.062284205108881, 0.00538865989074111, 0.019016481935977936, 0.014543715864419937, -0.016686642542481422, -0.08557448536157608, 0.06159299984574318, 0.010757028125226498, 0.047098953276872635, -0.05075468495488167, -0.05523693561553955, -0.052135542035102844, -0.019630521535873413, -0.021598953753709793, -0.044222936034202576, -0.028261052444577217, -0.008652147836983204, -0.03894049674272537, -0.033223703503608704, 0.019643176347017288, 5.107819379190914e-05, 0.049936920404434204, -0.05928095057606697, 0.022304939106106758, -0.07952481508255005, 0.08707454800605774, 0.041694339364767075, 0.005629546009004116, 0.03088686615228653, 0.038627441972494125, -0.060536812990903854, 0.0599566325545311, 0.006100689060986042, -0.004874575883150101, -0.03545287996530533, 0.05831513553857803, -0.003595075337216258, -0.00456969952210784, -0.006598030216991901, -0.03728771209716797, 0.0058625624515116215, -0.01718127168715, -0.0025949792470782995, -0.09326756745576859, -0.09391233325004578, 0.004655766766518354, 0.04100624844431877, 0.044603824615478516, -0.04038318991661072, -0.019344082102179527, 0.03215622156858444, 0.022067027166485786, 0.013224502094089985, -0.043314460664987564, 0.0394931398332119, -0.04342815279960632, 0.016625719144940376, 0.008688468486070633, 0.015292990021407604, -0.0489748939871788, 0.06028614193201065, 0.0034276568330824375, -0.03504928573966026, 0.04044543579220772, -0.04301389679312706, -0.01611149124801159, 0.004029677249491215, -0.006530913524329662, -0.06140696629881859, 0.016232093796133995, 0.05224526301026344, -0.03839799016714096, 0.05705125257372856, -0.05501778796315193, 0.011685259640216827, 0.06400473415851593, -0.011486840434372425, 0.027046045288443565, 0.006424731109291315, -0.006577519234269857, 0.011942006647586823, -0.024275749921798706, 0.02612648718059063, 0.039455026388168335, 0.010863810777664185, 0.02648138254880905, 0.014966433867812157, -0.00544912600889802, -0.015712380409240723, -0.029024003073573112, -0.007101755123585463, 0.006085437256842852, -0.0007950575673021376, 0.08710573613643646, -0.06186410412192345, 0.0423249825835228, -0.024957749992609024, -0.00682106614112854, -0.021290434524416924, 0.0053003341890871525, 0.03708064556121826, -0.047501735389232635, 0.03318043798208237, 0.060481440275907516, 0.021738244220614433, -0.0835363119840622, 0.017563508823513985, -0.04595842957496643, -0.011338543146848679, 0.024811364710330963, -0.07555343955755234, -0.017328042536973953, -0.09400200098752975, 0.04250267148017883, 0.086476631462574, -0.037150781601667404, -0.04944423586130142, -0.030823813751339912, 2.6883390091825277e-07, -0.009631875902414322, 0.0002795526525005698, 0.022856643423438072, 0.009030243381857872, -0.05686361342668533, 0.005885463673621416, -0.022400589659810066, 0.08462096005678177, 0.004679897800087929, 0.05363310128450394, -0.00855922419577837, -0.027530035004019737, -0.0002877464867196977, 0.03144833445549011, -0.05156642571091652, 0.06090903654694557, 0.0319000743329525, 0.0874318778514862, -0.014017599634826183, 0.03604631498456001, -0.02733057551085949, 0.025155281648039818, 0.02126496471464634, -0.012008924968540668, 0.10907091200351715, -0.0059256525710225105, 0.014872141182422638, 0.031804878264665604, 0.008583161048591137, -0.031527452170848846, 0.019355449825525284, 0.06415583938360214, -0.06425345689058304, -0.0802772045135498, -0.004649801645427942, 0.03996048867702484, 0.07334161549806595, 0.07614348828792572, -0.044256050139665604, 0.01667051576077938, -0.009774234145879745, -0.03805689886212349, 0.007666477933526039, 0.020661968737840652, 0.026437578722834587, 0.024804381653666496, -0.024448780342936516, -0.021742695942521095, 0.00336269149556756, -0.01631704904139042, -0.022505026310682297, 0.0627393126487732, 0.04736144095659256, -0.04562309756875038, -0.022884605452418327, -0.006012239493429661, -0.009215065278112888, 0.018710365518927574, -0.040320463478565216, -0.049022067338228226, 0.02305232733488083, 0.03211405500769615, 0.014172056689858437, 0.028354648500680923, 0.026603607460856438, 0.013510196469724178, -0.027910545468330383, 2.328081485071666e-34, -0.018198760226368904, 0.019310815259814262, -0.005517435260117054, 0.004904182627797127, -0.012862936593592167, -0.034139081835746765, -0.00026373835862614214, 0.0185551717877388, 0.03486398607492447, 0.052178699523210526, -0.008868290111422539]

['Jeff Shrager']

1308.1066v1

Adaptive trials are now mainstream science. Recently, researchers have taken the adaptive trial concept to its natural conclusion, proposing what we call "Global Cumulative Treatment Analysis" (GCTA). Similar to the adaptive trial, decision making and data collection and analysis in the GCTA are continuous and integrated, and treatments are ranked in accord with the statistics of this information, combined with what offers the most information gain. Where GCTA differs from an adaptive trial, or, for that matter, from any trial design, is that all patients are implicitly participants in the GCTA process, regardless of whether they are formally enrolled in a trial. This paper discusses some of the theoretical and practical issues that arise in the design of a GCTA, along with some preliminary thoughts on how they might be approached.

Theoretical Issues for Global Cumulative Treatment Analysis (GCTA)

http://arxiv.org/pdf/1308.1066v1

Title Theoretical Issues Global Cumulative Treatment Analysis GCTA Summary Adaptive trial mainstream science Recently researcher taken adaptive trial concept natural conclusion proposing call Global Cumulative Treatment Analysis GCTA Similar adaptive trial decision making data collection analysis GCTA continuous integrated treatment ranked accord statistic information combined offer information gain GCTA differs adaptive trial matter trial design patient implicitly participant GCTA process regardless whether formally enrolled trial paper discus theoretical practical issue arise design GCTA along preliminary thought might approached Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.04693889990448952, 0.02756294049322605, -0.019078847020864487, -0.08170562237501144, 0.01304059661924839, 0.015563363209366798, 0.05977760627865791, 0.010161353275179863, 0.014978239312767982, 0.013356964103877544, 0.05380336195230484, -0.03362307697534561, -0.03318587318062782, 0.0481780543923378, 0.0062515693716704845, -0.02773585170507431, 0.005775291007012129, -0.0013108095154166222, -0.021468644961714745, 0.01655983179807663, -0.00017171812942251563, -0.02072245441377163, -0.03420336917042732, 0.031761929392814636, 0.07509773969650269, -0.032637134194374084, 0.04378826543688774, -0.0120771499350667, 0.007900172844529152, -0.09206660836935043, 0.057836614549160004, 0.017782913520932198, 0.010092583484947681, 0.021231019869446754, 2.5383214961038902e-06, -0.06211106851696968, -0.014139171689748764, -0.00316634401679039, 0.02725057490170002, -0.014937794767320156, 0.021498000249266624, 0.03610164672136307, 0.022989759221673012, 0.012125127948820591, -0.0005208920338191092, -0.0012775823706761003, 0.015276100486516953, 0.0048064482398331165, -0.00874696858227253, -0.02912859618663788, -0.020209891721606255, -0.00628330372273922, -0.0273048784583807, -0.030451254919171333, 0.00741541339084506, -0.017099294811487198, 0.0056730397045612335, -0.025496110320091248, 0.049220867455005646, -0.07885468751192093, 0.0038299986626952887, 0.04935905709862709, -0.00857102032750845, 0.02758052572607994, 0.01790265366435051, 0.027840157970786095, 0.008724100887775421, -0.05110441520810127, -0.010190893895924091, 0.0002840092347469181, 0.08697584271430969, 0.050397880375385284, 0.03182285651564598, 0.01771511137485504, 0.041977789252996445, -0.008695554919540882, -0.03891047090291977, -0.05765527859330177, -0.02391195483505726, -0.01624361425638199, 0.03919806703925133, 0.04312412068247795, -0.032908741384744644, -0.05899707227945328, -0.0058907680213451385, 0.015228779055178165, -0.022109337151050568, 0.006234186235815287, 0.01510320883244276, 0.01591446064412594, -0.021671094000339508, -0.023007916286587715, -0.0021519174333661795, 0.017001228407025337, -0.04546840488910675, -0.030663389712572098, 0.04080706834793091, -0.005327731370925903, 0.0831509679555893, -0.04602348431944847, 0.07690956443548203, 0.004665992688387632, -0.0013321838341653347, -0.0244672279804945, 0.013678370043635368, -0.007923834957182407, -0.04760167747735977, 0.01869312673807144, 0.001580110634677112, 0.08161439001560211, -0.02620645985007286, 0.04883084073662758, 0.008500904776155949, 0.01637079380452633, -0.008456817828118801, -0.002513658022508025, -0.08161041885614395, 0.03879726678133011, -0.02041052281856537, -0.018203821033239365, 0.009020822122693062, 0.026478486135601997, -0.010024051181972027, 0.029554707929491997, 0.016551842913031578, -0.007532693911343813, -0.04212866723537445, 0.03153508901596069, 0.013513798825442791, 0.004002097528427839, 0.03329281881451607, -0.04230780154466629, -0.011267805472016335, -0.010939514264464378, 0.0007953927270136774, 0.04187976196408272, -0.0002580402360763401, 0.043910205364227295, -0.03428119793534279, 0.0334872305393219, -0.04679134115576744, -0.021094150841236115, -0.028893595561385155, -0.041812311857938766, -0.001991191180422902, 0.0023844290990382433, 0.02557392232120037, 0.016636334359645844, -0.023349091410636902, 0.0006407213513739407, -0.05805853009223938, 0.02208723872900009, -0.029386412352323532, 0.025889020413160324, 0.03029383346438408, 0.02831646427512169, 0.04989871010184288, 0.0008343626977875829, 0.011907892301678658, -0.02888019196689129, 0.01447638962417841, -0.015333583578467369, -0.02839553728699684, -0.0028267025481909513, 0.02855966053903103, 0.08560644090175629, -0.0008856151252985001, -0.007466405630111694, -0.006581453140825033, 0.017630228772759438, -0.08850108087062836, -0.025628648698329926, -0.019519036635756493, 0.07724426686763763, 0.0401412732899189, 0.0057011013850569725, 0.006612404249608517, 0.02454230934381485, -0.06884799152612686, -0.06726916879415512, -0.030952028930187225, 0.004195971414446831, -0.026085421442985535, -0.003997718449681997, -0.04876367002725601, 0.001448352704755962, -0.00967943575233221, -0.00662899250164628, -0.017682891339063644, -0.0204009972512722, -0.010626168921589851, 0.024078745394945145, -0.024273822084069252, 0.007137849926948547, -0.011274701915681362, -0.005459769628942013, 0.04313131794333458, -0.12633073329925537, 0.03218100592494011, 0.01996038109064102, -0.013701684772968292, -0.05788614973425865, -0.030663881450891495, -0.019199000671505928, 0.007781453430652618, -0.01594661734998226, -0.009534531272947788, -0.04550965502858162, -0.010184948332607746, -0.03761366754770279, -0.026238268241286278, 0.04172738268971443, -0.024790097028017044, 0.04681294411420822, -0.029985152184963226, 0.0003229513531550765, -0.03512567654252052, 0.03648209571838379, -0.02302631549537182, 0.032778479158878326, -0.05831167474389076, 0.043015915900468826, -0.026095103472471237, 0.025991294533014297, -0.041214779019355774, -0.008786279708147049, 0.04060406982898712, -0.03997431695461273, 0.038326870650053024, -0.019706081598997116, -0.01317500788718462, -0.001848094048909843, 0.01359239500015974, 0.019777826964855194, -0.05442952364683151, 0.08758244663476944, 0.04857326298952103, -0.023845095187425613, -0.04783076047897339, 0.021008793264627457, 0.028728904202580452, -0.03246103599667549, -0.005131860729306936, 0.022462498396635056, -0.022341540083289146, 0.026321863755583763, 0.06480653584003448, 0.03505358472466469, -0.026231562718749046, 0.004924288019537926, 0.019789541140198708, -0.043087590485811234, -0.052246637642383575, 0.017413068562746048, -0.05348709225654602, -0.005975627806037664, -0.0865488201379776, -0.014209840446710587, -0.02413800358772278, -0.04047105088829994, 0.001801632926799357, -0.03547137230634689, -0.06763805449008942, -0.024125508964061737, 0.02683836780488491, -0.03564426675438881, -0.01399694848805666, -0.057349950075149536, 0.038198478519916534, 0.0473446361720562, 0.0023397402837872505, -0.03326273337006569, -0.0057084085419774055, -0.008797493763267994, -0.01926593668758869, -0.011120005510747433, -0.004945819731801748, 0.08356571942567825, 0.036709971725940704, -0.0198499895632267, 0.038253750652074814, 0.031436339020729065, -0.04382728040218353, 0.012944145128130913, 0.0091091338545084, 0.03691916540265083, 0.025163061916828156, -0.05843484774231911, 0.023645495995879173, -0.038301706314086914, -0.01565166935324669, 0.004950878210365772, -0.001345546217635274, -0.042407579720020294, -0.03678757697343826, 0.07325563579797745, 0.03531260788440704, 0.03860487788915634, 0.018496133387088776, 0.021826453506946564, -0.013236349448561668, 0.02010040543973446, -0.01772174797952175, -0.012558987364172935, -0.016926411539316177, -0.08817785233259201, -0.007295885588973761, -0.032897599041461945, -0.0388430580496788, 0.07106492668390274, 0.03518068790435791, 0.015008939430117607, 0.01991439424455166, 0.006223396863788366, -0.009664010256528854, 0.003313350025564432, -0.06904113292694092, -0.02418132685124874, -0.038402725011110306, -0.01590537093579769, -0.032319437712430954, -0.04348402097821236, 0.0461057610809803, 0.06161632016301155, -0.0007691442151553929, -0.03389991074800491, 0.030476002022624016, 0.015733841806650162, -0.07864347845315933, -0.01957370527088642, -0.035623762756586075, 0.04876072704792023, 0.02615508995950222, 0.028226982802152634, -0.02890520542860031, -0.021372169256210327, 0.001889804727397859, 0.013036172837018967, -0.048307597637176514, 0.03467784449458122, 0.012717647477984428, -0.042676568031311035, -0.04242884740233421, 0.062326885759830475, 0.07390634715557098, -0.04228329658508301, 0.002415849594399333, 0.06558119505643845, -0.028340652585029602, -0.024675147607922554, 0.014338652603328228, 0.03316390514373779, -0.06761094927787781, -0.008241776376962662, 0.022624177858233452, -0.05783667042851448, -0.01741117425262928, -0.00875307247042656, -0.014839926734566689, -0.011272046715021133, 0.04619015008211136, 0.0426354818046093, 0.024732476100325584, -0.022628966718912125, 0.016596052795648575, 0.08727847039699554, 0.015356279909610748, 0.007535557262599468, -0.03791503235697746, 0.028342507779598236, 0.032599758356809616, 0.003402616363018751, 0.04457332566380501, 0.05093170702457428, -0.004704367835074663, -0.07669199258089066, -0.034739118069410324, -0.025045320391654968, -0.03892136737704277, -0.005811381619423628, -0.013821071945130825, -0.04831444472074509, 0.05385299772024155, -0.01558576337993145, 0.02236800640821457, -0.045417603105306625, -0.004229306243360043, 0.005279498640447855, 0.05690636485815048, 0.01077690813690424, 0.025343120098114014, -0.055419884622097015, 0.07669594883918762, 0.026216471567749977, 0.0647815465927124, -0.008702777326107025, -0.06511196494102478, 0.004214199725538492, 0.013915582560002804, -0.004101738799363375, 0.0017248629592359066, -0.053515493869781494, 0.029778599739074707, 0.018032487481832504, -0.025331297889351845, 0.09211508929729462, 0.015504050068557262, -0.019572513177990913, 0.013575234450399876, 0.027841150760650635, 0.02940579503774643, -0.05540810897946358, -0.001570555497892201, -0.002107481472194195, 0.09317464381456375, 0.052511632442474365, 0.046647705137729645, -0.006768701132386923, 0.032204315066337585, -0.046682409942150116, -0.004795998800545931, 0.057670269161462784, 0.039307527244091034, -0.011407524347305298, -0.0017765451921150088, -0.021430393680930138, 0.031522467732429504, 0.011966132558882236, -0.022027937695384026, 0.010170463472604752, -0.008402626030147076, 0.03442135453224182, -0.028322547674179077, 0.020002268254756927, -0.04989863187074661, -0.005565641447901726, 0.01743537373840809, -0.04255129024386406, 0.00540546327829361, -0.02305193431675434, -0.012061388231813908, -0.0023337556049227715, 0.04203103855252266, -0.011154523119330406, 0.023826250806450844, -0.049428269267082214, -0.025455975905060768, 0.013972274027764797, 0.01961701363325119, 0.060449909418821335, 0.03216797113418579, -0.04251890257000923, -0.04185868799686432, -0.06711343675851822, 0.018032092601060867, -0.03792493790388107, -0.0084402896463871, 0.051803939044475555, -0.009075057692825794, 0.03548986837267876, 0.040025074034929276, 0.022637855261564255, -0.03344015032052994, 0.007299143821001053, 0.04230765998363495, 0.036720629781484604, -0.08783610910177231, 0.07681666314601898, 0.0187966451048851, -0.03359871730208397, 0.03310254588723183, 0.01676737144589424, -0.02818787656724453, 0.04321380704641342, 0.05144515261054039, 0.016394469887018204, -0.0036959706339985132, 0.03584348410367966, 0.009697808884084225, 0.04744333401322365, -0.014487074688076973, 0.05122214928269386, -0.06276366114616394, 0.010640690103173256, -0.01630656234920025, 0.013475091196596622, -0.0118162976577878, -0.01140480488538742, -0.004272389225661755, -0.03613104671239853, -0.01601685956120491, 0.01222250796854496, -0.03340265154838562, 0.0011378586059436202, -0.138893261551857, -0.0258796364068985, -0.09808499366044998, 0.05028486251831055, 0.01611929200589657, 0.005699574016034603, 0.018978899344801903, 0.07511573284864426, -0.004741321317851543, 0.006535384338349104, -0.004296747036278248, 0.03516511246562004, -0.03912162035703659, 0.027021201327443123, -0.009281299076974392, -0.01611638069152832, 0.027728840708732605, 0.0338331013917923, 0.01381588913500309, -0.03179825842380524, -0.014603939838707447, 0.013068122789263725, -0.010599459521472454, 0.04299909994006157, 0.0240061916410923, 0.025596028193831444, 0.0243416428565979, -0.06320207566022873, -0.024449925869703293, -0.03185787424445152, 0.03255835175514221, -0.02036043256521225, -0.03296094760298729, -0.007734398357570171, -0.05606546625494957, 0.029104305431246758, 0.012018796987831593, -0.01655951887369156, -0.11413971334695816, 0.01068432629108429, -0.03193493187427521, -0.012398856692016125, 0.028176797553896904, -0.004947537090629339, -0.04138844087719917, 0.019456788897514343, -0.008376258425414562, -0.019712360575795174, -0.004163836129009724, -0.014319314621388912, 0.03406394273042679, 0.009922045283019543, -0.046327218413352966, -0.06308909505605698, -0.050513580441474915, -0.058395497500896454, -0.01014623511582613, 0.05622655898332596, 0.006104515865445137, -0.023968901485204697, 0.005053042434155941, -6.1346096739858744e-33, -0.005705947522073984, 0.03146367147564888, -0.004486302379518747, 0.013611613772809505, -0.06052159518003464, 0.0024752591270953417, -0.03957999497652054, 0.0050175064243376255, 0.03908668830990791, -0.009783570654690266, 0.018193811178207397, 0.007992656901478767, 0.0030167200602591038, 0.0030641257762908936, 0.020241929218173027, 0.02399456687271595, -0.041260313242673874, 0.013690960593521595, 0.007449932396411896, 0.02405627816915512, -0.03196120634675026, 0.02834615297615528, 0.03151826187968254, -0.009731692261993885, 0.05333806946873665, 0.05558054894208908, -0.008761467412114143, -0.03429726883769035, -0.039977919310331345, 0.02826574444770813, 0.03265705332159996, 0.003955722786486149, 0.0110204191878438, 0.0028391547966748476, 0.03341008722782135, -0.031577203422784805, -0.012117004953324795, 0.028576835989952087, -0.013088637962937355, -0.06487744301557541, -0.05055449530482292, 0.014125088229775429, 0.027240639552474022, 0.012406009249389172, -0.006007036659866571, -0.0058480822481215, 0.009170439094305038, -0.07712671160697937, 0.02065565064549446, -0.001945151248946786, -0.017054591327905655, 0.022568579763174057, -0.04214365780353546, 0.05703146383166313, -0.07450456917285919, 0.04052332416176796, -0.04307323694229126, 0.05663099139928818, 0.012388136237859726, 0.021276794373989105, -0.004639964085072279, 0.00217400467954576, -0.013075778260827065, -0.0030066927429288626, 0.03845673054456711, -0.026194164529442787, -0.04921497032046318, -0.00651300884783268, -0.018693121150135994, -0.03887483477592468, -0.01491303276270628, -0.07156991213560104, 0.015172453597187996, 0.03847750648856163, 0.019283907487988472, -0.04619007185101509, -0.031637612730264664, 0.030413255095481873, -0.03339652717113495, 0.008504511788487434, -0.037562329322099686, 0.01161554642021656, 0.033229365944862366, 0.007828147150576115, -0.03302750363945961, -0.033436115831136703, -0.040178488940000534, -0.012165802530944347, 0.03445381298661232, -0.03789598122239113, 0.04377097263932228, 0.01903882436454296, 0.06705054640769958, 0.001278890878893435, 0.05660692974925041, -0.03798789903521538, 0.051884762942790985, 0.030844250693917274, 0.02629535086452961, -0.0024120027665048838, -0.02292514778673649, 0.011853954754769802, -0.025316325947642326, 0.018168693408370018, 0.05619800090789795, -0.02481148950755596, 0.02262103371322155, -0.05120568722486496, -0.022550135850906372, 0.024433093145489693, -0.004422456491738558, 0.04256828501820564, 0.038082342594861984, -0.0384264700114727, -0.007101104129105806, -0.0008622405002824962, 0.02228468470275402, 0.05774321034550667, 0.05258796364068985, -0.06176971644163132, -0.10716328024864197, -0.03180401772260666, -0.014200927689671516, 0.038313865661621094, -0.01626482419669628, 0.03480365872383118, 0.004861073102802038, 0.0516139380633831, -0.043580763041973114, -0.05274222791194916, 0.020652830600738525, -0.03640241175889969, 3.112169792984787e-07, -0.01596030965447426, 0.01964542269706726, -0.02877398207783699, -0.06257957965135574, 0.04423882067203522, -0.0439203679561615, -0.04576179385185242, 0.033861637115478516, 0.05655237287282944, 0.057172223925590515, 0.05939453840255737, -0.054391734302043915, 0.027762489393353462, -0.014856030233204365, 0.03546557202935219, -0.0604180172085762, -0.03281246870756149, 0.02698613703250885, -0.00322096049785614, 0.005520801991224289, 0.017403308302164078, -0.03858012333512306, -0.006273409351706505, 0.0005631631356664002, -0.026373904198408127, -0.008242669515311718, 0.01655503734946251, -0.023260675370693207, -0.0076998258009552956, 0.0014971357304602861, -0.048653408885002136, 0.004737003240734339, 0.02004588209092617, 0.0027048217598348856, -0.04966308921575546, -0.027125267311930656, -0.05352030694484711, 0.031042229384183884, -0.04863366112112999, 0.03500720486044884, 0.03592754155397415, 0.0006090474198572338, 0.04791446402668953, -0.06765604019165039, 0.023644132539629936, -0.04676692187786102, 0.03364033252000809, 0.07928699254989624, 0.016265394166111946, -0.0648171678185463, 0.09071768820285797, 0.0020142258144915104, -0.027505481615662575, 0.05930719152092934, 0.019951600581407547, 0.04884443059563637, 0.002752941334620118, 0.05340946465730667, 0.03771603852510452, 0.06555312126874924, -0.02398056909441948, -0.046345219016075134, 6.827966717537493e-05, 0.008384271524846554, -0.03189452737569809, -0.05151067301630974, 0.015228858217597008, 3.350976465348066e-34, 0.026942722499370575, -0.010616199113428593, 0.014979187399148941, -0.04999949783086777, 0.028128545731306076, -0.02398012764751911, 0.06411989778280258, 0.028865618631243706, 0.0018504882464185357, -0.022368328645825386, -0.019471444189548492]

['Michal Aharon', 'Natalie Aizenberg', 'Edward Bortnikov', 'Ronny Lempel', 'Roi Adadi', 'Tomer Benyamini', 'Liron Levin', 'Ran Roth', 'Ohad Serfaty']

1308.1792v1

One of the most challenging recommendation tasks is recommending to a new, previously unseen user. This is known as the 'user cold start' problem. Assuming certain features or attributes of users are known, one approach for handling new users is to initially model them based on their features. Motivated by an ad targeting application, this paper describes an extreme online recommendation setting where the cold start problem is perpetual. Every user is encountered by the system just once, receives a recommendation, and either consumes or ignores it, registering a binary reward. We introduce One-pass Factorization of Feature Sets, OFF-Set, a novel recommendation algorithm based on Latent Factor analysis, which models users by mapping their features to a latent space. Furthermore, OFF-Set is able to model non-linear interactions between pairs of features. OFF-Set is designed for purely online recommendation, performing lightweight updates of its model per each recommendation-reward observation. We evaluate OFF-Set against several state of the art baselines, and demonstrate its superiority on real ad-targeting data.

OFF-Set: One-pass Factorization of Feature Sets for Online Recommendation in Persistent Cold Start Settings

http://arxiv.org/pdf/1308.1792v1

Title OFFSet Onepass Factorization Feature Sets Online Recommendation Persistent Cold Start Settings Summary One challenging recommendation task recommending new previously unseen user known user cold start problem Assuming certain feature attribute user known one approach handling new user initially model based feature Motivated ad targeting application paper describes extreme online recommendation setting cold start problem perpetual Every user encountered system receives recommendation either consumes ignores registering binary reward introduce Onepass Factorization Feature Sets OFFSet novel recommendation algorithm based Latent Factor analysis model user mapping feature latent space Furthermore OFFSet able model nonlinear interaction pair feature OFFSet designed purely online recommendation performing lightweight update model per recommendationreward observation evaluate OFFSet several state art baseline demonstrate superiority real adtargeting data Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.034689273685216904, 0.02178322896361351, -0.0010926139075309038, -0.03879596292972565, 0.02728884108364582, -0.01162137370556593, 0.03814912587404251, -0.01717694103717804, -0.0034535792656242847, -0.03243696317076683, -0.02262166514992714, -0.03502653166651726, -0.01970280520617962, 0.12635721266269684, -0.02539772354066372, -0.022403622046113014, -0.02424992062151432, -0.02930435910820961, -0.02264261245727539, 0.02410396747291088, 0.04867200925946236, -0.006139947101473808, 0.025649793446063995, 0.014782402664422989, 0.02229883149266243, -0.051742155104875565, -0.018562231212854385, -0.039845146238803864, 0.0073067378252744675, -0.029525935649871826, 0.028792988508939743, 0.022552015259861946, 0.005829293746501207, -0.008817160502076149, 2.374280029471265e-06, -0.032224949449300766, -0.04229762777686119, -0.03729987516999245, -0.023619450628757477, -0.011063623242080212, 0.028652874752879143, 0.06539789587259293, 0.048358768224716187, 0.016817696392536163, -0.07283424586057663, 0.03854347765445709, 0.042336318641901016, 0.053318463265895844, -0.042585618793964386, -0.014462954364717007, -0.007628149818629026, -0.021411292254924774, -0.0016538568306714296, 0.012149188667535782, 0.04004637524485588, -0.00927572138607502, 0.03471113368868828, -0.08155354857444763, -0.01365477591753006, -0.02721167542040348, 0.005211526528000832, -0.029853148385882378, -0.050779588520526886, -0.03155597299337387, 0.10236762464046478, 0.013363300822675228, 0.04233836755156517, -0.037451330572366714, -0.005807702429592609, 0.04181819409132004, -0.009044398553669453, 0.018852295354008675, 0.020541280508041382, -0.001829373650252819, -0.06021035462617874, 0.009103983640670776, -0.021795885637402534, 0.011172406375408173, -0.020843517035245895, 0.02167367748916149, -0.011072255671024323, -0.00745592312887311, -0.005459692794829607, 0.004588887561112642, 0.01414440292865038, 0.0768636092543602, -0.02998507022857666, -0.012034043669700623, 0.005747407209128141, -0.0022542483638972044, -0.008591360412538052, -0.029039129614830017, 0.04057477042078972, -0.021012553945183754, -0.06764587759971619, -0.038016561418771744, 0.014934799633920193, 0.003353254171088338, 0.0042015500366687775, -0.03507932648062706, 0.05715285614132881, -0.019982123747467995, -0.030282657593488693, 0.02201126515865326, 0.03126915171742439, -0.006536167114973068, 0.005885566119104624, -0.07253733277320862, -0.006549510173499584, 0.07195032387971878, -0.03333662077784538, 0.004182463977485895, 0.006427966058254242, 0.08676852285861969, 0.016314443200826645, -0.01695847697556019, -0.0771627426147461, 0.05856667086482048, -0.0188529621809721, 0.005568697117269039, 0.03157476708292961, 0.04874005168676376, 0.04407993704080582, 0.05399739742279053, -0.0274661798030138, 0.009207703173160553, -0.07606673240661621, 0.015950946137309074, 0.005353523418307304, 0.02961978130042553, 0.05053289234638214, 0.02855006419122219, 0.01807853952050209, -0.03737599775195122, 0.008940867148339748, 0.03936886787414551, 0.024906564503908157, -0.03363169729709625, -0.05335652083158493, -0.05542973801493645, 0.037131745368242264, -0.0014614892425015569, -0.08174432814121246, -0.024731062352657318, -0.015201265923678875, 0.02152424305677414, -0.01944991573691368, 0.027852576225996017, -0.02569412626326084, -0.014324912801384926, -0.029644183814525604, 0.04175368696451187, 0.04774375259876251, 0.02957506664097309, 0.021101875230669975, -0.017246980220079422, 0.0160831306129694, 0.02227962575852871, -0.023518087342381477, 0.07283944636583328, 0.05459092929959297, 0.0007660813862457871, -0.0028196184430271387, -0.005858518183231354, -0.04851941764354706, -0.00482241902500391, 0.031913794577121735, 0.03177502006292343, -0.02554175816476345, -0.03559282049536705, 0.00011657543655019253, -0.030336854979395866, -0.00939512625336647, 0.06532908976078033, 0.049551285803318024, -0.008451880887150764, 0.011635785922408104, 0.03285770118236542, 0.022486405447125435, 0.026390355080366135, -0.06433956325054169, -0.037026964128017426, 0.006729695945978165, 0.06423401832580566, -0.036642611026763916, -0.06349779665470123, 0.0058940742164850235, 0.04033547639846802, -0.05161607638001442, 0.00901486910879612, 0.02268785610795021, -0.017998795956373215, 0.0031899858731776476, 0.043525733053684235, 0.037909187376499176, -0.03308857977390289, 0.023564770817756653, -0.03697015717625618, -0.0001566208666190505, -0.0011847459245473146, -0.001888092141598463, -0.02582179382443428, 0.05080776661634445, 0.08641867339611053, 0.04248359426856041, 0.017280027270317078, 0.004029116127640009, -0.043184276670217514, 0.005068867467343807, -0.09299145638942719, 0.06027303263545036, -0.025554124265909195, -0.005150365177541971, 0.019958242774009705, -0.04767449200153351, 0.02764176018536091, -0.006435740273445845, 0.033346377313137054, -0.022740740329027176, 0.03629698604345322, -0.029589509591460228, 0.055814046412706375, 0.050712164491415024, -0.01040058396756649, -0.005482979118824005, 0.013202711939811707, 0.0524776428937912, 0.03716715797781944, 0.041066475212574005, 0.021087326109409332, 0.06733979284763336, -0.023348910734057426, 0.04588349536061287, -0.011055481620132923, -0.04562711715698242, -0.008889514952898026, 0.07705655694007874, 0.07826292514801025, 0.0446048267185688, -0.018202640116214752, 0.03537115454673767, 0.04275403544306755, 0.029203901067376137, -0.018161168321967125, 0.02952808141708374, 0.007607830688357353, 0.035151660442352295, 0.020162971690297127, 0.039205167442560196, 0.002845596754923463, 0.026021389290690422, 0.005157218314707279, 0.04883432015776634, 0.021210743114352226, 0.036937542259693146, -0.030412260442972183, -0.09238855540752411, 0.007909946143627167, -0.0349617563188076, 0.03350389376282692, -0.05255361273884773, 0.022957857698202133, -0.02920445241034031, -0.019010456278920174, -0.002248764270916581, -0.0026500870008021593, 0.015353601425886154, 0.00022919382899999619, 0.024901721626520157, 0.02523714303970337, -0.011810990050435066, 0.0032041347585618496, 0.010246737860143185, 0.031707920134067535, -0.014771007932722569, -0.04823826625943184, -0.010964499786496162, -0.04228720813989639, 0.030673857778310776, 0.013172572478652, 0.040835168212652206, -0.010600471869111061, 0.012728025205433369, 0.01132789347320795, -0.0042840163223445415, 0.004609578754752874, 0.02606784552335739, -0.02325710654258728, -0.05165398493409157, -0.019007284194231033, -0.055195402354002, -0.025609394535422325, -0.02060367353260517, 0.024854060262441635, -0.035800766199827194, -0.0052845473401248455, 0.022106032818555832, 0.03870043158531189, 0.02251797914505005, 0.03894316777586937, 0.02199525199830532, 0.034384552389383316, -0.02670583501458168, -0.04062401130795479, -0.018003933131694794, 0.006774431560188532, 0.034218840301036835, 0.03155193477869034, 0.013042939826846123, -0.023178061470389366, 0.0014457348734140396, 0.024577129632234573, 0.0009129403624683619, 0.06355112046003342, 0.014640573412179947, -0.02178535796701908, -0.08747392892837524, 0.01493070274591446, -0.024592068046331406, 0.044570889323949814, 0.0070267291739583015, -0.025601577013731003, 0.07691647112369537, 0.06877671927213669, 0.0010275701060891151, 0.04117688536643982, -0.0549597330391407, 0.005845288746058941, -0.051817022264003754, -0.010838025249540806, 0.030711151659488678, -0.038174260407686234, -0.015270295552909374, 0.027027219533920288, -0.017123287543654442, 0.04570154473185539, -0.03968273848295212, 0.01541127823293209, 0.06607543677091599, -0.046473581343889236, -0.015041019767522812, -0.0256790891289711, -0.027559299021959305, -0.092313252389431, 0.029203882440924644, -0.04320695996284485, 5.2320312533993274e-05, -0.03833207115530968, -0.05956461653113365, 0.031324367970228195, -0.012455428950488567, 0.0419725701212883, -0.04434167221188545, -0.023730827495455742, 0.027196593582630157, -0.004582631401717663, 0.06500023603439331, -0.027525518089532852, -0.033509477972984314, -0.001854100963100791, 0.023786017671227455, 0.04090046137571335, -0.001971092540770769, -0.0705576166510582, -0.010362393222749233, 0.013441352173686028, 0.05486588552594185, -0.046424150466918945, -0.02256983146071434, 0.022594215348362923, -0.01623884215950966, 0.02749520353972912, 0.04270736128091812, 0.008674477227032185, 0.03991715610027313, -0.12013804167509079, 0.005117432214319706, -0.04510394111275673, 0.030349867418408394, 0.02128594182431698, 0.01782296784222126, -0.03752915561199188, 0.010750740766525269, -0.003067329525947571, 0.09066159278154373, -0.011722060851752758, -0.0558423213660717, -0.03364456817507744, -0.019938964396715164, 0.03846465423703194, -0.016305217519402504, 0.022365469485521317, 0.02363337203860283, -0.07030128687620163, 0.0042322068475186825, -0.0558394119143486, -0.023519134148955345, 0.006209108047187328, -0.020362362265586853, 0.009694424457848072, -0.001561249722726643, 0.024075878784060478, 0.02670271135866642, 0.017601704224944115, -0.04662373289465904, 0.03730076551437378, 0.05234562233090401, 0.03603460639715195, 0.03245179355144501, -0.0440501943230629, -0.03918058052659035, 0.0050202058628201485, 0.0217873714864254, -0.01730569824576378, 0.07147253304719925, -0.028770901262760162, 0.04022893309593201, -0.010829376988112926, 0.06315450370311737, -0.04828925430774689, 0.020537657663226128, 0.04875944182276726, 0.025671757757663727, -0.00431238254532218, 0.01915830373764038, -0.024356238543987274, -0.02350793220102787, 0.029310233891010284, 0.030443845316767693, -0.020293138921260834, -0.08390232175588608, 0.009255800396203995, -0.020232614129781723, -0.010446828790009022, 0.06150605529546738, -0.04203148931264877, -0.028389807790517807, -0.03484508395195007, 0.018735185265541077, -0.04840715229511261, 0.0032294350676238537, -0.0009576455340720713, 0.04553483799099922, 0.014990771189332008, 0.052622873336076736, -0.06478798389434814, -0.024053409695625305, 0.023407181724905968, -0.004404311999678612, 0.03144492954015732, 0.02618243172764778, -0.034793708473443985, 0.033825524151325226, -0.0013720092829316854, -0.09240808337926865, -0.008308018557727337, -0.06308315694332123, -0.01416884083300829, 0.0017605079337954521, -0.0014241279568523169, 0.012289748527109623, 0.0291308481246233, 0.026505613699555397, -0.06970799714326859, -0.058079320937395096, -0.014607640914618969, -7.41745243431069e-05, 0.005998443346470594, -0.016599049791693687, -0.004805490840226412, 0.06058869883418083, -0.017757805064320564, 0.01831822097301483, -0.039992958307266235, -0.00015079439617693424, 0.006496306508779526, -0.07169918715953827, -0.006007918156683445, 0.001900305855087936, 0.008459104225039482, 0.04870307818055153, 0.05460207164287567, 0.010177718475461006, 0.017886819317936897, 0.007300117053091526, 0.023024871945381165, 0.006464481353759766, -0.016416560858488083, -0.058416564017534256, 0.012406411580741405, 0.04497150331735611, -0.00010952859884127975, -0.009737508371472359, -0.027822887524962425, -0.01784525066614151, -0.016384826973080635, -0.024065641686320305, 0.00017214978288393468, -0.06192968040704727, 0.05095851793885231, 0.011178898625075817, 0.02783333510160446, 0.026603683829307556, 0.030370624735951424, 0.04409581050276756, 0.040745146572589874, -0.04495476558804512, 0.02443128451704979, -0.03871016576886177, 0.014744594693183899, -0.018136095255613327, 0.042697373777627945, 0.01691456325352192, -0.05675247684121132, -0.058706142008304596, -0.0007260215352289379, -0.0028691210318356752, -0.00873431097716093, 0.07316655665636063, -6.134917930467054e-05, 0.019159380346536636, -0.024312084540724754, 0.013030486181378365, -0.035521771758794785, -0.041101910173892975, -0.035453684628009796, 0.0394551083445549, -0.024589814245700836, 0.024999206885695457, 0.055645763874053955, -0.010152856819331646, -0.024159248918294907, -0.047867339104413986, -0.07660017162561417, -0.03415106609463692, 0.06978166848421097, 0.03129429742693901, 0.04016691446304321, -0.0202373918145895, -0.03552030771970749, 0.0003159006009809673, -0.003876626957207918, -0.022399425506591797, -0.06318918615579605, 0.02367645502090454, -0.01872175931930542, 0.030916990712285042, 0.017561275511980057, -0.015785932540893555, -0.004483566619455814, -0.06135687232017517, -0.026185978204011917, -0.015859076753258705, -0.00991442333906889, -0.0486011877655983, -6.906938115150919e-33, 0.031514525413513184, -0.014327229000627995, -0.03980559483170509, 0.026803286746144295, -0.03956862539052963, -0.027686946094036102, 0.05227651819586754, 0.02886868268251419, 0.03973911330103874, -0.05972392112016678, -0.0141266118735075, -0.03621823713183403, 0.013043968006968498, -0.017125500366091728, 0.0298562403768301, -0.012560156174004078, 0.0301189161837101, -0.023540420457720757, -0.014483806677162647, 0.04222874343395233, 0.047258637845516205, 0.03075519949197769, -0.022060906514525414, -0.029552079737186432, 0.015614955686032772, -0.032969456166028976, -0.056728098541498184, 0.027415506541728973, 0.025678427889943123, 0.046635545790195465, -0.02430141158401966, 0.004816639702767134, 0.004356349352747202, -0.02547181025147438, 0.013137082569301128, -0.015201725997030735, -0.04647562652826309, 0.001541812438517809, 0.03688838332891464, 0.0009519932209514081, 0.03977382555603981, -0.003206405555829406, 0.0425800122320652, -0.011200052686035633, -0.00540570355951786, 0.04642070457339287, 0.04888764023780823, -0.013103817589581013, -0.03908051177859306, 0.019141560420393944, 0.008978188969194889, -0.0255290400236845, -0.02089753746986389, 0.0658399686217308, -0.00971680972725153, 0.05955414101481438, -0.036581654101610184, 0.045947711914777756, -0.08690399676561356, 0.034312810748815536, -0.01222009677439928, 0.004565699025988579, -0.0035302075557410717, -0.006814409047365189, 0.009030085057020187, 0.03633929789066315, -0.01347804069519043, -0.031466513872146606, 0.02983882836997509, -0.014249665662646294, -0.056025180965662, 0.038849666714668274, -0.025994742289185524, 0.017312901094555855, 0.056111518293619156, -0.04983242228627205, 0.003082187147811055, 0.026006067171692848, 0.036686234176158905, -0.059414446353912354, 0.04639487713575363, 0.005748707335442305, -0.017986301332712173, -0.006071662064641714, 0.017737694084644318, -0.00617879256606102, -0.07451904565095901, -0.11471100896596909, 0.0530291423201561, 0.0291642714291811, 0.0025154966861009598, -0.025593295693397522, -0.026402615010738373, -0.055345918983221054, -0.01567131280899048, -0.01362686324864626, 0.005018372554332018, 0.024838289245963097, 0.018490375950932503, -0.04876859486103058, -0.05428014695644379, -0.006198074668645859, -0.03646351397037506, -0.0337674617767334, -0.05183391273021698, -0.004544978961348534, 0.027014993131160736, 0.018379004672169685, -0.038585055619478226, 0.011124245822429657, 0.05170035734772682, -0.04373319074511528, 0.004063321277499199, 0.04644813761115074, 0.028264345601201057, -0.04716106504201889, -0.025119855999946594, 0.08045866340398788, 0.04479303956031799, 0.031868208199739456, -0.04758333042263985, -0.06522002816200256, 0.030467242002487183, 0.0016430040122941136, -0.024166574701666832, -0.002010683063417673, -0.038425058126449585, -0.0604620985686779, 0.06466368585824966, -0.0972968265414238, -0.0026042370591312647, -0.05364571139216423, 3.026491413038457e-07, -0.03777018561959267, 0.024057412520051003, -0.08063370734453201, -0.07774192094802856, 0.01866876892745495, 0.019625721499323845, -0.0017964555881917477, 0.02442059852182865, 0.05759333074092865, 0.05359558388590813, 0.01310340128839016, -0.04051051661372185, -0.025108855217695236, 0.04277472943067551, -0.04732710123062134, 0.016060518100857735, -0.009441228583455086, 0.020317958667874336, -0.06011997163295746, 0.00404610950499773, -0.022559110075235367, 0.045294079929590225, 0.056382451206445694, 0.011023979634046555, 0.02940487675368786, -0.00677070114761591, 0.003470376366749406, -0.009347233921289444, -0.05754118412733078, -0.059133656322956085, 0.03700855001807213, -0.03918739780783653, -0.017054814845323563, -0.025718815624713898, -0.03517560288310051, 0.03490800783038139, 0.00725158117711544, 0.03208731859922409, -0.004457848612219095, -0.032903317362070084, 0.011240282095968723, -0.014930648729205132, 0.028639541938900948, -0.02033475786447525, 0.05999881774187088, -0.0267613735049963, -0.054714303463697433, -0.014806985855102539, -0.021050618961453438, -0.022628281265497208, -0.010385390371084213, -0.001910434802994132, 0.04625600203871727, 0.021842503920197487, 0.023308884352445602, -0.010341028682887554, -0.02926737628877163, 0.006113904062658548, 6.574232975253835e-05, 0.01248425617814064, -0.020517149940133095, -0.04322507232427597, -0.023973900824785233, 0.035366225987672806, 0.04362098127603531, -0.023444829508662224, 0.0023834267631173134, 3.0438863722129167e-34, 0.022640595212578773, 0.038971759378910065, 0.0023962624836713076, -0.01186109147965908, -0.03253598511219025, -0.005644476041197777, 0.013591651804745197, -0.006770092993974686, 0.08710651844739914, -0.04665156826376915, -0.020655237138271332]

['Andrew R. Cohen', 'P. M. B. Vitanyi']

1308.3177v1

Normalized Google distance (NGD) is a relative semantic distance based on the World Wide Web (or any other large electronic database, for instance Wikipedia) and a search engine that returns aggregate page counts. The earlier NGD between pairs of search terms (including phrases) is not sufficient for all applications. We propose an NGD of finite multisets of search terms that is better for many applications. This gives a relative semantics shared by a multiset of search terms. We give applications and compare the results with those obtained using the pairwise NGD. The derivation of NGD method is based on Kolmogorov complexity.

Normalized Google Distance of Multisets with Applications

http://arxiv.org/pdf/1308.3177v1

Title Normalized Google Distance Multisets Applications Summary Normalized Google distance NGD relative semantic distance based World Wide Web large electronic database instance Wikipedia search engine return aggregate page count earlier NGD pair search term including phrase sufficient application propose NGD finite multisets search term better many application give relative semantics shared multiset search term give application compare result obtained using pairwise NGD derivation NGD method based Kolmogorov complexity Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.003526699496433139, 0.04202672839164734, -0.03809216991066933, 0.009240356273949146, -0.06527110189199448, -0.03365016728639603, 0.0502312034368515, 0.05385586619377136, -0.025409352034330368, -0.03801482915878296, 0.0431826077401638, 0.004843812435865402, -0.0034119109623134136, 0.0006025460315868258, -0.0056185005232691765, -0.0545794852077961, 0.05983179807662964, 0.04058678075671196, -0.06908082962036133, -0.007908704690635204, -0.010803531855344772, -0.013193325139582157, -0.009740457870066166, 0.024670064449310303, 0.019757097586989403, -0.036140117794275284, 0.002110301284119487, -0.031315792351961136, 0.037501975893974304, -0.04772687330842018, 0.0003240817750338465, 0.02071993425488472, -0.0523943193256855, 0.04277130216360092, 2.166320427932078e-06, -0.037348754703998566, -0.05191053822636604, -0.023555757477879524, 0.05642663314938545, 0.01579742319881916, 0.01523600798100233, 0.015680130571126938, 0.04133850336074829, 0.023720771074295044, -0.01359095424413681, -0.03686906769871712, 0.04539167508482933, -0.02480274997651577, 0.029665375128388405, 0.01845267228782177, -0.010579388588666916, -0.03525366261601448, -0.02834930829703808, 0.034869998693466187, 0.056621041148900986, 0.004968456923961639, -0.011071975342929363, 0.04908483847975731, 0.017149560153484344, 0.01252269558608532, -0.006033183541148901, 0.008158637210726738, -0.05652439966797829, 0.02232978865504265, 0.032672543078660965, 0.03138671815395355, -0.043593887239694595, 0.009231206960976124, 0.0194715429097414, 0.0449298694729805, -0.0007727802731096745, -0.009762294590473175, 0.03702718764543533, -0.0036222885828465223, -0.08083691447973251, 0.049436572939157486, 0.0025648418813943863, -0.01305035687983036, -0.057381726801395416, -0.00960494764149189, -0.07903075963258743, 0.042154304683208466, -0.00018693135643843561, 0.022566093131899834, -0.042356088757514954, 0.033385977149009705, 0.00906437449157238, -0.013359270989894867, -0.039741311222314835, -0.03856731206178665, 0.006406444124877453, -0.063563771545887, 0.04872014373540878, -0.008105753920972347, -0.019409630447626114, -0.001545448089018464, 0.015057194977998734, -0.02602154016494751, 0.058232251554727554, -0.04732581600546837, 0.03685494512319565, 0.0075253332033753395, 0.014143376611173153, 0.02552700787782669, 0.009339080192148685, 0.010365777648985386, -0.009547625668346882, 0.0004978504148311913, -0.006692178547382355, -0.008304486982524395, -0.06615710258483887, -0.0026825550012290478, 0.01470755971968174, 0.019815176725387573, 0.02540518343448639, -0.022903600707650185, -0.03549835458397865, 0.01589658483862877, -0.01331403385847807, -0.013556066900491714, -0.012577500194311142, -0.022967485710978508, 0.0483529232442379, -0.011065499857068062, -0.014226729050278664, 0.004722150973975658, -0.09553475677967072, 0.040846530348062515, -0.007422612514346838, 0.009177900850772858, 0.02944321744143963, 0.005821109749376774, 0.06813821941614151, 0.02165360376238823, 0.026285383850336075, 0.05620243772864342, 0.006928733084350824, -0.06874057650566101, -0.007734466344118118, -0.021336708217859268, 0.03017287887632847, 0.02400926500558853, -0.01320052333176136, -0.08441770076751709, 0.02935546450316906, -0.027118615806102753, 0.005599014926701784, -0.012557861395180225, -0.017612604424357414, 0.0012700249208137393, 0.011988760903477669, 0.08152489364147186, -0.060979537665843964, 0.040400490164756775, 0.041448358446359634, 0.01652238704264164, 0.023920392617583275, 0.020232563838362694, -0.03373019024729729, 0.012143701314926147, 0.0775623768568039, 0.006426020059734583, -0.07151074707508087, -0.03021109290421009, -0.03321089595556259, -0.007809145376086235, -0.018795635551214218, 0.0176563523709774, 0.01228235475718975, 0.00231035309843719, -0.06091206520795822, 0.01106018852442503, -0.048309531062841415, -0.007317114155739546, 0.02984491176903248, 0.09971572458744049, 0.030055848881602287, -0.014110898599028587, -0.037024546414613724, 0.025455351918935776, -0.0321357361972332, -0.007020315155386925, 0.04301257058978081, -0.010937653481960297, -0.025711704045534134, -0.004739043302834034, 0.06512469053268433, 0.06645775586366653, 0.0030827925074845552, -0.010177532210946083, -0.006369312759488821, -0.04952565208077431, 0.015547284856438637, -0.07015274465084076, 0.017938319593667984, -0.06482700258493423, 0.019732514396309853, 0.009661201387643814, 0.028551962226629257, -0.034278903156518936, -0.011579669080674648, 0.027935612946748734, -0.0010176603682339191, 0.022060798481106758, -0.00513962097465992, -0.07350629568099976, -0.039986807852983475, 0.04332593455910683, 0.017798272892832756, -0.018770629540085793, 0.015961211174726486, -0.0016462813364341855, -0.0060765184462070465, -0.025301534682512283, -4.885955422651023e-05, 0.06338116526603699, 0.0213745329529047, -0.009254551492631435, 0.007384032942354679, 0.07539641112089157, 0.02110559679567814, -0.014133080840110779, 0.06577868014574051, 0.0072950939647853374, 0.02688770368695259, 0.0760263055562973, -0.026666738092899323, 0.02886616811156273, -0.008675712160766125, 0.013953541405498981, 0.00883384607732296, 0.011763622052967548, 0.03773023560643196, -0.008879453875124454, -0.028581073507666588, -0.011184357106685638, 0.08572885394096375, 0.0468384213745594, 0.06037868186831474, -0.06139767915010452, 0.03705722093582153, 0.023765580728650093, 0.006729071959853172, -0.011591491289436817, -0.03282616659998894, -0.02919689379632473, 0.010820478200912476, 0.016956044360995293, 0.03866744786500931, -0.026257667690515518, -0.009365339763462543, -0.031199553981423378, 0.053917258977890015, 0.004838228225708008, 0.09042656421661377, -0.050098635256290436, -0.031820427626371384, 0.07559911906719208, 0.020087717100977898, 0.06477564573287964, -0.008971801027655602, -0.022047987207770348, 0.02189045213162899, 0.036245860159397125, 0.03477910906076431, -0.043071575462818146, -0.012346290051937103, -0.03228927403688431, -0.0015001969877630472, 0.03187602758407593, 0.039248187094926834, 0.0300750695168972, 0.04070774093270302, -0.00047973013715818524, -0.0029648595955222845, -0.009169446304440498, 0.00630952138453722, -0.02120521105825901, -0.020775970071554184, 0.043188244104385376, -0.03563215956091881, -0.0572294145822525, -0.011354572139680386, -0.03645356371998787, -0.01544872671365738, 0.021716084331274033, 0.01847437582910061, -0.02784750796854496, 0.004006020724773407, 0.008073320612311363, -0.0981309786438942, 0.0047242362052202225, 0.02191098779439926, -0.017583243548870087, 0.025839677080512047, -0.01329031027853489, -0.029199255630373955, 0.014508883468806744, 0.04158356040716171, -0.05246410146355629, 0.050595056265592575, 0.0018533451948314905, -0.037425003945827484, -0.018528053537011147, -0.024679405614733696, 0.025309031829237938, 0.010190635919570923, -0.039603136479854584, -0.005292103160172701, -0.014435580000281334, 0.022048750892281532, -0.024503488093614578, -0.00978472363203764, 0.0016421241452917457, -0.01571148820221424, 0.00048540192074142396, -0.06720048934221268, 0.026585353538393974, -0.006798769813030958, 0.09506813436746597, 0.014045019634068012, -0.022587357088923454, 0.0026877284981310368, -0.013530362397432327, 0.09550657123327255, -0.036852043122053146, -0.04969845339655876, 0.009026000276207924, 0.036387596279382706, -0.03163710609078407, 0.0642220750451088, -0.03686751797795296, -0.01631680503487587, -0.00029575577354989946, 0.03550342842936516, 0.023112205788493156, -0.03952213004231453, 0.020598843693733215, 0.003994781989604235, 0.00015792233170941472, 0.02015266939997673, -0.04391344264149666, 0.012154854834079742, 0.015269213356077671, 0.04667419195175171, -0.034267544746398926, 0.0016254886286333203, -0.06679613143205643, -0.009036093018949032, 0.04967401549220085, -0.008373667486011982, 0.050730399787425995, 0.043883152306079865, -0.0035806975793093443, -0.013995683752000332, 0.032205261290073395, 0.004284327384084463, -0.007099085953086615, -0.042356282472610474, 0.0498436838388443, -0.019893929362297058, 0.05559834837913513, 0.016550209373235703, -0.004977921023964882, -0.0042014592327177525, 0.012897412292659283, -0.004320187494158745, -0.04985330253839493, -0.045093707740306854, -0.0012714709155261517, 0.02676107920706272, 0.012741846032440662, -0.024780821055173874, 0.0777975395321846, 0.07329726219177246, -0.030462725088000298, 0.01581399329006672, -0.018764564767479897, -0.04331190511584282, 0.046409159898757935, 0.019596144556999207, -0.033676113933324814, 0.008853581734001637, 0.004794965032488108, -0.01905793324112892, -0.035724468529224396, -0.07382221519947052, -0.015277092345058918, -0.06427043676376343, -0.01777305081486702, 0.0009213861194439232, -0.05768222734332085, -0.04847261682152748, -0.06605512648820877, 0.02263915352523327, 0.035707276314496994, -0.09512761980295181, -0.016093986108899117, 0.0014613628154620528, -0.008116809651255608, 0.008029727265238762, -0.024637145921587944, -0.048046525567770004, 0.04461150988936424, -0.06582511216402054, -0.0207536444067955, -0.024377670139074326, 0.07631827145814896, -0.010564594529569149, -0.0715101882815361, -0.0009216867038048804, -0.009780322201550007, 0.011110078543424606, -0.022946517914533615, 0.016634615138173103, 0.02712210826575756, -0.0015783029375597835, 0.010280654765665531, -0.046765927225351334, -0.03261853754520416, -0.026523638516664505, 0.030947253108024597, 0.05344022810459137, 0.012900393456220627, 0.0719369500875473, -0.0325380302965641, 0.005365040618926287, 0.00010112922609550878, -0.018601683899760246, 0.007813854143023491, -0.004885788541287184, -0.022001637145876884, -0.009101864881813526, 0.03641460835933685, 0.027316559106111526, -0.009947964921593666, 0.007164293434470892, -0.06498173624277115, -0.04745735600590706, -0.07049474865198135, -0.007774000987410545, -0.04473601654171944, 0.07793819159269333, -0.032559897750616074, -0.011601398698985577, 0.031174244359135628, -0.009062918834388256, -0.06947419047355652, -0.07126197218894958, 0.02413557469844818, 0.034556854516267776, -0.007855108939111233, 0.044003427028656006, -0.00485715176910162, 0.054282333701848984, -0.05652237683534622, -0.012316460721194744, -0.039304934442043304, -0.05935424566268921, -0.029881883412599564, -0.04150283336639404, 0.03744925186038017, -0.04661997780203819, -0.029146913439035416, -0.030886175110936165, -0.0050817932933568954, 0.05214785784482956, -0.010418382473289967, -0.013242717832326889, 0.013013591058552265, -0.02039053477346897, -0.021055923774838448, 0.016638686880469322, -0.013282109051942825, 0.05390423536300659, -0.02930266410112381, -0.006296207662671804, -0.043067220598459244, 0.007544519379734993, 0.01651350036263466, 0.0738583654165268, 0.0778464525938034, 0.041296809911727905, 0.0019959246274083853, -0.028493177145719528, 0.007060609292238951, -0.049969956278800964, -0.009501117281615734, 0.016332466155290604, -0.040590330958366394, 0.017434880137443542, 0.004325748886913061, -0.018162626773118973, 0.029306957498192787, 0.04400307685136795, -0.023509573191404343, -0.03581814840435982, -0.010115995071828365, -0.004754246212542057, 0.056959476321935654, -0.0040562329813838005, -0.004674188327044249, 0.004816926550120115, -0.06225177273154259, 0.00732424296438694, -0.0022518434561789036, -0.038040850311517715, -0.020809585228562355, 0.044606465846300125, 0.012762762606143951, -0.04349084571003914, 0.036122873425483704, -0.022374210879206657, -0.021134542301297188, -0.002913558855652809, 0.014199973084032536, 0.023313170298933983, 0.02550337463617325, -0.00813215970993042, -0.011675882153213024, -0.0084248511120677, 0.022050388157367706, 0.025406161323189735, -0.00788148958235979, 0.005477156490087509, -0.0012050605146214366, 0.013672432862222195, 0.003402619156986475, 0.03465238958597183, 0.09145081788301468, -0.02943209931254387, 0.013921234756708145, -0.03851183503866196, -0.07492431998252869, -0.006598820444196463, 0.03051110915839672, 0.01648370549082756, 0.030149146914482117, -0.00038378246244974434, 0.0033775416668504477, -0.029307467862963676, -0.04100015386939049, -0.002310829935595393, -0.0009053329122252762, 0.06093774735927582, 0.03195197135210037, 0.030786365270614624, 0.053155045956373215, 0.03943672776222229, -0.013348828069865704, -0.009487424045801163, -0.03268767520785332, -0.10875656455755234, -0.00914072897285223, 0.01001795008778572, -6.837163709221985e-33, 0.0022172785829752684, -0.045757025480270386, -0.04508066922426224, -0.03897562250494957, -0.07102417945861816, 0.00411771098151803, 0.013404319994151592, -0.019059525802731514, -0.03416016325354576, -0.03126906603574753, 0.006180115509778261, 0.046933501958847046, 0.01502991933375597, -0.025151314213871956, 0.016730017960071564, 0.018422871828079224, -0.03846711665391922, 0.017744887620210648, -0.0262225940823555, -0.039659127593040466, 0.07713023573160172, -0.0035914012696594, -0.007787283044308424, -0.044568099081516266, -0.014612553641200066, 0.006460861302912235, -0.008511769585311413, 0.01706974394619465, -0.00830933265388012, 0.05983046814799309, 0.015600628219544888, 0.05516959726810455, 0.0023806686513125896, -0.01589033752679825, -0.015310797840356827, -0.02507735602557659, -0.024303661659359932, -0.08736944198608398, -0.024580955505371094, -0.027127625420689583, 0.016158748418092728, 0.02398551255464554, 0.029374076053500175, 0.011506278067827225, -0.011545316316187382, -0.0295574888586998, 0.05231650918722153, -0.017701713368296623, -0.07073848694562912, 0.005076310597360134, 0.028074128553271294, 0.012046946212649345, -0.04375152662396431, 0.07825085520744324, 0.023891963064670563, -0.019723467528820038, -0.009975256398320198, 0.0433492548763752, -0.013227878138422966, 0.07971436530351639, -0.002690185559913516, 0.04968557506799698, 0.009263629093766212, 0.0007705571479164064, 0.03698410838842392, 0.053969867527484894, 0.03345884382724762, -0.07341369241476059, 0.03847811743617058, -0.01410518679767847, 0.0006542032933793962, 0.045618947595357895, -0.012450781650841236, -0.002518454333767295, 0.03151321038603783, -0.04316655173897743, -0.0626261979341507, 0.010509051382541656, -0.06370474398136139, 0.025302719324827194, -0.01805044710636139, 0.02345440164208412, -0.043265052139759064, -0.008267328143119812, 0.019381437450647354, -0.011818629689514637, -0.02164025418460369, -0.02896927297115326, 0.006406001280993223, -0.0004287059127818793, -0.03480720520019531, 0.02432612143456936, -0.045580580830574036, -0.017158327624201775, -0.015076692216098309, 0.020394379273056984, -0.012291090562939644, 0.04154450446367264, -0.02000807225704193, -0.021570777520537376, -0.007723958231508732, -0.04496355727314949, -0.04928930848836899, 0.0023444865364581347, 0.03757743164896965, -0.02297389693558216, -0.007252385374158621, -0.01238990854471922, -0.09271571785211563, 0.005261296406388283, 0.011282543651759624, -0.0937531515955925, -0.0234962310642004, -0.037948742508888245, 0.031979307532310486, -0.017414897680282593, 0.03314026817679405, 0.07656451314687729, 0.0817209854722023, -0.027754509821534157, 0.015062836930155754, -0.027652114629745483, -0.010792220011353493, 0.0055048600770533085, -0.006564750336110592, 0.00906510278582573, -0.0692756399512291, -0.012836587615311146, 0.07908179610967636, 0.0100305350497365, -0.038597822189331055, -0.022913124412298203, 2.8818709552069777e-07, 0.05603836849331856, 0.053250472992658615, 0.019802935421466827, 0.09595925360918045, -0.010464498773217201, -0.006661602295935154, 0.01140203233808279, 0.042713042348623276, -0.07561825960874557, 0.019212786108255386, 0.04894356057047844, -0.030236434191465378, 0.024829711765050888, 0.04985572770237923, -0.00183849164750427, 0.05635939911007881, -0.07959731668233871, -0.022467471659183502, -0.07091331481933594, 0.02857578918337822, 0.0647454708814621, 0.01464642770588398, 0.04642757028341293, 0.0166032612323761, -0.01027756929397583, -0.047670673578977585, -0.003570730332285166, -0.06398002058267593, 0.024003027006983757, 0.003132834332063794, 0.05563399940729141, -0.05627335235476494, 0.009180981665849686, 0.03622474893927574, -0.0067310878075659275, 0.005735378246754408, 0.08765389770269394, 0.001389546669088304, -0.022026192396879196, 0.07359372079372406, 0.0008002669201232493, -0.07811399549245834, -0.008349733427166939, -0.04326561838388443, 0.03986081853508949, 0.06827067583799362, -0.016862642019987106, 0.04625537246465683, -0.025602133944630623, -0.008344723843038082, 0.04350737854838371, 0.028444427996873856, -0.019377533346414566, -0.017446868121623993, -0.028999192640185356, 0.021086085587739944, 0.01855422556400299, -0.02930642105638981, -0.007458575535565615, 0.04696820676326752, -0.0016109419520944357, -0.025323640555143356, 0.019596228376030922, 0.040476374328136444, 0.029818719252943993, -0.01346882525831461, -0.0259254090487957, 2.837425253581627e-34, -0.005674905143678188, 0.03617017716169357, -0.031130999326705933, -0.04007909074425697, 0.010604113340377808, -0.04151032865047455, -0.030279194936156273, 0.018809672445058823, -0.014335147105157375, -0.030249128118157387, 0.0073663038201630116]

['Leon Wenliang Zhong', 'James T. Kwok']

1308.3558v1

In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as existing stochastic ADMM algorithms, the proposed algorithm improves the convergence rate on convex problems from $O(\frac 1 {\sqrt{T}})$ to $O(\frac 1 T)$, where $T$ is the number of iterations. This matches the convergence rate of the batch ADMM algorithm, but without the need to visit all the samples in each iteration. Experiments on the graph-guided fused lasso demonstrate that the new algorithm is significantly faster than state-of-the-art stochastic and batch ADMM algorithms.

Fast Stochastic Alternating Direction Method of Multipliers

http://arxiv.org/pdf/1308.3558v1

Title Fast Stochastic Alternating Direction Method Multipliers Summary paper propose new stochastic alternating direction method multiplier ADMM algorithm incrementally approximates full gradient linearized ADMM formulation Besides low periteration complexity existing stochastic ADMM algorithm proposed algorithm improves convergence rate convex problem Ofrac 1 sqrtT Ofrac 1 number iteration match convergence rate batch ADMM algorithm without need visit sample iteration Experiments graphguided fused lasso demonstrate new algorithm significantly faster stateoftheart stochastic batch ADMM algorithm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.027536818757653236, 0.021112872287631035, 0.014197850599884987, -0.025315653532743454, 0.01824192702770233, -0.013817127794027328, -0.012790792621672153, -0.04342789575457573, -0.00833034235984087, 0.02939675562083721, 0.015454246662557125, -0.0493474081158638, 0.0063592735677957535, -0.015756849199533463, 0.017452243715524673, 0.0300503708422184, -0.011749813333153725, -0.05660419538617134, -0.03267410397529602, -0.023926695808768272, 0.06336981803178787, -0.04823164641857147, 0.024840939790010452, 0.008596296422183514, 0.001173608936369419, -0.01898862048983574, -0.041439179331064224, 0.019154326990246773, 0.03468363359570503, -0.03635405749082565, 0.04274120181798935, -0.040246348828077316, 0.01980496011674404, 0.04164007306098938, 2.047283715000958e-06, -0.01671314239501953, 0.028802018612623215, 0.0007648224709555507, 0.04445953294634819, 0.06895763427019119, -0.01875765062868595, 0.04072284698486328, 0.023505428805947304, 0.010853571817278862, -0.03128043934702873, -0.05100971460342407, 0.015915531665086746, 0.009136420674622059, 0.009390749037265778, 0.04402365908026695, 0.006154443137347698, -0.03139536455273628, 0.013949461281299591, -0.029602184891700745, -0.024952908977866173, -0.05597779527306557, 0.0265707578510046, -0.01641266420483589, -0.009723478928208351, 0.004311028867959976, 0.027838941663503647, 0.03882694989442825, 0.004824137780815363, -0.0020506319124251604, 0.067206971347332, -0.0064726825803518295, 0.04348338395357132, 0.03546074032783508, -0.002698536729440093, 0.030656393617391586, -0.004881681874394417, 0.00464188028126955, -0.034323401749134064, 0.019655968993902206, -0.040014415979385376, 0.00988916214555502, -0.0561247393488884, -0.01780041493475437, -0.034443993121385574, 0.015360034070909023, -0.05395197868347168, -0.05457199364900589, 0.035122714936733246, 0.032795052975416183, -0.010551419109106064, 0.1049574464559555, -0.013247611932456493, -0.0007132570608519018, 0.015668313950300217, 0.0061479853466153145, -0.07807644456624985, -0.011173762381076813, 0.021936805918812752, 0.051742445677518845, -0.07003806531429291, 0.000670064240694046, -0.02447117306292057, -0.08711884170770645, -0.00666578346863389, -0.022408820688724518, 0.08808859437704086, -0.023576730862259865, -0.003520412603393197, 0.030338361859321594, -0.033026400953531265, -0.018748825415968895, -0.05192239210009575, -0.007727511692792177, 0.0016567441634833813, 0.027905454859137535, 0.01746068336069584, 0.005581388715654612, -0.0007190299802459776, 0.0640961304306984, 0.005389007739722729, -0.02775094471871853, -0.0629856064915657, -0.02533761039376259, -0.002077199751511216, -0.07179372012615204, 0.07250113040208817, 0.03610454499721527, 0.006152104586362839, -0.005400134716182947, 0.004041078966110945, -0.007676992565393448, -0.058772940188646317, 0.046493228524923325, 0.00035846419632434845, 0.057404473423957825, -0.006565423216670752, 0.03666761890053749, -0.02911507524549961, 0.023734452202916145, -0.0003726205322891474, 0.049498300999403, -0.053671032190322876, 0.04287053272128105, -0.06434020400047302, 0.022804075852036476, -0.0032268865033984184, -0.01046378817409277, -0.02753080241382122, -0.06739737093448639, 0.0075883762910962105, 0.01263795793056488, 0.022405635565519333, -0.003038500901311636, 0.05147138983011246, -0.027068518102169037, 0.005472342949360609, 0.026862263679504395, -0.03900275006890297, -0.002106608124449849, 0.059175726026296616, 0.02045397274196148, -0.06740046292543411, 0.03377000242471695, -0.012473098002374172, 0.04244065284729004, 0.023168286308646202, 0.05812063068151474, 0.003063253592699766, 0.0015413487562909722, 0.015481838025152683, 0.0009243703680112958, 0.018045706674456596, -0.04559386149048805, -0.046929940581321716, 0.03891464322805405, 0.024624789133667946, 0.057128701359033585, -0.04677026346325874, -0.05675337836146355, -0.008953477256000042, -0.028585314750671387, 0.01386475469917059, -0.008182617835700512, 0.018652617931365967, 0.019612504169344902, 0.002156822243705392, -0.00961197167634964, 0.032385509461164474, 0.05605411157011986, -0.05379417538642883, -0.011492593213915825, 0.015741538256406784, 0.049655672162771225, -0.051679983735084534, 0.010546105913817883, 0.009396631270647049, -0.010902468115091324, 0.014473305083811283, -0.0018080113222822547, -3.742102489923127e-05, -0.028403233736753464, -0.01267331000417471, -0.06536297500133514, 0.05500205606222153, -0.014916994608938694, -0.07596680521965027, -0.016992362216114998, -0.037889398634433746, -0.07633019983768463, 0.016109416261315346, -0.004721886944025755, -0.02837020345032215, -0.03381006792187691, 0.011461912654340267, -0.06455059349536896, -0.04290943220257759, 0.020686767995357513, 0.022947322577238083, -0.002135115209966898, -0.018118608742952347, 0.057698629796504974, -0.025647597387433052, 0.033933497965335846, 0.06231512129306793, 0.010572491213679314, -0.01811336539685726, 0.013739840127527714, -0.010476170107722282, 0.011631567031145096, -0.04484334588050842, -0.0061953323893249035, 0.0919509157538414, 0.0037767505273222923, 0.023977769538760185, 0.024446966126561165, 0.044954512268304825, -0.039776336401700974, 0.004318667575716972, -0.04787952080368996, -0.06767662614583969, 0.002494086278602481, 0.007664715871214867, -0.03275800868868828, 0.03985194116830826, -0.046541426330804825, 0.019116368144750595, 0.011309153400361538, 0.023235348984599113, -0.04423293098807335, 0.035214733332395554, -0.020719634369015694, -0.04061815142631531, -0.07791652530431747, 0.027866527438163757, 0.015476076863706112, 0.05003854259848595, 0.017590392380952835, 0.04024147987365723, -0.05662950128316879, 0.04125937446951866, 0.02394052967429161, 0.029395978897809982, 0.015641340985894203, 0.01984715834259987, -0.027132343500852585, -0.0642244890332222, -0.013449321500957012, 0.0013862954219803214, -0.010754797607660294, 0.013674821704626083, 0.059973157942295074, 0.04436633735895157, -0.02048058994114399, -0.03776686266064644, -0.04751809686422348, 0.008182327263057232, -0.012538835406303406, 0.005032524466514587, 0.042527154088020325, 0.030366098508238792, -0.018132565543055534, 0.06342419981956482, -0.09748214483261108, -0.05178425833582878, -0.005917490925639868, 0.009900535456836224, 0.014471670612692833, 0.0069695995189249516, -0.040630362927913666, 0.04496269300580025, -0.01220861729234457, -0.04197775945067406, -0.014709016308188438, -0.027863260358572006, 0.03723535314202309, -0.004136118572205305, -0.0033366915304213762, -0.025359176099300385, 0.004888087511062622, -0.011856045573949814, -0.03751488775014877, 0.010731871239840984, -0.010790560394525528, -0.006052564363926649, -0.02414785325527191, -0.008942904882133007, 0.06918834894895554, 0.00794590450823307, -0.010865220800042152, 0.03372100368142128, 0.0140916733071208, 0.01938815414905548, 0.015566980466246605, -0.004823366180062294, 0.028328435495495796, -0.020132288336753845, -0.03441144526004791, 0.062021996825933456, -0.023981502279639244, -0.020580898970365524, -0.050508297979831696, -0.03924577310681343, 0.0399283729493618, -0.014259163290262222, 0.006608015391975641, 0.02489268220961094, 0.0041347043588757515, 0.05902223289012909, -0.00468551367521286, -0.008685270324349403, 0.025260917842388153, -0.05217095836997032, -0.006143941078335047, -0.09010732173919678, -0.022151291370391846, 0.01953144557774067, -0.09152287989854813, -0.027140192687511444, 0.03703827038407326, 0.032708991318941116, 0.020832277834415436, -0.02382824942469597, 0.03841221332550049, 0.07081456482410431, 0.03203989192843437, 0.04650857299566269, -0.01219120342284441, -0.006298006046563387, -7.321375596802682e-05, 0.01669459603726864, 0.0004761217860504985, 0.00473936740309, -0.038187649101018906, -0.015318306162953377, 0.020763639360666275, 0.026955582201480865, -0.015013810247182846, -0.06184496730566025, -0.009702526032924652, 0.008185990154743195, 0.05107014626264572, 0.02371717244386673, -0.0519491471350193, -0.07797185331583023, -0.016404129564762115, 0.05259193107485771, -0.02949608862400055, 0.05357258394360542, 0.02200663462281227, -0.04249710589647293, -0.017093928530812263, 0.0009070344385690987, 0.01239302009344101, -0.003908082377165556, 0.0034728844184428453, 0.015264407731592655, 0.020203396677970886, 0.027508055791258812, -0.006156018935143948, 0.003131805919110775, -0.0776343047618866, -0.02193807065486908, -0.0470956526696682, 0.04586353152990341, 0.019598333165049553, -0.018852384760975838, -0.06827922910451889, -0.028842853382229805, -0.010888869874179363, 0.04196859523653984, 0.008517798036336899, -0.0004753119428642094, 0.026055607944726944, -0.020424434915184975, -0.02347855269908905, -0.010069787502288818, -0.055553313344717026, -0.01893792487680912, -0.06462329626083374, 0.02443380281329155, -0.045961227267980576, 0.05684378743171692, 0.0673401728272438, -0.0036102309823036194, 0.016215631738305092, -0.020765330642461777, -0.033757418394088745, -0.007749671116471291, -0.027884500101208687, -0.0830966979265213, -0.0026679839938879013, 0.029024945572018623, -0.03253687918186188, -0.05912686511874199, -0.017151374369859695, -0.010320437140762806, 0.07416321337223053, 0.018028022721409798, -0.012738469988107681, -0.04351690784096718, 0.018616417422890663, -0.02135634981095791, -0.0053599863313138485, 0.08856011927127838, -0.01135142520070076, 0.09104886651039124, 0.012405002489686012, 0.043527718633413315, 0.03291015326976776, 0.029638541862368584, 0.008167479187250137, 0.0014176409458741546, 0.05470876768231392, -0.015937697142362595, -0.027635760605335236, -0.05249803885817528, -0.02680964022874832, -0.0028431247919797897, 0.01593107543885708, -0.0016088931588456035, 0.021378306671977043, -0.02651066519320011, 0.003162986133247614, 0.010246312245726585, -0.012301187962293625, -0.01996465027332306, 0.004860146902501583, 0.04198799282312393, 9.809254697756842e-05, 0.06039467081427574, 0.015639055520296097, 0.02302761748433113, -0.03327960893511772, -0.03565724939107895, 0.04382587969303131, 0.043818362057209015, 0.02501627616584301, 0.027581915259361267, -0.014063074253499508, 0.002646604087203741, 0.044113487005233765, 0.030623378232121468, -0.08711639046669006, -0.044368352741003036, -0.010156475007534027, -0.02003229781985283, -0.013127346523106098, 0.040884606540203094, -0.004543566610664129, -0.02113315463066101, -0.04164842888712883, 0.004412088077515364, 0.06055990234017372, 0.053227901458740234, 0.012832324020564556, -0.001848625484853983, -0.006661105435341597, 0.03116540051996708, 0.03334067389369011, 0.022223858162760735, -0.0035484093241393566, 0.10285590589046478, -0.0667426586151123, -0.013777609914541245, -0.02119220234453678, 0.03667881339788437, 0.04078367352485657, 0.008325713686645031, -0.0008876811480149627, -0.05429035425186157, 0.01074621919542551, 0.05255996063351631, 0.0424208827316761, -0.015038816258311272, 0.05170157179236412, 0.024471260607242584, -0.04323370382189751, -0.021223442628979683, 0.00818877574056387, 0.06769844144582748, -0.015810901299118996, 0.00025022492627613246, -0.0010344971669837832, 0.003247135318815708, 0.032923076301813126, -0.012770035304129124, 0.005228409077972174, 0.009554100222885609, 0.035880111157894135, 0.06659131497144699, -0.028441911563277245, -0.01354990340769291, 0.05454450845718384, -0.05075015872716904, 0.04830464348196983, 0.0073977573774755, -0.04825356975197792, 0.019106823951005936, -0.07068908214569092, -0.04358745738863945, 0.02115267515182495, 0.03877229616045952, 0.038561321794986725, 0.06484267115592957, -0.018719492480158806, -0.012497409246861935, -0.035908292979002, 0.044846296310424805, -0.06659965962171555, 0.07585664838552475, -0.012854749336838722, -0.004999815486371517, -0.004482918418943882, 0.06261802464723587, 0.02975608967244625, -0.029236488044261932, -0.005197106394916773, -0.019795918837189674, 0.004452376160770655, -0.020406175404787064, 0.006332301534712315, 0.10291139781475067, 0.05115408077836037, -0.00873168371617794, 0.0191970095038414, 0.05100611597299576, 0.029705781489610672, -0.020819440484046936, -0.015973389148712158, 0.012981822714209557, -0.03674737736582756, 0.013871695846319199, 0.041850075125694275, -0.02375580370426178, 0.08933551609516144, -0.006105297710746527, -0.02944898046553135, 0.030834561213850975, -0.024882543832063675, -0.00530697125941515, -5.8074200049841065e-33, -0.008494885638356209, 0.012527641840279102, -0.0384155735373497, -0.03819824010133743, -0.02767339162528515, 0.0005662179901264608, 0.05095529556274414, 0.07971946895122528, 0.0009041780140250921, -0.008336655795574188, -0.014352868311107159, 0.007187346927821636, -0.01134447194635868, 0.0318024680018425, 0.03566330671310425, 0.03877398371696472, -0.010348963551223278, -0.022791573777794838, 0.056724414229393005, 0.034501299262046814, 0.0249360091984272, 0.04117804020643234, -0.02631956897675991, -0.04907325655221939, 0.0010156035423278809, 0.03209970146417618, -0.031636252999305725, -0.03244011476635933, 0.03896404430270195, -0.03244888409972191, -0.02192753367125988, 0.01937621459364891, -0.024323809891939163, -0.03731830418109894, -0.011814516969025135, -0.07342089712619781, -0.0472717247903347, 0.00879167765378952, 0.01103415247052908, -0.003593300236389041, -0.07118033617734909, 0.05182426795363426, 0.009410971775650978, -0.004735960625112057, -0.03836192935705185, 0.00456994166597724, 0.0394248366355896, 0.005205375608056784, -0.05659018084406853, -0.01896108314394951, -0.02619967982172966, 0.001041355892084539, 0.001064939540810883, 0.012876773253083229, 0.02002597041428089, -0.028264621272683144, -0.05026714876294136, -0.037242356687784195, -0.041795916855335236, -0.023067478090524673, 0.015009679831564426, 0.030424240976572037, -0.013758352026343346, 0.03315022960305214, 0.015295339748263359, 0.011089620180428028, 0.037311311811208725, -0.03554095700383186, 0.004093259107321501, 0.003112024161964655, -0.019044602289795876, -0.011497565545141697, -0.005418822634965181, -0.00027082968153990805, 0.044409655034542084, -0.0012050260556861758, -0.05658483877778053, 0.0500887893140316, 0.03581641614437103, 0.02027273364365101, 0.03577873855829239, -0.005144196562469006, -0.003619543509557843, -0.0014843065291643143, 0.028521692380309105, -0.048357196152210236, -0.01705741509795189, -0.04339556396007538, -0.02655578777194023, 0.040369912981987, -0.004869337659329176, 0.002871621400117874, -0.012799730524420738, -0.023152824491262436, 0.024887805804610252, 0.015857361257076263, 0.03512800484895706, -0.01451166532933712, 0.018390795215964317, -0.015291699208319187, -0.020736029371619225, 0.030447423458099365, -0.06800546497106552, 0.02546779438853264, -0.010496165603399277, 0.011154656298458576, 0.04443841800093651, -0.015550695359706879, 0.018709201365709305, -0.03741002082824707, -0.010136700235307217, 0.011118258349597454, -0.0014720450853928924, 0.03235447406768799, 0.03964754939079285, -0.10695004463195801, -0.0017921555554494262, 0.07362941652536392, -0.02693289890885353, 0.01296327356249094, -0.03967629745602608, -0.048424527049064636, 0.007226103916764259, -0.001489986781962216, -0.05854957178235054, 0.06329350173473358, 0.008657015860080719, -0.09199948608875275, -0.0443318635225296, -0.06954062730073929, -0.0025954830925911665, -0.050433430820703506, 2.5378565737810277e-07, -0.021261215209960938, 0.03273496776819229, -0.02919263392686844, 0.0521298423409462, 0.005654330365359783, -0.021462203934788704, -0.07351181656122208, -0.013455158099532127, -0.045188650488853455, -0.03322705626487732, 0.021044595167040825, 0.01151985302567482, -0.009660209529101849, -0.03960883989930153, 0.0014481727266684175, -0.05292106047272682, -0.04613180458545685, 0.10243705660104752, 0.012584448792040348, -0.045007411390542984, -0.011864706873893738, 0.02701800875365734, 0.002287334529682994, -0.059540361166000366, 0.01694212295114994, -0.005642982199788094, 0.042122770100831985, 0.0472409687936306, 0.02408076450228691, -0.01612801104784012, 0.0427214689552784, -0.0002950363850686699, 0.0040530068799853325, -0.08252839744091034, 0.018120598047971725, 0.006355872377753258, 0.05821215733885765, 0.043846309185028076, -0.029088923707604408, -0.024599742144346237, 0.04504181072115898, 0.05235686153173447, 0.009576389566063881, 0.0003931120445486158, -0.002925978973507881, 0.05763377249240875, 0.02033539116382599, -0.04581382870674133, 0.0009789312025532126, 0.0067467596381902695, 0.06807789951562881, -0.06255241483449936, 0.06229667365550995, -0.02064964361488819, -0.019076509401202202, 0.013351745903491974, -0.017627475783228874, -0.023150071501731873, 0.01079307496547699, 0.07992345839738846, -0.024974042549729347, -0.039460595697164536, -0.0030127051286399364, 0.0947113111615181, 0.024967970326542854, 0.0014408713905140758, -0.028406649827957153, 2.004187562438268e-34, 0.07009358704090118, 0.027402786538004875, -0.040954720228910446, 0.052895497530698776, -0.044850558042526245, -0.046857915818691254, -0.03188041225075722, -0.011597828939557076, -0.025392163544893265, -0.06284436583518982, -0.0124592250213027]

['Lingsong Zhang', 'J. S. Marron', 'Shu Lu']

1308.4206v2

Motivated by the analysis of nonnegative data objects, a novel Nested Nonnegative Cone Analysis (NNCA) approach is proposed to overcome some drawbacks of existing methods. The application of traditional PCA/SVD method to nonnegative data often cause the approximation matrix leave the nonnegative cone, which leads to non-interpretable and sometimes nonsensical results. The nonnegative matrix factorization (NMF) approach overcomes this issue, however the NMF approximation matrices suffer several drawbacks: 1) the factorization may not be unique, 2) the resulting approximation matrix at a specific rank may not be unique, and 3) the subspaces spanned by the approximation matrices at different ranks may not be nested. These drawbacks will cause troubles in determining the number of components and in multi-scale (in ranks) interpretability. The NNCA approach proposed in this paper naturally generates a nested structure, and is shown to be unique at each rank. Simulations are used in this paper to illustrate the drawbacks of the traditional methods, and the usefulness of the NNCA method.

Nested Nonnegative Cone Analysis

http://arxiv.org/pdf/1308.4206v2

Title Nested Nonnegative Cone Analysis Summary Motivated analysis nonnegative data object novel Nested Nonnegative Cone Analysis NNCA approach proposed overcome drawback existing method application traditional PCASVD method nonnegative data often cause approximation matrix leave nonnegative cone lead noninterpretable sometimes nonsensical result nonnegative matrix factorization NMF approach overcomes issue however NMF approximation matrix suffer several drawback 1 factorization may unique 2 resulting approximation matrix specific rank may unique 3 subspace spanned approximation matrix different rank may nested drawback cause trouble determining number component multiscale rank interpretability NNCA approach proposed paper naturally generates nested structure shown unique rank Simulations used paper illustrate drawback traditional method usefulness NNCA method Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.05849961191415787, 0.017573051154613495, -0.042856231331825256, 0.06267349421977997, 0.014103725552558899, -0.013568051159381866, 0.02988782338798046, 0.00764035526663065, -0.06103413924574852, 0.010937811806797981, -0.014731330797076225, -0.022790422663092613, 0.013705614022910595, 0.008993546478450298, -0.018819767981767654, -0.0076443469151854515, 0.007206272333860397, -0.015735121443867683, -0.039369549602270126, 0.008138752542436123, -0.0332537516951561, -0.03850242868065834, -0.0007153250044211745, -0.008106864988803864, 0.0022846651263535023, -0.04001876339316368, -0.0171903558075428, 0.021714799106121063, 0.04756063595414162, -0.060602813959121704, 0.02442334033548832, 0.032860781997442245, 0.026400063186883926, 0.012287398800253868, 2.1408604879979976e-06, -0.023548606783151627, -0.01630888320505619, 0.011968187056481838, 0.05542021244764328, 0.03215472400188446, 0.0070899734273552895, -0.003138189436867833, -0.005211038514971733, -0.06775998324155807, 0.011201154440641403, 0.01008929405361414, -0.012485086917877197, 0.03471032902598381, 0.041034065186977386, -0.02399713546037674, -0.007105500902980566, -0.009816378355026245, -0.0525672473013401, -0.001905505545437336, -0.017209602519869804, -0.023893272504210472, -0.004231023136526346, -0.005822939798235893, 0.0011954185320064425, 0.03977932408452034, -0.02589660882949829, 0.013313926756381989, -0.002280580811202526, -0.03439759835600853, 0.07862893491983414, 0.04470180347561836, 0.003939887508749962, 0.04633060842752457, 0.013469209894537926, 0.05245764181017876, -0.015181678347289562, 0.006438333075493574, 0.02652614563703537, -0.015159488655626774, -0.010527151636779308, -0.05161305516958237, -0.04758670926094055, -0.002376019023358822, 0.022995086386799812, -0.01796445995569229, -0.03105084039270878, 0.10438637435436249, -0.055559515953063965, -0.052229445427656174, 0.016995253041386604, 0.09277232736349106, 0.022894088178873062, -0.044091470539569855, 0.024760151281952858, -0.04854785278439522, 0.025634411722421646, 0.028733735904097557, 0.029422279447317123, -0.018806571140885353, -0.0728410854935646, -0.021288156509399414, 0.07186314463615417, -0.007496898993849754, 0.026118146255612373, -0.02776234596967697, 0.06073310226202011, 0.010904614813625813, 0.017104007303714752, 0.0185710396617651, -0.05725832283496857, 0.005731149110943079, -0.0651877224445343, -0.026207847520709038, -0.013087880797684193, 0.06787963211536407, -0.0179615281522274, -0.030487455427646637, 0.03208836168050766, 0.040677811950445175, -0.04021384194493294, 0.03070857562124729, -0.046380363404750824, -0.0032973713241517544, -0.06144474074244499, -0.04230962693691254, 0.024414751678705215, 0.043271079659461975, 0.06526931375265121, 0.005731525830924511, 0.021154461428523064, 0.04714881628751755, -0.0070741078816354275, 0.01297422032803297, -0.05200960859656334, 0.09645392000675201, 0.011081698350608349, 0.036021072417497635, -0.00423179566860199, -0.03333562612533569, -0.02948279306292534, 0.03914209455251694, -0.003002915997058153, 0.031144866719841957, 0.004448787309229374, 0.0039044050499796867, -0.05512141436338425, -0.0264494176954031, -0.029304618015885353, -0.04164310544729233, 0.03718120977282524, -0.04714612290263176, -0.008684835396707058, -0.0011040944373235106, 0.025525761768221855, -0.013636312447488308, -0.011342634446918964, 0.02679884061217308, -0.006592176854610443, 0.0024175194557756186, 0.010759234428405762, 0.017187008634209633, 0.045702602714300156, -0.0002920340048149228, 0.005025322549045086, 0.006092988420277834, 0.01208152063190937, -0.005113745573908091, -0.04565933719277382, -0.03610329329967499, 0.018305186182260513, 0.004935152363032103, -0.0757683515548706, 0.001908970414660871, -0.051934290677309036, -0.028804656118154526, -0.026063134893774986, 0.003542059101164341, 0.02068784274160862, -0.007521368563175201, 0.02620336040854454, 0.009216890670359135, -0.02120307646691799, -0.009424284100532532, -0.02686091884970665, -0.040803130716085434, -0.02460205741226673, -0.023895831778645515, 0.03243027999997139, 0.021703939884901047, -0.10416767001152039, -0.03454356640577316, -0.0712195634841919, -0.003123015630990267, -0.01788388192653656, -0.025611357763409615, 0.02065414935350418, -0.009543489664793015, -0.02298683114349842, -0.057246435433626175, 0.020923158153891563, -0.03757885470986366, 0.0031750660855323076, -0.08248486369848251, 0.020691534504294395, -0.0676596611738205, -0.017445813864469528, 0.00925497431308031, 0.036687880754470825, -0.05444535240530968, -0.044820792973041534, -0.06570544093847275, -0.06838826835155487, 0.026472175493836403, -0.033813200891017914, -0.010048173367977142, -0.0759795531630516, -0.00498097063973546, 0.0025321445427834988, 0.00936884805560112, 0.02376907877624035, 0.04265699163079262, 0.030681181699037552, -0.014081208035349846, -0.08212852478027344, 0.0017985188169404864, 0.002835214603692293, 0.002023432170972228, 0.04494249075651169, -0.021015213802456856, 0.008901616558432579, 0.07144685834646225, 0.06836904585361481, 0.014310161583125591, 0.020289961248636246, 0.07619572430849075, 0.06846509128808975, -0.03591902554035187, 0.07573264837265015, -0.03191916644573212, -0.11879049241542816, -0.03192278742790222, 0.008242474868893623, -0.0282917320728302, 0.0065153781324625015, -0.03728072717785835, 0.0074157859198749065, 0.007827259600162506, 0.02885490655899048, -0.002727261045947671, 0.02368849329650402, 0.019738946110010147, -0.03019876405596733, -0.0010826917132362723, 0.04814955219626427, -0.01690543070435524, 0.007807500194758177, -0.017880422994494438, 0.0986081138253212, -0.027113253250718117, 0.04554435610771179, 0.0638137012720108, -0.08319241553544998, 0.020803743973374367, -0.007237662095576525, -0.01436456199735403, -0.015602626837790012, -0.03098193183541298, -0.05986194685101509, -0.016814514994621277, 0.02814500965178013, 0.010331662371754646, 0.01737627387046814, 0.015539288520812988, 0.011849847622215748, 0.028405407443642616, -0.001776675577275455, 0.011425300501286983, -0.014462163671851158, 0.010912427678704262, 0.015317917801439762, -0.014632617123425007, -0.027507059276103973, -0.013409501872956753, -0.02476130612194538, 0.03704118728637695, -0.03795112296938896, -0.026269597932696342, -0.017762988805770874, -0.014379308559000492, -0.032240595668554306, 0.031369898468256, -0.015914825722575188, -0.05607535317540169, 0.001673049875535071, 0.10767295956611633, -0.03224349766969681, -0.009663890115916729, -0.035449203103780746, 0.011646261438727379, -0.03659943491220474, 0.026517357677221298, 0.09023543447256088, 0.03455844521522522, 0.011303968727588654, 0.008698304183781147, 0.014823740348219872, 0.02190246805548668, 0.006861027795821428, 0.030937284231185913, -0.02042989432811737, 0.050653181970119476, 0.06446407735347748, 0.0008210231899283826, 0.023062294349074364, 0.034883737564086914, 0.03388117998838425, -0.02828485332429409, -0.005306918639689684, 0.04433881491422653, -0.0536259263753891, -0.02422613464295864, -0.11603348702192307, -0.014827392995357513, -0.044816527515649796, 0.059404853731393814, 0.016651177778840065, 0.007848788052797318, -0.007846959866583347, 0.008251764811575413, -0.020266368985176086, 0.008260486647486687, -0.0061428905464708805, -0.011550907045602798, -0.03894137218594551, -0.0032838021870702505, 0.006180851254612207, -0.01603967882692814, 0.0003327407466713339, 0.016522472724318504, 0.035579778254032135, -0.04002640023827553, -0.02931021898984909, 0.0038520696107298136, 0.06114457920193672, -0.005528552923351526, -0.007780673447996378, -0.012965778820216656, -0.039659690111875534, 0.028101740404963493, 0.07648248225450516, -0.017249533906579018, 0.03202805668115616, 0.01795356534421444, 0.056467436254024506, 0.06017313525080681, 0.025108039379119873, -0.006804068107157946, -0.03510718420147896, 0.006500481627881527, 0.004158445633947849, 0.0684678703546524, -0.012950140982866287, -0.0041204942390322685, -0.02015739679336548, 0.008008749224245548, 0.03550063073635101, 0.023600030690431595, 0.007949693128466606, -0.00874185562133789, -0.01233802642673254, 0.008881757035851479, -0.0009785391157492995, 0.07111532241106033, 0.010523172095417976, -0.022834064438939095, -0.010973215103149414, 0.015657709911465645, 0.03250431641936302, 0.03305266052484512, 0.04602383077144623, -0.0647391602396965, 0.022738508880138397, -0.03949132561683655, 0.025257082656025887, 0.0369272381067276, -0.0107010118663311, -0.033340346068143845, 0.07137902826070786, -0.008016406558454037, 0.006911467295140028, 0.02410009317100048, -0.059317655861377716, -0.005230375565588474, -0.07018234580755234, 0.02535494975745678, -0.013624451123178005, -0.017359524965286255, -0.043397873640060425, 0.00253876275382936, 0.017972024157643318, -0.003804946318268776, -0.08891221880912781, 0.051191408187150955, 0.006244200747460127, -0.019889159128069878, -0.005499076563864946, -0.07541516423225403, -0.0371759869158268, 0.023242726922035217, -0.023714862763881683, 0.015097467228770256, -0.0868930071592331, 0.03947065770626068, -0.03639047592878342, -0.07120771706104279, 0.009725309908390045, -0.04498923569917679, -0.006739395204931498, -0.06969694793224335, 0.015402332879602909, 0.05918765068054199, 0.0053652264177799225, -0.050234105437994, 0.06120028346776962, 0.0008445573039352894, 0.011903789825737476, 0.0005840645171701908, 0.09979777038097382, 0.03232036530971527, -0.005106817465275526, -0.02524513006210327, 0.030527792870998383, 0.02909144014120102, -0.002293587662279606, -0.004195280373096466, -0.012822302989661694, 0.009240283630788326, 0.016035210341215134, 0.025848891586065292, 0.022014258429408073, -0.0416068471968174, 0.023403745144605637, 0.02173675410449505, -0.005760655272752047, -0.056403178721666336, 0.058808833360672, -0.02535770833492279, 0.06326261907815933, -0.01086549460887909, -0.0014597016852349043, 0.007383657153695822, -0.0418785959482193, 0.03543037921190262, -0.06380322575569153, 0.030468866229057312, 0.029401620849967003, -0.0004766648344229907, 0.06027614697813988, 0.009737865068018436, 0.00826124008744955, -0.04973850026726723, -0.14498721063137054, -0.013459586538374424, -0.014462047256529331, -0.05388152226805687, 0.03830128535628319, 0.003933566156774759, -0.07508835196495056, -0.009682998061180115, 0.0009980712784454226, 0.015778079628944397, 0.0337863527238369, -0.018123798072338104, 0.03375936672091484, -0.015430032275617123, -0.019342947751283646, 0.0013763196766376495, -0.006693295203149319, 0.02246266044676304, 0.07691238075494766, -0.015362388454377651, 0.022659027948975563, 0.01320794690400362, -0.004608723800629377, 0.023037347942590714, -0.0010699743870645761, 0.09651506692171097, 0.03737773001194, 0.005611318629235029, -0.024459902197122574, 0.0409933440387249, -0.0876750573515892, -0.023386236280202866, 0.04558204486966133, -0.011284026317298412, -0.023710213601589203, 0.008043781854212284, -0.04130062833428383, -0.030041862279176712, -0.014449253678321838, 0.00439626956358552, -0.014043704606592655, 0.03210361301898956, 0.04993847385048866, -0.03507259115576744, -0.02973565272986889, 0.03962971270084381, 0.017227577045559883, -0.008814286440610886, 0.03762882575392723, 0.0738653615117073, -0.01673605665564537, -0.002097860909998417, -0.02539789490401745, 0.01668832078576088, -0.053406283259391785, 0.022775322198867798, 0.021880805492401123, 0.09015960246324539, 0.006818889174610376, -0.08927913010120392, 0.02321525104343891, 0.04161491617560387, 0.04298402741551399, 0.037552397698163986, -0.00316020124591887, -0.026366854086518288, 0.0143959391862154, 0.004070435184985399, 0.012838900089263916, 0.021935448050498962, -0.008497674018144608, -0.03115551359951496, -0.010645685717463493, 0.05488906800746918, 0.010774183087050915, -0.07386204600334167, -0.045463722199201584, -0.0033285049721598625, -0.03996189311146736, 0.05924656614661217, -0.0013017060700803995, 0.05466597527265549, -0.027475794777274132, -0.020416636019945145, -0.06870747357606888, -0.017176244407892227, -0.0466606542468071, -0.0019859338644891977, 0.06269676983356476, 0.025170765817165375, -0.04088335856795311, -0.07850399613380432, -0.046274106949567795, -0.024237433448433876, 0.012700950726866722, -0.04195260629057884, 0.0011612214148044586, -0.04437962919473648, -0.013296565972268581, -5.6683715129093074e-33, -0.011614610441029072, -0.02373029850423336, -0.051385533064603806, 0.08401434123516083, -0.040171436965465546, 0.023299196735024452, 0.022655978798866272, 0.04039645195007324, 0.02592724934220314, -0.047681715339422226, -0.024289598688483238, -0.02599785104393959, 0.013514524325728416, 0.009339630603790283, 0.039766013622283936, 0.03408340737223625, -0.018287254497408867, 0.031079020351171494, 0.016353849321603775, 0.006253601051867008, 0.007237839978188276, 0.0217051412910223, -0.00910482183098793, -0.08702057600021362, -0.009427412413060665, 0.007814548909664154, -0.016991885378956795, 0.0066678873263299465, 0.005673056468367577, 0.007678922265768051, -0.00020670986850745976, -0.00763825373724103, 0.02619989588856697, 0.0032007258851081133, 0.0206195879727602, -0.04774639755487442, 0.0053537278436124325, 0.007828764617443085, 0.0076013291254639626, -0.024377746507525444, -0.025913458317518234, 0.004216337576508522, -0.013991755433380604, 0.0343012772500515, 0.0034869995433837175, -0.013563618995249271, 0.044842418283224106, 0.011486108414828777, 0.0333089679479599, -0.04358939081430435, -0.05176711082458496, 0.023397892713546753, -0.03682761639356613, 0.041987963020801544, -0.003264005994424224, 0.048539575189352036, -0.018125729635357857, 0.04080221801996231, -0.030256444588303566, 0.04867442324757576, 0.004403038881719112, 0.04670065641403198, 0.02986551821231842, 0.016969745978713036, -0.003559335134923458, -0.0017646433552727103, 0.042578231543302536, 0.0003130475233774632, -0.022123176604509354, -0.040220387279987335, 0.011634896509349346, 0.014271277002990246, 0.020889241248369217, -0.003973742946982384, 0.028859516605734825, -0.03850076347589493, -0.052042342722415924, 0.061112962663173676, -0.024144835770130157, -0.016099805012345314, -0.008599849417805672, 0.0222312044352293, 0.00846232008188963, -0.012365086935460567, 0.03003331646323204, -0.01684597134590149, -0.037334151566028595, -0.021349260583519936, 0.03391901031136513, -0.04464038833975792, -0.05609818547964096, 0.007546990178525448, 0.018258675932884216, -0.01265895925462246, 0.01783706061542034, 0.026654498651623726, 0.01455073431134224, 0.0415395051240921, 0.010845187120139599, -0.01761220209300518, 0.021955708041787148, 0.00633045332506299, 0.01950228214263916, 0.006957502570003271, 0.030105015262961388, -0.03562116250395775, 0.02844042144715786, 0.011283653788268566, -0.03952150046825409, -0.015113894827663898, 0.04883421212434769, -0.03880418464541435, 0.00875783246010542, 0.030193030834197998, -0.029544390738010406, -0.05117585510015488, -0.017038069665431976, 0.07033855468034744, 0.07395605742931366, 0.027753543108701706, -0.059226155281066895, -0.03316876292228699, 0.0007671993225812912, -0.01808803156018257, 0.004541121888905764, 0.011103465221822262, 0.026860754936933517, 0.06140943616628647, 0.03366071730852127, -0.03939901664853096, -0.023224787786602974, -0.02955947071313858, 2.8039951871505764e-07, -0.004150674678385258, 0.051249124109745026, -0.06123361364006996, -0.012934149242937565, 0.03726528212428093, -0.013752114959061146, -0.05375855043530464, 0.022221148014068604, -0.017229417338967323, 0.0006718621007166803, 0.019654376432299614, -0.058610230684280396, -0.03661937266588211, 0.032452650368213654, 0.023075157776474953, -0.02758651226758957, -0.023742742836475372, -0.016842594370245934, -0.04909743741154671, -0.03851282596588135, 0.08385438472032547, -0.018479913473129272, 0.007941296324133873, -0.04695628210902214, -0.033711906522512436, 0.043882254511117935, 0.03025389276444912, 0.023127850145101547, 0.009127981029450893, -0.039427585899829865, 0.002504002768546343, -0.041713960468769073, -0.004690110217779875, 0.03442629054188728, 0.035234734416007996, 0.047115303575992584, 0.030262421816587448, 0.006801341660320759, -0.000724047189578414, 0.060372792184352875, 0.0711812973022461, 0.05142587050795555, -0.012150579132139683, -0.03717571496963501, 0.038848504424095154, -0.0007369039813056588, 0.01425172295421362, -0.017778826877474785, -0.012720800004899502, 0.02985242009162903, 0.048791009932756424, -0.012604420073330402, -0.013106536120176315, 0.018578162416815758, -0.05485772714018822, -0.0058042495511472225, 0.03803609311580658, 0.031982630491256714, 0.053042132407426834, 0.04615325853228569, -0.007532865274697542, 0.0017456518253311515, 0.07617956399917603, 0.017177877947688103, 0.02449778839945793, 0.015570773743093014, -0.011582487262785435, 3.1414342658206754e-34, 0.004510790109634399, 0.011939079500734806, -0.025822024792432785, -0.0369088239967823, -0.0432552807033062, -0.027529530227184296, -0.04961990937590599, -0.00559414504095912, -0.0417623296380043, -0.015868553891777992, -0.027140352874994278]

['Cem Tekin', 'Mihaela van der Schaar']

1308.4565v2

Distributed, online data mining systems have emerged as a result of applications requiring analysis of large amounts of correlated and high-dimensional data produced by multiple distributed data sources. We propose a distributed online data classification framework where data is gathered by distributed data sources and processed by a heterogeneous set of distributed learners which learn online, at run-time, how to classify the different data streams either by using their locally available classification functions or by helping each other by classifying each other's data. Importantly, since the data is gathered at different locations, sending the data to another learner to process incurs additional costs such as delays, and hence this will be only beneficial if the benefits obtained from a better classification will exceed the costs. We assume that the classification functions available to each processing element are fixed, but their prediction accuracy for various types of incoming data are unknown and can change dynamically over time, and thus they need to be learned online. We model the problem of joint classification by the distributed and heterogeneous learners from multiple data sources as a distributed contextual bandit problem where each data is characterized by a specific context. We develop distributed online learning algorithms for which we can prove that they have sublinear regret. Compared to prior work in distributed online data mining, our work is the first to provide analytic regret results characterizing the performance of the proposed algorithms.

Decentralized Online Big Data Classification - a Bandit Framework

http://arxiv.org/pdf/1308.4565v2

Title Decentralized Online Big Data Classification Bandit Framework Summary Distributed online data mining system emerged result application requiring analysis large amount correlated highdimensional data produced multiple distributed data source propose distributed online data classification framework data gathered distributed data source processed heterogeneous set distributed learner learn online runtime classify different data stream either using locally available classification function helping classifying others data Importantly since data gathered different location sending data another learner process incurs additional cost delay hence beneficial benefit obtained better classification exceed cost assume classification function available processing element fixed prediction accuracy various type incoming data unknown change dynamically time thus need learned online model problem joint classification distributed heterogeneous learner multiple data source distributed contextual bandit problem data characterized specific context develop distributed online learning algorithm prove sublinear regret Compared prior work distributed online data mining work first provide analytic regret result characterizing performance proposed algorithm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0075630908831954, 0.06978728622198105, -0.02203996852040291, -0.02756408415734768, -0.005289183463901281, 0.018340175971388817, 0.056203391402959824, 0.004971372429281473, 0.03965851664543152, -0.008860891684889793, -0.002129702130332589, 0.011426125653088093, -0.015925724059343338, 0.061156757175922394, 0.0037015171255916357, -0.017819276079535484, -0.003165015485137701, -0.0069827730767428875, 0.007324191741645336, -0.053116995841264725, 0.019139349460601807, -0.030746839940547943, 0.011676124297082424, -0.014673613011837006, 0.0024846522137522697, -0.01912834867835045, -0.0179730374366045, -0.005193198099732399, -0.009739650413393974, -0.054101165384054184, 0.05691906809806824, -0.03943559154868126, 0.013713139109313488, 0.06654500961303711, 1.9089341094513657e-06, -0.033296748995780945, -0.060784947127103806, -0.024255268275737762, 0.026266131550073624, -0.02592630311846733, 0.023042107000947, -0.0017689118394628167, -0.0007044215453788638, 0.03734869882464409, -0.02812514454126358, -0.019331714138388634, 0.0369560644030571, 0.04582595080137253, 0.0034393637906759977, 0.00400540791451931, -0.0024952825624495745, -0.05232471227645874, 0.014923933893442154, -0.019488971680402756, -0.02915649302303791, 0.030330665409564972, 0.0166066475212574, 0.02006031759083271, 0.0020146716851741076, -0.041581545025110245, -0.0013860596809536219, 0.00335809332318604, -0.0015941306483000517, 0.0362931452691555, 0.0344599224627018, -0.017523089423775673, -0.06105738878250122, 0.02484174072742462, -0.056872498244047165, -0.026062268763780594, -0.007324850186705589, 0.01129419170320034, 0.013255071826279163, -0.01579885557293892, -0.008748368360102177, 0.0031140479259192944, 0.0009169568074867129, 0.04474525898694992, -0.03612339869141579, 0.015355301089584827, 0.021496379747986794, 0.03177514299750328, -0.0062903608195483685, 0.053202684968709946, -8.587133925175294e-05, 0.05497847497463226, -0.0573558583855629, -0.0027171256951987743, -0.027265969663858414, 0.02148512937128544, -0.05421609431505203, -0.006236283108592033, 0.05634118616580963, -0.005829926114529371, -0.058720603585243225, -0.019016863778233528, 0.011875957250595093, -0.0023164968006312847, 0.017584525048732758, -0.0379936583340168, 0.0509679801762104, -0.07093021273612976, 0.055554479360580444, 0.032930638641119, 0.007662831339985132, 0.018082203343510628, -0.04863492399454117, -0.001823627739213407, 0.0438607856631279, 0.020186210051178932, -0.06637366861104965, -0.008400553837418556, 0.01860758289694786, 0.08727360516786575, 0.053120195865631104, 0.011155497282743454, -0.05522947013378143, 0.06417951732873917, -0.03915752097964287, -0.01459481194615364, -0.005535333417356014, 0.018420061096549034, 0.03365832939743996, 0.027007542550563812, -0.052879754453897476, -0.0038826330564916134, -0.026010366156697273, 0.06624376028776169, -0.010884047485888004, -0.022129114717245102, 0.041765693575143814, 0.022371280938386917, -0.01296539232134819, 0.002394995419308543, 0.01374817080795765, 0.020472010597586632, 0.0323842354118824, 0.03778543323278427, -0.03482462838292122, -0.033007774502038956, 0.044802773743867874, 0.021607425063848495, -0.08948925882577896, -0.0498606376349926, -0.010084793902933598, -0.05003893002867699, -0.012648317031562328, 0.03322864696383476, -0.03322331979870796, -0.03262278810143471, -0.01387645211070776, 0.02043892815709114, -0.0279989093542099, -0.008547884412109852, 0.05656353756785393, -0.016383444890379906, -0.04828451946377754, 0.041729480028152466, 0.01969332806766033, 0.050629615783691406, 0.03222400322556496, -0.014303392730653286, -0.015050174668431282, -0.01658044569194317, 0.028712069615721703, -0.03824189677834511, -0.002515053143724799, 0.018212398514151573, 0.006359257269650698, 0.08151321858167648, -0.021144935861229897, 0.012843579053878784, -0.029023848474025726, -0.009465128183364868, 0.05868100747466087, 0.024586854502558708, 0.08198311924934387, -0.0060794539749622345, -0.04536745324730873, 0.06386110186576843, -0.04442799463868141, -0.01520930603146553, 0.021087128669023514, -0.002982854610309005, -0.01898963749408722, -0.026517674326896667, -0.00989627093076706, 0.05652039125561714, -0.014378881081938744, -0.003848803462460637, 0.0035265497863292694, 0.018207931891083717, -0.07916244119405746, 0.03862159699201584, 0.03387707099318504, -0.03750220313668251, -0.039135076105594635, -0.05648268759250641, 0.04161236435174942, 0.04503132402896881, -0.003508076537400484, -0.033834028989076614, 0.05345006287097931, -0.02904963120818138, 0.04784048721194267, -0.013841219246387482, 0.015348981134593487, -0.07715053856372833, 0.027438336983323097, -0.041884422302246094, -0.034687113016843796, -0.011435041204094887, -0.016715403646230698, 0.0004413797869347036, -0.03952274098992348, 0.0621696338057518, -0.016403472051024437, -0.01465829648077488, -0.0007433976861648262, 0.01744656264781952, -0.05014533922076225, 0.0590013787150383, 0.023098381236195564, 0.009299672208726406, 0.037981342524290085, -0.025929970666766167, 0.06645496934652328, 0.034949980676174164, 0.09691184014081955, -0.045125626027584076, 0.002651435090228915, -0.03903649002313614, 0.028828836977481842, 0.004981259349733591, -0.08600939810276031, -0.014325148425996304, 0.02105778269469738, -0.022616062313318253, 0.03279414772987366, 0.015671413391828537, 0.06706982105970383, 0.030749551951885223, -0.011271041817963123, -0.019957836717367172, 0.0024556126445531845, -0.004862624686211348, -0.02147267945110798, -0.021396100521087646, -0.005165756214410067, 0.0011414382606744766, 0.06470925360918045, -0.04448122903704643, 0.03119550086557865, 0.019389934837818146, 0.027433952316641808, -0.06442742794752121, -0.0317499004304409, 0.052152812480926514, -0.04814925789833069, 0.050697460770606995, 0.00012610116391442716, -0.04981277510523796, 0.0107351029291749, 0.010446318425238132, -0.006056182086467743, 0.020020538941025734, -0.004053020384162664, 0.01470325980335474, 0.03511190041899681, -0.00120788742788136, 0.01244267076253891, 0.005582667421549559, -0.012760533951222897, 0.001213991898111999, -0.0396825447678566, 0.021348988637328148, 0.060556355863809586, -0.010502955876290798, 0.02820231020450592, 0.004877522587776184, 0.04077079892158508, 0.016604334115982056, 0.05445815250277519, -0.022861553356051445, 0.011705046519637108, 0.03794711083173752, 0.055080585181713104, 0.01463976688683033, -0.0546845868229866, -0.0721428245306015, -0.06715100258588791, 0.0010347755160182714, 0.029570888727903366, 0.02113662287592888, -0.04598557576537132, 0.006921233609318733, -0.07149407267570496, 0.012405461631715298, 0.022096198052167892, -0.018591707572340965, 0.02535475604236126, 0.00777079164981842, -0.030077975243330002, 0.017220694571733475, -0.010992204770445824, 0.001307173864915967, -0.003778139827772975, 0.04824037104845047, 0.021331004798412323, 0.009520701132714748, 0.028849096968770027, -0.006926230154931545, -0.00808580219745636, 0.0025973604060709476, 0.022975420579314232, -0.04570543393492699, -0.10158158093690872, 0.025945603847503662, 0.013556644320487976, -0.06447253376245499, 0.03580116108059883, -0.0465351827442646, 0.06860582530498505, 0.06683115661144257, 0.011120299808681011, -0.013562677428126335, -0.09741377085447311, -0.026852313429117203, -0.009953433647751808, -0.01108780037611723, 0.028938574716448784, -0.04920879378914833, -0.014281229116022587, 0.010716505348682404, -0.003436287632212043, 0.0560491569340229, -0.029047679156064987, -0.10264311730861664, 0.03699490800499916, -0.011872904375195503, -0.0342605821788311, -0.06916909664869308, 0.0007473787409253418, -0.04780035465955734, -0.010776810348033905, -0.008863836526870728, 0.007315714843571186, 0.004997245501726866, -0.026502372696995735, 0.031039288267493248, -0.012072889134287834, 0.057911187410354614, -0.03253621608018875, -0.03145153820514679, 0.024804778397083282, 0.03896006941795349, 0.01901516132056713, -0.04540722817182541, 0.014327745884656906, -0.021268097683787346, 0.05744721740484238, 0.04406232759356499, 0.047597307711839676, -0.06623183190822601, -0.005633520428091288, 0.005091820377856493, 0.04746401682496071, -0.05780641734600067, -0.010561476461589336, -0.018953965976834297, 0.007783097214996815, -0.018110573291778564, 0.030554627999663353, 0.016222471371293068, -0.0026493638288229704, -0.061596401035785675, -0.03545113652944565, -0.029771868139505386, 0.08394505828619003, -0.0072266338393092155, 5.7534041843609884e-05, -0.05935385823249817, -0.024131104350090027, -0.029414786025881767, 0.036559268832206726, -0.027096739038825035, -0.08021757006645203, 0.005518174264580011, -0.03780212625861168, 0.06490354984998703, -0.015498742461204529, -0.07002824544906616, 0.013835519552230835, -0.06087980046868324, -0.01069722417742014, -0.07402360439300537, -0.06336051225662231, 0.005392953287810087, 0.0063866013661026955, 0.013156699016690254, 0.04105135053396225, -0.037612736225128174, 0.04570749029517174, -0.039568208158016205, -0.06833583861589432, 0.008789272978901863, -0.007067195139825344, -0.009122342802584171, 0.02070813998579979, -0.02473977394402027, -0.021127531304955482, -0.0014598791021853685, 0.00846733245998621, -0.031976368278265, 0.0349002443253994, -0.011180022731423378, 0.0183236263692379, -0.022353019565343857, 0.033158060163259506, 0.020905591547489166, 0.03473048657178879, 0.06491339206695557, 0.08968112617731094, -0.01667081005871296, 0.010496755130589008, 0.0180806964635849, -0.02359551377594471, 0.08030949532985687, 0.01195522304624319, -0.07629410922527313, -0.04240739345550537, -0.036569274961948395, 0.043233487755060196, 0.006195747293531895, 0.05037316307425499, 0.060948025435209274, 0.019035907462239265, 0.006368703208863735, -0.013968645595014095, -0.05770274996757507, 0.01906135119497776, -0.012574637308716774, 0.015227215364575386, -0.015505271963775158, 0.05882208049297333, -0.015573584474623203, 0.023867398500442505, -0.060059625655412674, -0.007164474111050367, 0.025595061480998993, 0.04258172959089279, -0.05731950327754021, 0.052222587168216705, 0.029286446049809456, -0.039536964148283005, -0.015886196866631508, 0.009069797582924366, -0.0812535211443901, -0.022527417168021202, 0.018599124625325203, 0.0039388700388371944, -0.003330848179757595, -0.005284423474222422, -0.005321087781339884, -0.033768512308597565, 0.04129459708929062, 0.007640109397470951, -0.0011546892346814275, -0.007969687692821026, 0.03842632845044136, -0.005659610498696566, -0.0049852910451591015, 0.013146725483238697, -0.0039507681503891945, 0.014107026159763336, -0.02051740698516369, -0.0873793289065361, -0.0400865413248539, 0.035371121019124985, -0.02932516299188137, 0.006879079155623913, 0.06195471063256264, 0.0006036445847712457, -0.052621129900217056, -0.005230545066297054, 0.047015588730573654, 0.08448714017868042, -0.005555491894483566, -0.038321539759635925, 0.017579473555088043, 0.04788218438625336, -0.026959311217069626, 0.009553737007081509, 0.019477125257253647, 0.10981684178113937, -0.1052321270108223, -0.03478978946805, 5.737721221521497e-05, 0.04069160297513008, 0.025529665872454643, -0.007809567730873823, 0.042670395225286484, 0.03160107508301735, -0.005539789330214262, 0.04371818155050278, 0.05140991136431694, -0.004491680301725864, 0.03461679071187973, 0.002696947893127799, 0.005788728129118681, 0.032973043620586395, -0.021749060600996017, -0.013314291834831238, -0.027874954044818878, 0.008573170751333237, 0.0016585689736530185, 0.028180988505482674, 0.04099910333752632, -0.028653070330619812, 0.01964002102613449, -0.007913846522569656, -0.017110545188188553, 0.015438208356499672, -0.09445211291313171, -0.044985752552747726, 0.05338858813047409, -0.0050284285098314285, -0.03356499224901199, 0.08317358046770096, 0.028508229181170464, 0.020586084574460983, 0.016541093587875366, -0.03303864598274231, -0.0460701622068882, -0.050555866211652756, 0.01918058842420578, 0.04456605762243271, 0.06743089109659195, -0.04747302085161209, -0.0059866877272725105, 0.045618847012519836, 0.03881810978055, 0.01985470950603485, -0.008951516821980476, 0.037556085735559464, -0.021238896995782852, 0.004482510033994913, -0.03718769550323486, -0.02191871963441372, 0.03372516483068466, -0.07190222293138504, -0.0069696297869086266, 0.009524302557110786, 0.0183733981102705, -0.03132276237010956, -5.2909794189197966e-33, 0.05396692082285881, -0.030338678508996964, -0.019738389179110527, -0.03836798667907715, -0.02632337622344494, 0.014280134811997414, 0.038299355655908585, -0.011932296678423882, 0.049075208604335785, -0.018720192834734917, 0.008596275933086872, 0.011485944502055645, 0.009726379998028278, 0.029865682125091553, 0.03337348252534866, -0.007713101338595152, -0.001818071468733251, -0.006146723870187998, -0.03186342865228653, -0.012350346893072128, 0.049316056072711945, 0.024617144837975502, -0.018474603071808815, -0.03413449227809906, -0.04765573889017105, -0.005307293031364679, -0.05282064527273178, -0.011914985254406929, -0.05642515793442726, 0.02189018204808235, -0.006719405297189951, -0.0079953046515584, -0.027388617396354675, -0.04761083796620369, -0.008172215893864632, -0.040962088853120804, 0.017651354894042015, 0.012861213646829128, -0.06716997921466827, 0.044476218521595, -0.0022961904760450125, 0.034032776951789856, 0.00029939369414933026, -0.00800184067338705, -0.022254522889852524, -0.0012549154926091433, 0.024857470765709877, 0.007288633845746517, -0.06710094958543777, -0.021893315017223358, 0.049577586352825165, 0.03797329217195511, -0.009773073717951775, 0.03927769139409065, 0.012792244553565979, 0.02465229481458664, 0.006547530181705952, 0.005636323243379593, -0.03365974873304367, 0.05439502000808716, -0.02452191896736622, -0.0215707179158926, -0.049582190811634064, 0.017717551440000534, 0.05074729025363922, 0.02236599661409855, 0.011652376502752304, -0.022894760593771935, 0.009105931036174297, -0.0047848583199083805, -0.05967741459608078, -0.016527757048606873, 0.03470131754875183, 0.05869852378964424, 0.04051925241947174, -0.06542707234621048, -0.03731224313378334, 0.010007668286561966, 0.044126756489276886, -0.07293757796287537, -0.018185468390583992, 0.024872492998838425, -0.02278980053961277, 0.0006207933183759451, 0.034020304679870605, -0.023181328549981117, 0.02241642028093338, -0.0098526980727911, -0.011442840099334717, 0.04959671199321747, 0.02547936514019966, 0.04241351783275604, -0.0001866048260126263, -0.060356538742780685, -0.03783373162150383, 0.01419262308627367, 0.024224761873483658, 0.02399212121963501, 0.04200437664985657, -0.041784342378377914, -0.06803081929683685, -0.016732966527342796, -0.02799561806023121, -0.011591723188757896, -0.014572998508810997, -0.01610645279288292, 0.054750338196754456, 0.02071119099855423, -0.026995327323675156, 0.0288225244730711, 0.039962977170944214, 0.005002887919545174, -0.002590814372524619, -0.012265238910913467, 0.031366605311632156, -0.06058809533715248, 0.016358651220798492, 0.05743323266506195, 0.03133354336023331, 0.0003213686868548393, -0.008835304528474808, -0.008086335845291615, -0.03227721154689789, -0.03691182658076286, 0.009363350458443165, 0.015604998916387558, -0.0466054268181324, 0.00741120520979166, -0.026063257828354836, -0.028156528249382973, 0.010580719448626041, -0.04002600535750389, 2.5306255224677443e-07, -0.05338815599679947, 0.0426005981862545, -0.061456140130758286, -0.061129771173000336, 0.013710500672459602, 0.0121170524507761, -0.01539564598351717, 0.004640533588826656, -0.00989607721567154, 0.07852469384670258, 0.044947657734155655, -0.036216869950294495, 0.06596757471561432, -0.005416438449174166, -0.0449654720723629, -0.038856033235788345, -0.0222660843282938, 0.07173009216785431, -0.05507311224937439, -0.0023909318260848522, -0.04889559745788574, 0.040040235966444016, 0.0587380975484848, -0.03686415031552315, 0.06216274946928024, -0.009697449393570423, 0.007083340547978878, 0.0028972183354198933, -0.02175826020538807, -0.028321394696831703, 0.02021694742143154, 0.01386781595647335, -0.03846150264143944, -0.002727799816057086, -0.022277021780610085, 0.02438223734498024, -0.031244980171322823, -0.01139488909393549, 0.026157494634389877, 0.06645002961158752, -0.001164735178463161, -0.028060125187039375, 0.025935042649507523, -0.015538058243691921, 0.03808365762233734, 0.020492706447839737, -0.04711245745420456, -0.03054272197186947, 0.04428396373987198, -0.06287591904401779, 0.08724069595336914, 0.007511584088206291, -0.018392369151115417, -0.03285197541117668, -0.0273224338889122, -0.01853940449655056, -0.019200630486011505, -0.004603730048984289, 0.017325345426797867, 0.03431005775928497, -0.009425043128430843, 0.017926786094903946, -0.0014583300799131393, 0.061412710696458817, 0.05403602123260498, -0.06844884157180786, 0.029804669320583344, 2.1185016329908508e-34, 0.006850615609437227, 0.01052621379494667, 0.0015376406954601407, -0.026116956025362015, -0.002919994993135333, -0.04179588332772255, 0.037778228521347046, -0.041519615799188614, 0.035237498581409454, -0.002654947340488434, 0.02546130307018757]

['Babajide Afolabi', 'Odile Thiery']

cs/0610158v1

In this paper, our aim is to propose a model that helps in the efficient use of an information system by users, within the organization represented by the IS, in order to resolve their decisional problems. In other words we want to aid the user within an organization in obtaining the information that corresponds to his needs (informational needs that result from his decisional problems). This type of information system is what we refer to as economic intelligence system because of its support for economic intelligence processes of the organisation. Our assumption is that every EI process begins with the identification of the decisional problem which is translated into an informational need. This need is then translated into one or many information search problems (ISP). We also assumed that an ISP is expressed in terms of the user's expectations and that these expectations determine the activities or the behaviors of the user, when he/she uses an IS. The model we are proposing is used for the conception of the IS so that the process of retrieving of solution(s) or the responses given by the system to an ISP is based on these behaviours and correspond to the needs of the user.

Considering users' behaviours in improving the responses of an information base

http://arxiv.org/pdf/cs/0610158v1

Title Considering user behaviour improving response information base Summary paper aim propose model help efficient use information system user within organization represented order resolve decisional problem word want aid user within organization obtaining information corresponds need informational need result decisional problem type information system refer economic intelligence system support economic intelligence process organisation assumption every EI process begin identification decisional problem translated informational need need translated one many information search problem ISP also assumed ISP expressed term user expectation expectation determine activity behavior user heshe us model proposing used conception process retrieving solution response given system ISP based behaviour correspond need user Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.06504572927951813, 0.0073564606718719006, -0.031579870730638504, -0.010160064324736595, -0.036304011940956116, -0.025208383798599243, 0.018278708681464195, 0.041172094643116, 0.002647529589012265, -0.05120033770799637, 0.005361950024962425, 0.04227329045534134, -0.02037172205746174, 0.05993805453181267, -0.027524830773472786, -0.04625256732106209, 0.018905218690633774, 0.03983697667717934, -0.013632219284772873, 0.03628985583782196, 0.08140682429075241, -0.0027519806753844023, 0.03383791819214821, 0.022118357941508293, 0.03830377757549286, 0.007870735600590706, -0.007598222233355045, -0.032856401056051254, 0.003322778968140483, -0.05593135952949524, 0.10135439783334732, 0.02902478538453579, 0.005932406522333622, 0.021196773275732994, 2.496849219824071e-06, -0.05086979269981384, -0.05122955143451691, -0.005715371575206518, -0.04895363748073578, 0.004022641573101282, 0.040028613060712814, 0.04945126175880432, 0.037110064178705215, 0.018566183745861053, -0.043956171721220016, 0.03457721322774887, 0.0088611776009202, 0.06752064824104309, 0.01736229471862316, -0.018754692748188972, -0.01691141352057457, -0.04160216823220253, -0.057193297892808914, 0.02751004695892334, 0.01356593705713749, 0.011402427218854427, 0.035628415644168854, 0.02309728041291237, 0.04167730361223221, -0.006812667939811945, 0.032769910991191864, -0.03735252097249031, -0.04853564128279686, 0.0005915720830671489, 0.01481124758720398, -0.007584925275295973, 0.06608931720256805, -0.021106548607349396, -0.005982978269457817, 0.011526507325470448, 0.07012181729078293, 0.024738367646932602, 0.001223866012878716, 0.015529357828199863, -0.02433488890528679, 0.049824632704257965, -0.011096978560090065, -0.03765123710036278, -0.034333981573581696, -0.037524472922086716, 0.014758745208382607, 0.06836846470832825, -0.030996523797512054, 0.02311645820736885, -0.021557969972491264, 0.031949687749147415, -0.04400506988167763, -0.04656674712896347, -0.03219536691904068, -0.03881091624498367, 0.05625344067811966, -0.029289603233337402, 0.0050682625733315945, 0.04075763747096062, -0.051220864057540894, -0.014690818265080452, 0.03566817194223404, -0.07801859080791473, 0.03941040113568306, -0.04740110784769058, 0.05961041525006294, 0.017842499539256096, 0.08921581506729126, -0.00011933696805499494, 0.053635962307453156, -0.015330838039517403, -0.012720201164484024, -0.024131078273057938, -0.007448086980730295, 0.05403904989361763, -0.0697016566991806, -0.009378528222441673, -0.010694602504372597, 0.07146123051643372, 0.019172200933098793, -0.007781146559864283, -0.05468079820275307, 0.04552292451262474, -0.008675580844283104, -0.002300584688782692, 0.0020992395002394915, 0.014593685045838356, -0.010229521431028843, 0.004821006674319506, -0.06536989659070969, -0.0025053368881344795, -0.06942348182201385, 0.019367055967450142, -0.02874899096786976, 0.032527096569538116, 0.06474920362234116, 0.0034052953124046326, 0.007352414540946484, 0.0017753859283402562, 0.018974341452121735, 0.0471525602042675, 0.04360024258494377, 0.019871098920702934, -0.10734617710113525, -0.06586569547653198, 0.06808813661336899, -0.011335019022226334, -0.0620202012360096, -0.046308889985084534, -0.022874485701322556, 0.01538923755288124, -0.0666845291852951, 0.05753989517688751, -0.030704649165272713, 0.0070876250974833965, -0.060913000255823135, 0.025970526039600372, -0.028834212571382523, 0.03711599484086037, 0.045920293778181076, 0.004741230048239231, 0.09497378021478653, -0.015407761558890343, -0.01049552857875824, 0.00035413465229794383, 0.025878392159938812, 0.0018801767146214843, 0.028820239007472992, 0.00836519617587328, -0.03850146383047104, -0.01667480170726776, 0.08402863889932632, 0.0401751883327961, -0.05893243849277496, -0.04492799937725067, -0.012652656063437462, 0.0170018021017313, -0.019656384363770485, 0.07261098921298981, 0.012853886932134628, 0.044640544801950455, 0.023079201579093933, -0.017875395715236664, -0.04430167004466057, 0.07755102962255478, -0.0385248102247715, -0.002558345440775156, 0.05875015631318092, 0.044525422155857086, -0.022598769515752792, -0.0006492761895060539, -0.03161925449967384, -0.047531891614198685, -0.04497021809220314, -0.0175459161400795, 0.0006057466962374747, -0.01109027024358511, -0.004452078603208065, 0.04504237323999405, 0.03473149985074997, 0.02756711281836033, -0.010309099219739437, -0.046696823090314865, -0.025494683533906937, 0.023409022018313408, -0.01725045219063759, -0.09203769266605377, 0.07953228056430817, 0.08138692378997803, 0.02804451249539852, -0.04055352881550789, 0.02622389607131481, -0.03277407959103584, -0.012264498509466648, -0.01808442920446396, 0.039124950766563416, -0.019037051126360893, -0.05466881021857262, 0.011719005182385445, -0.009750716388225555, 0.06429734826087952, -0.023633895441889763, 0.0295052882283926, -0.012487507425248623, -0.0036994339898228645, -0.013730743899941444, 0.07194884866476059, -0.0028311775531619787, 0.01978738233447075, 0.02177109383046627, -0.009570041671395302, -0.000867116788867861, 0.023327047005295753, 0.06475356966257095, 0.01996191032230854, 0.01761181280016899, 0.03420437127351761, 0.009230563417077065, -0.006749777588993311, -0.06064264848828316, 0.01365840807557106, 0.07022394239902496, 0.04166059568524361, -0.042897578328847885, 0.003476420184597373, 0.03682864457368851, 0.01953672058880329, 0.03567945957183838, -0.02423747070133686, 0.04137928783893585, -0.025541134178638458, 0.04055505245923996, 0.01264507882297039, 0.02489950880408287, 0.009382986463606358, -0.006862490903586149, -0.06341765820980072, 0.016789881512522697, -0.012843095697462559, 0.022840799763798714, -0.028794946148991585, -0.07398676872253418, 0.014471269212663174, -0.027387915179133415, 0.0030733286403119564, 0.01809590496122837, -0.01788998208940029, 0.022211618721485138, 0.06125769391655922, 0.03054153546690941, -0.014852048829197884, 0.03706292435526848, -0.031745873391628265, -0.003642823314294219, 0.00829643290489912, 0.028037630021572113, 0.03856782242655754, 0.04634469002485275, -0.006241132039576769, -0.01814977452158928, -0.010996968485414982, -0.004630647599697113, 0.050401464104652405, 0.009289988316595554, 0.05763796716928482, 0.04698045551776886, -0.02385609969496727, -0.02670397236943245, -0.006058086175471544, -0.016696948558092117, -0.014924711547791958, 0.04499880224466324, -0.07309503108263016, -0.047008682042360306, 0.014993543736636639, 0.0014625866897404194, 0.006951061077415943, -0.00457591051235795, -0.007592733483761549, 0.005153616424649954, -0.026627067476511, 0.03593641519546509, 0.0021553330589085817, 0.010306508280336857, 0.014675706624984741, -0.01629800535738468, 0.008323169313371181, -0.06684506684541702, -0.024908684194087982, -0.024573007598519325, 0.002334460848942399, 0.04269079118967056, -0.05928030237555504, 0.07444833219051361, -0.025474077090620995, 0.031289972364902496, 0.000771181657910347, 0.030016090720891953, 0.03331926092505455, -0.021587539464235306, -0.0015016868710517883, -0.08223789930343628, -0.0411074198782444, -0.011825080960988998, 0.06516019254922867, 0.022948065772652626, -0.0014762354549020529, 0.01776215061545372, 0.07064411789178848, 0.03492872416973114, -0.018344175070524216, -0.042251259088516235, 0.022215979173779488, 0.010893617756664753, -0.003713302779942751, 0.0324956439435482, -0.0387146957218647, -0.026570715010166168, -0.003323356853798032, -0.05695459246635437, 0.04163699969649315, -0.03365439549088478, -0.016741329804062843, 0.010623175650835037, -0.018954863771796227, -0.025891555473208427, -0.022168157622218132, -0.010901538655161858, -0.025586778298020363, 0.049756553024053574, -0.00695901270955801, 0.028038842603564262, 0.0018859667470678687, -0.007143819238990545, 0.0054035065695643425, 0.055392421782016754, 0.026314349845051765, -0.011442356742918491, -0.042136300355196, 0.026559390127658844, -0.020119110122323036, 0.03178761154413223, -0.029885612428188324, -0.0545848086476326, 0.025279035791754723, 0.01309233158826828, 0.03933904320001602, -0.007741795387119055, -0.017667850479483604, -0.02775273658335209, -0.005749217234551907, 0.05931473523378372, -0.039745621383190155, -0.00709250383079052, 0.012490389868617058, -0.01123508345335722, -0.004556251689791679, 0.040639061480760574, 0.027607997879385948, 0.035392411053180695, -0.05655486136674881, -0.03923410922288895, -0.04468521475791931, -0.05915819853544235, 0.0022818392608314753, 0.07165645062923431, -0.003594891633838415, 0.04610319808125496, -0.0306252408772707, 0.03162937983870506, -0.05483870208263397, -0.03977621719241142, -0.0008848191937431693, -0.020202482119202614, 0.011669863946735859, -0.043181806802749634, -0.021017322316765785, -0.03806353360414505, -0.05159638077020645, -0.008393902331590652, -0.003793560666963458, -0.032126445323228836, 0.028426915407180786, 0.013743187300860882, -0.027432065457105637, 0.019061293452978134, -0.07391425967216492, -0.017778536304831505, 0.01465119980275631, -0.037092313170433044, 0.00977330096065998, 0.05339144170284271, 0.030605200678110123, -0.0395837128162384, -0.013549518771469593, -0.024118417873978615, -0.002370293717831373, -0.00524540850892663, -0.02332405000925064, 0.06187894940376282, -0.032055288553237915, 0.04409699887037277, -0.05426698923110962, 0.024359440430998802, -0.0349719300866127, 0.02842526137828827, 0.05302884802222252, 0.031199365854263306, -0.05499940738081932, 0.04340757057070732, -0.07338781654834747, -0.0012330989120528102, 0.0472024530172348, -0.0024507204070687294, -0.031766362488269806, -0.048701778054237366, -0.020043877884745598, 0.01483851857483387, -0.029545027762651443, -0.016166899353265762, -0.004814889281988144, 0.0022454189602285624, -0.03412613272666931, -0.0123890470713377, -0.06330199539661407, -0.06602955609560013, -0.0027716404292732477, 0.04965846613049507, 0.019684920087456703, -0.016122279688715935, -0.036514777690172195, -0.007746993098407984, -0.005763068795204163, -0.08355693519115448, 0.04713258147239685, 0.051078494638204575, -0.06943068653345108, 0.01710372231900692, -0.021865995600819588, 0.01385687105357647, 0.0022794222459197044, -0.07313687354326248, 0.023120637983083725, -0.01655571535229683, 0.007563529536128044, 0.07552343606948853, 0.04049896448850632, -0.03665400296449661, -0.008784953504800797, 0.003007957711815834, -0.04367329552769661, -0.024588478729128838, -0.000528682314325124, -0.0512307807803154, -0.0023333567660301924, 0.032365817576646805, -0.014894613064825535, -0.03783996403217316, -0.016683518886566162, 0.03001156449317932, -0.0003767619782593101, -0.07106564193964005, -0.0938335508108139, -0.02099766582250595, 0.023850634694099426, 0.05038543790578842, 0.00013004307402297854, -0.002549681579694152, -0.04996522516012192, 0.0031479340977966785, -0.033211372792720795, -0.032684676349163055, -0.02407989650964737, 0.01185635942965746, -0.043499257415533066, 0.02431655302643776, -0.00729399174451828, 0.027693258598446846, 0.02142193168401718, -0.044517308473587036, -0.08541864901781082, 0.015095673501491547, 0.05231336131691933, -0.018475472927093506, 0.0460783950984478, -0.02837122604250908, 0.017131030559539795, -0.014815444126725197, -0.02153450809419155, 0.035396378487348557, 0.03326339274644852, 0.0019452624255791306, 0.04056438431143761, -0.04930318146944046, -0.006026321090757847, 0.009077786467969418, 0.021051578223705292, 0.012055862694978714, -0.04567258432507515, -0.000541281362529844, -0.028358299285173416, -0.04958460107445717, -0.02299581840634346, -0.047958653420209885, -0.0013533327728509903, 0.014738173224031925, 0.0015631519490852952, 0.054728902876377106, -0.020910505205392838, 0.01497010886669159, 0.014024792239069939, 0.031897153705358505, -0.022481869906187057, -0.04711262136697769, 0.051116231828927994, 0.005368041340261698, -0.08025133609771729, -0.0910213440656662, -0.0567350760102272, -0.06023261696100235, 0.023077256977558136, 0.03263614699244499, 0.0553005114197731, -0.02796066179871559, -0.013247865252196789, -0.011429999023675919, -0.011548150330781937, -0.057663608342409134, 0.011979009956121445, 0.056055814027786255, 0.01077698078006506, 0.03137395530939102, 0.03631846234202385, 0.014199363999068737, -0.014934321865439415, -0.0708351731300354, -0.024345755577087402, -0.06493557244539261, -0.002313709119334817, -0.05397402122616768, -6.206312625334126e-33, 0.013941941782832146, -0.01835840754210949, 0.026930779218673706, 0.01950669288635254, 0.009079831652343273, -0.05176016315817833, 0.012906871736049652, 0.02589956484735012, -0.024510376155376434, -0.0471106693148613, -0.01558700855821371, -0.013649114407598972, 0.007986580953001976, -0.012342606671154499, 0.026769833639264107, 0.03332286700606346, 0.0032309952657669783, -0.029712999239563942, -0.0014292518608272076, -0.047798849642276764, 0.05114810913801193, -0.00434056855738163, 0.03715239465236664, -0.04677871987223625, 0.03790336847305298, -0.03864457085728645, -0.004448159597814083, 0.02614278346300125, 0.0022445572540163994, 0.012360269203782082, -0.006543124094605446, -0.006702240090817213, 0.031284209340810776, -0.025401711463928223, -0.007725832052528858, 0.06990989297628403, -0.029811326414346695, -0.042585186660289764, -0.014556613750755787, 0.033151522278785706, 0.004213223699480295, 0.014975516125559807, 0.036122772842645645, -0.019170841202139854, -0.02293127030134201, 0.05651436746120453, 0.05577283725142479, 0.015487953089177608, 0.0029224823229014874, 0.032492104917764664, -0.06003550440073013, -0.007278171367943287, -0.0031484090723097324, 0.07547038793563843, -0.01645493507385254, 0.11404120177030563, -0.014194043353199959, -0.03759794682264328, -0.05737956985831261, 0.015789050608873367, -0.008696691133081913, 0.00046000161091797054, 0.025495929643511772, 0.04610231891274452, 0.029473943635821342, -0.02024434693157673, -0.05229121819138527, 0.006946094334125519, -0.009136509150266647, -0.036430779844522476, 0.00245839124545455, 0.021123751997947693, 0.006886505521833897, 0.01428934931755066, -0.0038518765941262245, -0.06986425817012787, -0.011430650018155575, 0.0665210410952568, 0.05514001473784447, 0.02014048956334591, 0.037709273397922516, 0.01555716898292303, -0.06344136595726013, -0.04542075842618942, 0.07037381827831268, 0.037242814898490906, -0.023565951734781265, -0.05652562528848648, 0.037623316049575806, -0.007624789606779814, 0.001933974795974791, -0.016482193022966385, 0.019056256860494614, -0.02101212926208973, -0.025842882692813873, -0.028041182085871696, 0.03221788629889488, 8.666774374432862e-05, -0.0013262864667922258, -0.03415968269109726, -0.07943502068519592, -0.015867838636040688, -0.06081821396946907, 0.03598786145448685, -0.008432113565504551, 0.009553971700370312, 0.0027172546833753586, -0.029174868017435074, -0.04713577777147293, -0.0012899497523903847, 0.03703901171684265, 0.002067822962999344, 0.024924807250499725, -0.0017390924040228128, -0.019156763330101967, -0.012670581229031086, -0.004140026401728392, 0.014922527596354485, 0.00590460654348135, -0.02446144074201584, -0.046909481287002563, -0.049745112657547, -0.004049825482070446, -0.02353646233677864, -0.003907840233296156, 0.004259198438376188, -0.043855927884578705, 0.034853797405958176, 0.006488816346973181, -0.005636824760586023, -0.0017828403506428003, -0.04533014073967934, 2.996707735292148e-07, 0.008706330321729183, -0.018168330192565918, -0.05345238000154495, 0.06596654653549194, -0.0030049956403672695, 0.006100159604102373, 0.03189206123352051, 0.01620524190366268, 0.03743276372551918, 0.013223172165453434, 0.08227063715457916, -0.06527125090360641, -0.01573178544640541, 0.04018242284655571, -0.045148950070142746, -0.09587911516427994, 0.010638769716024399, 0.00013235661026556045, -0.04186389967799187, 0.0038555085193365812, 0.060149919241666794, -0.00594116048887372, 0.0396026074886322, 0.02163431979715824, -0.015176107175648212, -0.02395281009376049, -0.017123142257332802, -0.0249433945864439, 0.006211909931153059, -0.006950074806809425, 0.051238764077425, 0.02259434014558792, 0.019618434831500053, 0.05728854238986969, -0.016888294368982315, -0.04514892399311066, 0.009790605865418911, 0.02644422836601734, -0.015214473940432072, 0.031200386583805084, 0.0300788301974535, -0.07791188359260559, 0.03748336061835289, -0.014444825239479542, -0.0028293514624238014, -0.019749540835618973, -0.014423207379877567, 0.03579943627119064, -0.042443323880434036, -0.037107132375240326, 0.0018606286030262709, -0.017848756164312363, -0.02392084151506424, 0.04045164957642555, 0.011817694641649723, -0.009392677806317806, 0.005083078518509865, 0.012837676331400871, 0.05290272459387779, 0.03795827180147171, -0.02573675476014614, -0.014076076447963715, 0.027826422825455666, 0.006379134487360716, 0.0410345084965229, 0.008368106558918953, -0.002318401588127017, 3.046815465362876e-34, -0.011555565521121025, 0.04993627220392227, 0.009510653093457222, 0.006131978705525398, 0.014467930421233177, 0.030471863225102425, 0.019479786977171898, 0.014147398993372917, 0.06854125112295151, -0.02189132757484913, -0.03389047086238861]

['David N. Levin']

cs/0612096v1

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) seeks to find a "source" time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series with local velocity cross correlations that vanish everywhere in stimulus state space. However, in an earlier paper the local velocity correlation matrix was shown to constitute a metric on state space. Therefore, nonlinear BSS maps onto a problem of differential geometry: given the metric observed in the measurement coordinate system, find another coordinate system in which the metric is diagonal everywhere. We show how to determine if the observed data are separable in this way, and, if they are, we show how to construct the required transformation to the source coordinate system, which is essentially unique except for an unknown rotation that can be found by applying the methods of linear BSS. Thus, the proposed technique solves nonlinear BSS in many situations or, at least, reduces it to linear BSS, without the use of probabilistic, parametric, or iterative procedures. This paper also describes a generalization of this methodology that performs nonlinear independent subspace separation. In every case, the resulting decomposition of the observed data is an intrinsic property of the stimulus' evolution in the sense that it does not depend on the way the observer chooses to view it (e.g., the choice of the observing machine's sensors). In other words, the decomposition is a property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. The technique is illustrated with analytic and numerical examples.

Using state space differential geometry for nonlinear blind source separation

http://arxiv.org/pdf/cs/0612096v1

Title Using state space differential geometry nonlinear blind source separation Summary Given time series multicomponent measurement evolving stimulus nonlinear blind source separation BSS seek find source time series comprised statistically independent combination measured component paper seek source time series local velocity cross correlation vanish everywhere stimulus state space However earlier paper local velocity correlation matrix shown constitute metric state space Therefore nonlinear BSS map onto problem differential geometry given metric observed measurement coordinate system find another coordinate system metric diagonal everywhere show determine observed data separable way show construct required transformation source coordinate system essentially unique except unknown rotation found applying method linear BSS Thus proposed technique solves nonlinear BSS many situation least reduces linear BSS without use probabilistic parametric iterative procedure paper also describes generalization methodology performs nonlinear independent subspace separation every case resulting decomposition observed data intrinsic property stimulus evolution sense depend way observer chooses view eg choice observing machine sensor word decomposition property evolution real stimulus broadcasting energy observer technique illustrated analytic numerical example Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.03268766775727272, 0.045038748532533646, -0.006858861539512873, 0.03298724442720413, -0.025362053886055946, -0.01331263780593872, 0.03528734669089317, 0.050268203020095825, -0.00559951039031148, 0.004279153887182474, 0.006765918806195259, 0.029945822432637215, 0.031724851578474045, 0.04351959750056267, 0.00281083513982594, -0.03266283497214317, 0.01775025762617588, -0.001273863366805017, -0.04391511529684067, 0.008257570676505566, -0.021075312048196793, -0.06150345504283905, -0.0174286849796772, -0.029516078531742096, -0.008648770861327648, -0.028534388169646263, -0.014823432080447674, -0.026086993515491486, 0.0033340284135192633, -0.018744518980383873, -0.002702476689592004, -0.0025619822554290295, 0.031510088592767715, 0.06989305466413498, 1.7517213564133272e-06, 0.014837116934359074, 0.013337873853743076, -0.014720866456627846, 0.07414306700229645, -0.00400605658069253, -0.061801113188266754, 0.02115977182984352, 0.03910364955663681, -0.03734170272946358, -0.053552139550447464, -0.05145402252674103, -0.029476840049028397, -0.0036773995961993933, 0.030119575560092926, 0.04355020821094513, -0.0077211749739944935, 0.03673434257507324, -0.038311928510665894, -0.04049939662218094, 0.046604614704847336, -0.003180072410032153, 0.01162474974989891, -0.025943785905838013, -0.014066323637962341, -0.014477559365332127, -0.04894440248608589, 0.07067461311817169, -0.015206942334771156, -0.004364978522062302, 0.0680379793047905, 0.007054006215184927, 0.0318676196038723, 0.04141512140631676, -0.05725758895277977, 0.06060760095715523, 0.0031389726791530848, 0.037253107875585556, 0.040699902921915054, 0.03085785172879696, -0.008961799554526806, -0.004461833741515875, -0.006685232277959585, -0.04001052305102348, -0.019429150968790054, -0.012358907610177994, -0.07232023030519485, 0.01417645625770092, -0.0601750910282135, -0.0471501387655735, -0.028324924409389496, 0.050889916718006134, 0.0007101380033418536, -0.02470032498240471, -0.05066562071442604, -0.011782926507294178, 0.07547547668218613, -0.007948171347379684, 0.001604153192602098, 0.008796624839305878, -0.04820738732814789, 0.0090015335008502, 0.02681807056069374, -0.0382402241230011, -0.07193217426538467, -0.0383707694709301, 0.05445089936256409, -0.00013593296171166003, 0.019207023084163666, 0.021115630865097046, -0.0007141514797694981, 0.06321269273757935, -0.08148013800382614, 0.022710463032126427, -0.02686638943850994, 0.04660062491893768, -0.0153533685952425, -0.02741517499089241, 0.03197765350341797, 0.026773715391755104, -0.0022944442462176085, 0.016913119703531265, 0.022166522219777107, 0.023587916046380997, -0.009701662696897984, -0.052936144173145294, -0.014649709686636925, 0.0318499431014061, 0.04248159006237984, -0.01391333993524313, -0.013970823027193546, 0.01996494084596634, 0.05506192147731781, 0.011835596524178982, -0.01128729060292244, 0.07027972489595413, -0.0018232213333249092, 0.01044969167560339, 0.0035731373354792595, 0.02598591335117817, -0.024582115933299065, 0.022746890783309937, 0.019195936620235443, 0.06747672706842422, -0.06276092678308487, 0.005167817696928978, -0.0004990589804947376, -0.0019987178966403008, 0.038477763533592224, -0.010060964152216911, 0.020139995962381363, -0.028849991038441658, 0.011343139223754406, -0.008042729459702969, 0.016126472502946854, -0.03344004601240158, -0.03706889972090721, 0.06030421704053879, -0.012532626278698444, 0.002388071734458208, 0.0509486049413681, -0.009998884983360767, 0.03734288364648819, 0.01993996649980545, -0.01107440609484911, -0.017284134402871132, 0.01721011847257614, 0.006124407052993774, -0.008857239037752151, -0.021173082292079926, -0.015254689380526543, 0.01659156195819378, -0.11105545610189438, -0.022421248257160187, -0.009786076843738556, -0.0015952455578371882, -0.013883042149245739, 0.0007397060398943722, -0.0025207670405507088, 0.04624376818537712, 0.02661232464015484, 0.03316028416156769, 0.0377146378159523, -0.038043998181819916, -0.006700800731778145, 0.0372052825987339, -0.004152415785938501, 0.04002969339489937, 0.021645471453666687, 0.041103996336460114, -0.03581131249666214, -0.03964098170399666, -0.0226993840187788, 0.007303363177925348, -0.011684591881930828, -0.05516292154788971, -0.01516436692327261, -0.059370286762714386, -0.002837021602317691, -0.029085587710142136, 0.06220414116978645, 0.015140396542847157, 0.026374975219368935, -0.032727114856243134, 0.024985652416944504, -0.033578697592020035, 0.017795756459236145, 0.05110780522227287, 0.08100513368844986, -0.06053759530186653, -0.015806395560503006, -0.04219089448451996, -0.02154894359409809, -0.059127531945705414, -0.013301864266395569, -0.017176605761051178, -0.056434404104948044, 0.01610228233039379, -0.038469940423965454, 0.0276761706918478, -0.0607478991150856, 0.05076185613870621, -0.010398216545581818, -0.04554823786020279, -0.0676545649766922, -0.010384923778474331, 0.011243141256272793, 0.024083862081170082, 0.058676496148109436, -0.005377658177167177, -0.018428437411785126, 0.02443826198577881, 0.04908846318721771, 0.02359997108578682, 0.06532816588878632, 0.04089949652552605, 0.018838973715901375, -0.002079269615933299, 0.0036265805829316378, -0.033308569341897964, -0.0029741444159299135, 0.067633718252182, 0.0412588007748127, -0.05886227637529373, 0.005505692679435015, -0.04285925626754761, 0.022534573450684547, 0.010943600907921791, -0.015256485901772976, -0.0597490556538105, 0.027263233438134193, -0.012065506540238857, -0.08856863528490067, -0.0366123728454113, -0.023046838119626045, -0.024058828130364418, -0.006746293976902962, -0.004789228551089764, 0.0016783884493634105, -0.01756875403225422, 0.006293605547398329, -0.020501749590039253, 0.04541019722819328, 0.032961077988147736, 0.022058503702282906, 0.001300548086874187, 0.01323168445378542, -0.006527460180222988, -0.07232071459293365, 0.01414322480559349, 0.029078567400574684, 0.02417849376797676, -0.02269134856760502, 0.05099409446120262, -0.025508137419819832, 0.04570509493350983, 0.01868891529738903, 0.020519135519862175, 0.022454747930169106, 0.014532420784235, 0.04529417306184769, -0.018529411405324936, 0.038464341312646866, -0.0021089157089591026, -0.08194877207279205, 0.029166676104068756, -0.03455463424324989, -0.008683178573846817, 0.0009565040818415582, 0.01602664589881897, -0.007816133089363575, 0.021672159433364868, 0.017100799828767776, -0.02898138388991356, -0.05884517356753349, -0.032138776034116745, 0.008624684996902943, 0.058355662971735, 0.0296188835054636, -0.0073529393412172794, -0.04490623623132706, -0.010058150626718998, 0.024738600477576256, 0.024495350196957588, 0.04011266678571701, -0.004643603228032589, 0.0198521725833416, 0.008306206203997135, -0.00022301881108433008, 0.02606729231774807, -0.00942547433078289, 0.09686079621315002, 0.048694875091314316, 0.0026608072221279144, 0.06597387045621872, 0.009656528942286968, 0.05082404986023903, -0.027855386957526207, 0.013603652827441692, 0.03440780192613602, -0.023594345897436142, -0.023239009082317352, -0.08616764843463898, -0.050247494131326675, -0.05828602612018585, -0.04354434460401535, -0.012953214347362518, 0.016802247613668442, -0.009348246268928051, 0.015077938325703144, 0.03050665557384491, -0.013990404084324837, 0.019545122981071472, -0.02789171040058136, -0.06782747060060501, -0.03282453492283821, -0.020067015662789345, -0.028491852805018425, 0.016803354024887085, 0.03526841104030609, 0.04972880706191063, -0.03062949888408184, -0.014577486552298069, -0.06055133044719696, -0.0020452612079679966, 0.02763267792761326, 0.01954173855483532, 0.037115439772605896, -0.03163979947566986, 0.028875209391117096, 0.09134530276060104, -0.05735243111848831, -0.015485432930290699, 0.0015818839892745018, 0.05394437536597252, 0.025325341150164604, 0.01615280471742153, 0.00806194543838501, -0.002987471641972661, 0.0010530747240409255, -0.06567666679620743, 0.024890001863241196, 0.020798424258828163, -0.046469032764434814, -0.02137947827577591, -0.02099841646850109, -0.0041726562194526196, 0.013373694382607937, 0.08228223025798798, 0.01294188853353262, -0.020085886120796204, -0.003473946824669838, -0.004712138790637255, 0.05495006963610649, -0.06144500523805618, -0.040403902530670166, -0.05907771363854408, 0.023547306656837463, -0.015382956713438034, 0.0044014230370521545, -0.003887027036398649, -0.08851415663957596, -0.02664882317185402, -0.02256300486624241, -0.0954977348446846, -0.003753385040909052, -0.009502168744802475, 0.0028187173884361982, 0.049790333956480026, -0.009511909447610378, -0.014130818657577038, 0.014035876840353012, 0.00313815800473094, -0.04402836039662361, 0.0030368103180080652, -0.016274752095341682, 0.008181888610124588, 0.001325062708929181, -0.046024490147829056, -0.04729423671960831, 0.013810020871460438, 0.014701633714139462, 0.0006918392609804869, 0.04668627679347992, 0.0044621750712394714, -0.004818774294108152, 0.02903355285525322, -0.041854128241539, 0.03240208327770233, -0.07014622539281845, -0.029236353933811188, -0.03322076052427292, -0.015628207474946976, 0.08404859900474548, -0.013940739445388317, -0.09117396175861359, -0.0333922915160656, -0.017772814258933067, 0.0048687937669456005, -0.041833702474832535, -0.019036265090107918, 0.06719551980495453, 0.021257076412439346, -0.014863761141896248, 0.058393847197294235, -0.0686684250831604, 0.06264343112707138, -9.810821211431175e-05, 0.0474698580801487, 0.004093436058610678, 0.022148508578538895, -0.04368789494037628, -0.016736552119255066, 0.04603609815239906, -0.006936985068023205, -0.008731125853955746, -0.04739178717136383, -6.127876076789107e-06, 0.041831351816654205, 0.011994029395282269, 0.039457447826862335, 0.008670789189636707, -0.019061123952269554, -0.011072845198214054, -0.053852297365665436, -0.09909670054912567, 0.0591178759932518, -0.033549241721630096, 0.07511772960424423, -0.0027769224252551794, 0.0877152755856514, 0.06997783482074738, -0.032773785293102264, 0.02936319075524807, 0.016928575932979584, 0.05459428206086159, -0.029823601245880127, -0.012609891593456268, 0.04870760440826416, -0.014588282443583012, -0.02313193865120411, -0.043540485203266144, -0.030735870823264122, -0.025564944371581078, -0.062497563660144806, 0.049951426684856415, -0.013704861514270306, 0.0017122600693255663, 0.009598835371434689, -0.042420245707035065, 0.053706295788288116, -0.055357471108436584, -0.02838912419974804, 0.04565636068582535, 0.034537173807621, -0.02873549796640873, -0.0005087885656394064, 0.021902143955230713, -0.0017245124327018857, 0.03401676192879677, 0.014496853575110435, 0.036958158016204834, -0.03934654965996742, -0.004631591495126486, 0.02369409240782261, -0.06623154133558273, 0.045210957527160645, 0.08662819862365723, 0.029506098479032516, -0.021869979798793793, -0.026630375534296036, 0.006485429592430592, -0.05213035270571709, 0.022074466571211815, -0.028799735009670258, 0.04163508489727974, -0.02612362615764141, -0.0033234136644750834, -0.04482414945960045, 0.0011353122536092997, 0.02665858156979084, -0.10400892049074173, -0.005748985800892115, -0.031079579144716263, 0.014286398887634277, 0.0025647967122495174, -0.05460986867547035, -0.006519010290503502, 0.0832628458738327, 0.051442671567201614, 0.017311468720436096, -0.031070079654455185, -0.038603924214839935, -0.0023836945183575153, 0.003883522469550371, -0.0011382937664166093, -0.02284575253725052, 0.003347288118675351, -0.022102879360318184, 0.05125315859913826, 0.013452245853841305, -0.00567491864785552, 0.059076834470033646, 0.013816984370350838, 0.03670041635632515, 0.05145696550607681, 0.04003976285457611, 0.004724294878542423, 0.03592706471681595, -0.016256431117653847, 0.08175729960203171, 0.0071184090338647366, -0.03394630178809166, -0.02666526474058628, 0.04322720319032669, 0.05407722666859627, -0.012223539873957634, -0.0003255062911193818, -0.059637993574142456, 0.010036502033472061, -0.026792824268341064, 0.11674680560827255, 0.02253996767103672, -0.02054833620786667, -0.0019050288246944547, 0.03459473326802254, 0.017147351056337357, 0.01686822809278965, 0.06315436959266663, -0.01800522394478321, 0.022391069680452347, 0.010405178181827068, 0.03556567803025246, 0.010184749029576778, -0.047368574887514114, 0.04949971288442612, 0.031351346522569656, -0.03572193533182144, 0.03437557443976402, -0.051262710243463516, 0.013062255457043648, -5.054140082432153e-33, 0.01531289704144001, 0.0009430124191567302, -0.06598960608243942, -0.02281739003956318, -0.026674292981624603, -0.006140019744634628, 0.026507284492254257, -0.01539342850446701, 0.03066130541265011, -0.04703911766409874, -0.036045245826244354, 0.004630745388567448, 0.0020569374319165945, -0.0057677011936903, -0.007547263987362385, 0.024614432826638222, -0.026224683970212936, -0.016599345952272415, 0.035858068615198135, 0.026436822488904, 0.14223065972328186, 0.05172004923224449, 0.01401530485600233, -0.05954547971487045, -0.014087622053921223, 0.03297368064522743, -0.002445134799927473, 0.03438194468617439, -0.021161599084734917, -0.05517231300473213, -0.023028986528515816, -0.02158482000231743, -0.017002776265144348, 0.04855962097644806, -0.03486265987157822, -0.001923937234096229, 0.002143303630873561, -0.011372879147529602, -0.03293237090110779, 0.010576159693300724, -0.02568933367729187, -0.032539598643779755, 0.04420584440231323, 0.034458063542842865, -0.029061319306492805, 0.024817468598484993, 0.02748296409845352, -0.001990441931411624, 0.03554903715848923, -0.019598551094532013, 0.009462328627705574, -0.009856011718511581, -0.042821019887924194, 0.03201628848910332, 0.030560771003365517, 0.013481617905199528, -0.05590985715389252, -0.05092591047286987, 0.002984446007758379, 0.06112833321094513, 0.054568901658058167, 0.013600175268948078, 0.024958889931440353, -0.020476147532463074, 0.09006150811910629, 0.006694837473332882, 0.04680522531270981, -0.0616503581404686, -0.02640308439731598, -0.06606756150722504, 0.003245140425860882, 0.01297012809664011, 0.004575647413730621, -0.03202759101986885, 0.026235710829496384, -0.09181622415781021, -0.013212412595748901, 0.0418161004781723, 0.004042475018650293, 0.0016164290718734264, -0.004472527652978897, 0.002010331954807043, -0.0031769026536494493, -0.0031710865441709757, 0.06211313232779503, 0.00820273719727993, -0.0018387788441032171, 0.010560780763626099, 0.0001307424099650234, -0.049345288425683975, -0.002214492531493306, -0.06962542235851288, 0.004062804393470287, -0.0138434749096632, 0.05896840989589691, -0.0063684601336717606, 0.03286663070321083, -0.03160184994339943, 0.038517531007528305, -0.026796787977218628, 0.0010358127765357494, -0.013707362115383148, 0.02506701461970806, 0.0077246082946658134, -0.01987437717616558, -0.029789499938488007, -0.03784043341875076, -0.00929610151797533, 0.002599625615403056, 0.015851305797696114, 0.03563185781240463, -0.018626928329467773, 0.035284318029880524, -0.001164945075288415, 0.04867437854409218, -0.052703965455293655, -0.006666401866823435, 0.07364886999130249, 0.029579997062683105, -0.02384510077536106, -0.023693082854151726, 0.0042338562197983265, -0.012412087991833687, 0.05342280492186546, -0.035316385328769684, -0.02085416205227375, 0.026109246537089348, -0.01810031197965145, 0.029987839981913567, -0.01779559627175331, -0.016563529148697853, -0.012927960604429245, 2.562893826052459e-07, -0.07567352801561356, 0.03300069645047188, 0.004424389451742172, -0.01851656474173069, 0.026700938120484352, -0.046612657606601715, -0.034520842134952545, 0.045652177184820175, -0.02605622261762619, 0.01830131746828556, -0.02834259159862995, -0.07381203770637512, 0.01662522368133068, -0.029469463974237442, 0.0042763324454426765, -0.046416088938713074, -0.020804526284337044, 0.048975177109241486, 0.0025627929717302322, -0.017443373799324036, -0.006635039113461971, -0.06003930792212486, 0.02414330653846264, -0.012373835779726505, 0.0005489412578754127, 0.017252525314688683, 0.006925476714968681, 0.023822586983442307, 0.0256082471460104, -0.005322588142007589, 0.02733120135962963, -0.04506376385688782, 0.0044901506043970585, -0.08095160126686096, 0.0067400140687823296, 0.03334338217973709, 0.01584997959434986, -0.019619649276137352, -0.022136755287647247, 0.014935795217752457, 0.030868960544466972, 0.07596565783023834, -0.007015763781964779, 0.02233375608921051, 0.03189839422702789, 0.005929822567850351, 0.009030776098370552, -0.02849956974387169, -0.02507098764181137, 0.06876599788665771, 0.01679639331996441, 0.05565475672483444, 0.043212756514549255, -0.013276597484946251, -0.07057121396064758, -0.028547806665301323, 0.040140409022569656, 0.02920101396739483, 0.005505098029971123, 0.02279721386730671, -0.04641933739185333, 0.043768659234046936, 0.03504171594977379, 0.03493970260024071, 0.0450715646147728, -0.017446810379624367, -0.048154931515455246, 2.533345068833056e-34, -0.06000678241252899, -0.01616298407316208, -0.0029065855778753757, -0.0096320491284132, -0.03442159667611122, -0.02121998369693756, -0.033030007034540176, 0.03364008665084839, 0.005959525238722563, -0.02412782981991768, 0.010983937419950962]

['Masahiro Urakami', 'Seiji Miyoshi', 'Masato Okada']

cs/0612117v1

In the framework of on-line learning, a learning machine might move around a teacher due to the differences in structures or output functions between the teacher and the learning machine. In this paper we analyze the generalization performance of a new student supervised by a moving machine. A model composed of a fixed true teacher, a moving teacher, and a student is treated theoretically using statistical mechanics, where the true teacher is a nonmonotonic perceptron and the others are simple perceptrons. Calculating the generalization errors numerically, we show that the generalization errors of a student can temporarily become smaller than that of a moving teacher, even if the student only uses examples from the moving teacher. However, the generalization error of the student eventually becomes the same value with that of the moving teacher. This behavior is qualitatively different from that of a linear model.

Statistical Mechanics of On-line Learning when a Moving Teacher Goes around an Unlearnable True Teacher

http://arxiv.org/pdf/cs/0612117v1

Title Statistical Mechanics Online Learning Moving Teacher Goes around Unlearnable True Teacher Summary framework online learning learning machine might move around teacher due difference structure output function teacher learning machine paper analyze generalization performance new student supervised moving machine model composed fixed true teacher moving teacher student treated theoretically using statistical mechanic true teacher nonmonotonic perceptron others simple perceptrons Calculating generalization error numerically show generalization error student temporarily become smaller moving teacher even student us example moving teacher However generalization error student eventually becomes value moving teacher behavior qualitatively different linear model Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03822742775082588, -0.0021037845872342587, -0.03751002624630928, -0.017100714147090912, 0.0017674722475931048, -0.0015050717629492283, 0.027496034279465675, -0.03138023242354393, -0.07028447091579437, -0.006017658859491348, 0.08260170370340347, 0.03726232051849365, -0.01099121943116188, 0.04348098486661911, 0.011345523409545422, -0.10335671156644821, 0.014470626600086689, -0.03614838421344757, -0.04268362745642662, -0.020524872466921806, 0.01805620640516281, -0.05838514864444733, -0.006663904525339603, 0.0025838252622634172, -0.009174775332212448, -0.019600020721554756, -0.035152457654476166, -0.011987383477389812, 0.035523172467947006, -0.009583313949406147, 0.025245772674679756, -0.03249530494213104, 0.030377274379134178, 0.08917174488306046, 2.181430545533658e-06, -0.008522262796759605, -0.02918979525566101, -0.004049559123814106, 0.043783027678728104, -0.04318757727742195, 5.8407196775078773e-05, -0.009219723753631115, -0.008912199176847935, 0.013579657301306725, -0.025889722630381584, 0.023062463849782944, 0.04325680434703827, -0.020720873028039932, 0.033686768263578415, 0.06735537201166153, 0.002715101931244135, -0.039490386843681335, -0.00865508895367384, 0.03380175307393074, 0.02570665441453457, -0.023665865883231163, 0.03134903684258461, 0.027215860784053802, -0.050634682178497314, -0.027286572381854057, -0.09099588543176651, 0.021316159516572952, 0.000576728256419301, -0.028572577983140945, 0.04154320806264877, 0.0010912484722211957, -0.006493772845715284, 0.002874593250453472, 1.0676185411284678e-05, 0.02511749044060707, -0.011325914412736893, 0.010275042615830898, 0.03539115935564041, 0.00933674443513155, -0.0035358290188014507, 0.06937196105718613, -0.047702934592962265, 0.04756607115268707, -0.006777608301490545, -0.00887206383049488, -0.05696481466293335, 0.03217042610049248, -0.025433693081140518, 0.002308635739609599, -0.020862970501184464, 0.06688127666711807, -0.03183474764227867, -0.034478332847356796, -0.026080936193466187, 0.031925976276397705, 0.014361144974827766, 0.007440956775099039, 0.05736983194947243, 0.07032197713851929, -0.009757552295923233, 0.01837974227964878, -0.0213870108127594, 0.017594769597053528, -0.011233221739530563, -0.04406655579805374, 0.06345250457525253, -0.005391623824834824, 0.06015562638640404, 0.022338921204209328, -0.008180909790098667, 0.04716302081942558, -0.04875720292329788, 0.07222431153059006, 0.00941181555390358, 0.10077950358390808, -0.08081052452325821, 0.020225737243890762, 0.02482622303068638, 0.060710228979587555, 0.09299085289239883, -0.005257657263427973, -0.06318860501050949, 0.0633540078997612, 0.0002911296032834798, 0.024551112204790115, -0.045634590089321136, 0.023747432976961136, 0.02582879178225994, 0.01932900957763195, -0.04322283715009689, 0.03143312782049179, -0.006069863215088844, -0.006175441667437553, -0.006908768322318792, -0.010188429616391659, 0.02002827450633049, -0.012621852569282055, -0.019802151247859, 0.04363807290792465, -0.009966535493731499, 0.06936821341514587, 0.050162896513938904, 0.06732521951198578, -0.05143728479743004, -0.04254191741347313, 0.008972018025815487, -0.013857217505574226, -0.029727285727858543, -0.057614997029304504, -0.022879313677549362, -0.00895091611891985, -0.015515388920903206, 0.03906545788049698, 0.01109105721116066, -0.014061449095606804, -0.03171791508793831, 0.010706504806876183, 0.02317020110785961, 0.023841967806220055, 0.08081506937742233, 0.005413410719484091, -0.0013307217741385102, 0.025155680254101753, 0.014982282184064388, -0.032716915011405945, 0.0322406031191349, -0.030279554426670074, 0.014983822591602802, 0.012153832241892815, 0.00253197830170393, -0.03538116440176964, -0.0051468112505972385, -0.0530952624976635, 0.013609672896564007, 0.04468204826116562, -0.030267104506492615, 0.020078513771295547, -0.013024769723415375, 0.02834218740463257, 0.03197087347507477, 0.03163115307688713, -0.02156204544007778, 0.03007368929684162, -0.04268191009759903, 0.02745595946907997, -0.006633041426539421, 0.04044730216264725, -0.011184915900230408, 0.005490786395967007, -0.05494237318634987, -0.03720943629741669, -0.023463163524866104, 0.03982789069414139, -0.02036460116505623, -0.06610654294490814, -0.006682747509330511, -0.02865065634250641, -0.02623073011636734, -0.023345105350017548, 0.082710862159729, -0.02024243213236332, 0.0015812823548913002, -0.019924668595194817, 0.023761222139000893, 0.014321979135274887, -0.016092153266072273, -0.06490886211395264, 0.014662111178040504, -0.009413115680217743, 0.03295310214161873, -0.053632669150829315, -0.05789518728852272, -0.05657811835408211, -0.0022671050392091274, -0.013436122797429562, 0.026856916025280952, 0.022141773253679276, -0.03496020287275314, -0.0061790053732693195, -0.022911567240953445, 0.03499579429626465, 0.004659486468881369, -0.029794154688715935, -0.031201083213090897, 0.039503760635852814, 0.004065738059580326, 0.006263896822929382, -0.01737019419670105, 0.0465739481151104, -0.031714361160993576, 0.031106701120734215, -0.024302177131175995, 0.02200268767774105, -0.014447239227592945, -0.017259739339351654, 0.038026195019483566, -0.04208257421851158, 0.025851380079984665, -0.02072436735033989, -0.023315081372857094, -0.0051862141117453575, -0.03371187299489975, 0.005801917985081673, 0.041092418134212494, -0.021743878722190857, 0.0512518584728241, -0.009106346406042576, -0.02908407524228096, -0.06218494102358818, 0.023922599852085114, -0.006884048692882061, 0.00824572890996933, 0.04388688877224922, 0.0830923467874527, 0.010975244455039501, 0.016897335648536682, -0.02650422416627407, 0.005047854967415333, 0.03277921304106712, 0.028888197615742683, -0.02054007351398468, 0.015738867223262787, 0.04322856664657593, -0.03646545112133026, -0.03850426524877548, -0.008221169002354145, -0.07623527944087982, 0.0011787413386628032, -0.018046598881483078, -0.022819209843873978, -0.01610640436410904, 0.011467344127595425, 0.05360361561179161, -0.06100553646683693, 0.03460473567247391, -0.017549488693475723, 0.02992509864270687, -0.035882264375686646, -0.017831850796937943, 0.0055328006856143475, -0.021989546716213226, 0.039341915398836136, 0.013045331463217735, -0.05983784794807434, 0.054528240114450455, -0.03703390061855316, -0.03892228752374649, -0.025455687195062637, -0.02029583789408207, -0.024880874902009964, 0.026893578469753265, 0.050551727414131165, 0.001487553003244102, -0.0646866112947464, 0.04686448350548744, -0.04343961551785469, 0.026857169345021248, 0.008276022039353848, -0.0036669792607426643, -0.016862917691469193, -0.06209982559084892, -0.03909163177013397, 0.06551497429609299, 0.011539153754711151, 0.0261019729077816, 0.05363020673394203, 0.025632260367274284, -0.0511527881026268, -0.006756162736564875, -0.005403351970016956, -0.02051517739892006, 0.031094403937458992, -0.009943675249814987, -0.032235875725746155, 0.02557702548801899, 0.027449052780866623, 0.0073885624296963215, 0.01921316608786583, 0.029343074187636375, -0.03493654355406761, 0.00927484780550003, -0.062406767159700394, 0.02222484163939953, 0.02168259210884571, -0.006432575173676014, 0.01986093260347843, -0.015345771797001362, 0.03232674300670624, 0.06120085343718529, 0.033748023211956024, 0.009354718960821629, -0.037912216037511826, 0.03942807763814926, -0.002263170899823308, 0.01618247851729393, 0.03752729669213295, -0.04174402728676796, -0.004453994333744049, -0.006460082717239857, -0.0035479734651744366, 0.046675171703100204, -0.03760334476828575, -0.0479874461889267, -0.01953902095556259, 0.004988925065845251, -0.019763965159654617, -0.001946407719515264, -0.040246691554784775, 0.0201724860817194, 0.035673562437295914, -0.043838709592819214, -0.0698503777384758, -0.03980783000588417, 0.05063766613602638, 0.006205470766872168, 0.025395087897777557, 0.039627913385629654, -0.0487397238612175, -0.014515478163957596, -0.01159841101616621, 0.0025648209266364574, 0.024778839200735092, -0.01924876682460308, -0.07788535952568054, -0.03817296400666237, 0.0552501305937767, 0.04267393425107002, 0.01738847978413105, -0.014490966685116291, -0.05606365203857422, 0.009720956906676292, 0.01464828196913004, -0.025147635489702225, -0.05542213097214699, 0.030964931473135948, 0.00949715543538332, -0.0761144757270813, -0.08387594670057297, 0.006600184366106987, 0.010321476496756077, -0.010730852372944355, -0.03716674819588661, -0.042659733444452286, 0.009918796829879284, -0.023279329761862755, 0.03439827263355255, 0.003324506338685751, 0.02547485940158367, -0.018839579075574875, 0.0294001754373312, -0.01690305955708027, -0.034618329256772995, 0.004081722814589739, -0.0467657595872879, 0.010905428789556026, 0.015392862260341644, -0.06734064221382141, -0.06908783316612244, -0.0190934706479311, -0.030987437814474106, -0.03382386639714241, -0.018099376931786537, 0.029044929891824722, 0.009201864711940289, 0.0709676519036293, 0.05604196712374687, -0.08680372685194016, 0.018750961869955063, -0.030333204194903374, -0.024419931694865227, -0.01394643634557724, 0.047234732657670975, -0.01488704327493906, -0.07477536052465439, -0.08679290860891342, 0.04137256741523743, 0.048326607793569565, 0.03268400579690933, -0.008836315013468266, 0.04340401291847229, 0.019665123894810677, -0.002656848169863224, -0.020612388849258423, 0.014381096698343754, -0.025145402178168297, 0.0384051613509655, 0.05594294145703316, 0.08452627807855606, -0.02038336731493473, 0.00039904002915136516, -0.05454351380467415, 0.0016328651690855622, 0.0035934611223638058, -0.025456570088863373, -0.06174140051007271, -0.04491610452532768, -0.05941973626613617, -0.03775503858923912, 0.03465840965509415, 0.0658465251326561, 0.012275437824428082, -0.035630982369184494, 0.005285962484776974, 0.030451806262135506, -0.04914122819900513, 0.014122862368822098, -0.04069345071911812, 0.08137983083724976, 0.029292790219187737, 0.010707112960517406, 0.0415385365486145, 0.030620615929365158, -0.04672890901565552, -0.0437263585627079, 0.019714230671525, 0.024933336302638054, -0.02461821585893631, 0.03955049067735672, 0.010582542046904564, -0.011630100198090076, -0.014636681415140629, -0.09191138297319412, -0.050767868757247925, -0.06113998219370842, 0.04326643422245979, 0.020550960674881935, 0.029645204544067383, 0.040690500289201736, -0.026741867884993553, 0.025509869679808617, 0.029579129070043564, -0.03282991424202919, 0.041407033801078796, -0.007152135018259287, 0.038663435727357864, 0.007782456930726767, -0.00040425918996334076, -0.005294909235090017, -0.002672365866601467, 0.0026837894693017006, 0.009058579802513123, -0.03668022155761719, -0.09192310273647308, 0.019851528108119965, -0.03343944996595383, -0.004740613978356123, 0.0847715362906456, 0.07010344415903091, -0.051887985318899155, -0.0065000406466424465, 0.010629273019731045, 0.03433871641755104, 0.017054874449968338, -0.04131343588232994, 0.004938680678606033, 0.09479670226573944, 0.033128466457128525, 0.009380493313074112, -0.02772931195795536, 0.053034037351608276, -0.06540796905755997, 0.030455274507403374, 0.019521845504641533, -0.019442785531282425, 0.046340394765138626, -0.009991521015763283, -0.009388478472828865, 0.006541861686855555, 0.02341240830719471, 0.023362845182418823, 0.0409001000225544, 0.01602470688521862, 0.08069129288196564, 0.012684316374361515, 0.06124694272875786, 0.0045546540059149265, -0.060446515679359436, -0.016250524669885635, -0.04824523627758026, -0.07174219191074371, 0.03380264714360237, 0.012594219297170639, 0.02377457730472088, 0.020412353798747063, 0.01989775337278843, 0.007671917788684368, 3.902610842487775e-05, 0.019335320219397545, -0.016971971839666367, 0.023110413923859596, 0.030135871842503548, -0.004079580307006836, 0.008061185479164124, 0.06718312203884125, 0.017180269584059715, -0.04031636193394661, 0.008376103825867176, -0.06096801906824112, 0.005077445413917303, -0.005801624618470669, 0.09224467724561691, 0.06428712606430054, -0.01496923714876175, 0.058969177305698395, -0.04962167888879776, 0.016817845404148102, -0.019473418593406677, -0.015809154137969017, 0.021752871572971344, 0.07858932018280029, -0.030990973114967346, 0.0235434677451849, -0.0066801076754927635, -0.025458384305238724, 0.05649915710091591, -0.03762071952223778, -0.04733508825302124, 0.05746501311659813, 0.019258886575698853, -0.02422606386244297, -5.6478370959683805e-33, -0.02616984024643898, -0.01474418118596077, -0.029762281104922295, 0.025622116401791573, -0.03763595223426819, -0.05835139751434326, 0.01187568437308073, 0.019204530864953995, -0.019517093896865845, -0.044075749814510345, 0.0007547280983999372, 0.024301491677761078, 0.037380874156951904, 0.029963655397295952, 0.06526397913694382, -0.006780005060136318, -0.015429774299263954, -0.004682844504714012, 0.005030865781009197, -0.0286856722086668, 0.04473331570625305, 0.05731068179011345, 0.013717304915189743, -0.06735417246818542, 0.00833785068243742, -0.022233914583921432, -0.04466736316680908, -0.05862275883555412, -0.05920467525720596, -0.011774323880672455, -0.016657615080475807, -0.008124267682433128, -0.013395087793469429, 0.00827302411198616, -0.027074499055743217, -0.004462535493075848, -0.00044108089059591293, -0.029679635539650917, -0.07495073974132538, 0.06111304461956024, -0.011586091481149197, -0.0004217578680254519, 0.12103856354951859, -0.017638741061091423, -0.03482985123991966, 0.016142278909683228, 0.07496876269578934, -0.019518006592988968, -0.010814595967531204, 0.023788923397660255, -0.037476249039173126, 0.007586190942674875, -0.031225139275193214, 0.020581286400556564, -0.01546347513794899, 0.01703076809644699, -0.014635585248470306, -0.04602980241179466, -0.01862478256225586, 0.06503123044967651, 0.01969149149954319, 0.03654033690690994, 0.0004151153552811593, 0.00993969477713108, 0.01782052032649517, 0.019971957430243492, 0.04090817645192146, -0.017959928140044212, -0.005077651236206293, -0.026447439566254616, -0.0018331346800550818, 0.02372395247220993, 0.03530175983905792, -0.008633527904748917, 0.07246153801679611, -0.03227870911359787, -0.03770275413990021, -0.0023021295201033354, 0.028368832543492317, 0.0033994801342487335, -0.029109692201018333, -0.017077676951885223, -0.05779293179512024, -0.030567580834031105, 0.032877884805202484, -0.08377449214458466, 0.0038623791188001633, -0.029943739995360374, 0.03249146416783333, -0.021286455914378166, 0.018570492044091225, -0.044915731996297836, -0.04090927168726921, -0.03752504661679268, -0.02127142623066902, -0.040404729545116425, 0.010930981487035751, 0.010266837663948536, -0.004537219647318125, 0.002066723071038723, -0.04624585807323456, -0.0833127573132515, -0.046663910150527954, -0.02643776871263981, -0.0021697795018553734, 0.03290644660592079, 0.01239081285893917, 0.03205427527427673, -0.032277051359415054, -0.0055154296569526196, 0.01769416406750679, -0.05224387347698212, 0.02774379961192608, -0.03296375274658203, 0.04490910843014717, -0.09064660221338272, -0.03385177254676819, 0.10179317742586136, 0.03666262701153755, 0.015752336010336876, -0.036772843450307846, -0.018076473847031593, -0.025838833302259445, 0.00821821391582489, -0.037726663053035736, -0.04152354970574379, 0.0009494973346590996, 0.03785485029220581, -0.013423824682831764, -0.0710882768034935, -0.011657925322651863, -0.042133357375860214, 2.8201861823617946e-07, -0.005069867242127657, 0.04118666425347328, -0.011936183087527752, -0.05076932907104492, 0.029190760105848312, -0.01855108141899109, -0.045818429440259933, 0.017840035259723663, 0.02980072982609272, 0.02450348250567913, 0.04172046482563019, -0.0269328486174345, 0.023644791916012764, -0.00828818790614605, -0.004314776510000229, -0.03334956616163254, 0.004656413570046425, 0.04461634159088135, 0.006488929968327284, 0.03758187219500542, 0.02152981422841549, 0.034816667437553406, 0.07462336868047714, -0.014019847847521305, 0.029476430267095566, -0.036162905395030975, -0.009195062331855297, 0.010544014163315296, 0.03953918442130089, -0.037528425455093384, 0.019981050863862038, -0.001835607341490686, -0.01244417205452919, -0.032624129205942154, 0.009951469488441944, 0.02380683831870556, 0.0019053166033700109, 0.028131980448961258, -0.008315393701195717, 0.03970868140459061, 0.015439104288816452, 0.0013946754625067115, 0.05330762267112732, -0.015198305249214172, 0.045527588576078415, -0.014604633674025536, 0.006928458344191313, 8.893160702427849e-05, -0.03333848714828491, -0.02946617268025875, 0.04306326434016228, 0.026141919195652008, -0.005405853036791086, -0.029827995225787163, -0.031592585146427155, -0.014378226362168789, -0.025670528411865234, -0.009764212183654308, -0.02515462227165699, -0.003108882112428546, -0.031173985451459885, -0.029327120631933212, 0.0319032296538353, -0.007040303200483322, 0.030118931084871292, 0.019733192399144173, -0.021892933174967766, 2.5992712460487333e-34, 0.023733440786600113, 0.013862377032637596, 0.02967977151274681, -0.04825153574347496, -0.040408775210380554, -0.005116722546517849, 0.037018079310655594, 0.030674532055854797, 0.04163041710853577, 0.03948795422911644, -0.02603098191320896]

['Bart Kuijpers', 'Vanessa Lemmens', 'Bart Moelans', 'Karl Tuyls']

0803.1555v1

We consider privacy preserving decision tree induction via ID3 in the case where the training data is horizontally or vertically distributed. Furthermore, we consider the same problem in the case where the data is both horizontally and vertically distributed, a situation we refer to as grid partitioned data. We give an algorithm for privacy preserving ID3 over horizontally partitioned data involving more than two parties. For grid partitioned data, we discuss two different evaluation methods for preserving privacy ID3, namely, first merging horizontally and developing vertically or first merging vertically and next developing horizontally. Next to introducing privacy preserving data mining over grid-partitioned data, the main contribution of this paper is that we show, by means of a complexity analysis that the former evaluation method is the more efficient.

Privacy Preserving ID3 over Horizontally, Vertically and Grid Partitioned Data

http://arxiv.org/pdf/0803.1555v1

Title Privacy Preserving ID3 Horizontally Vertically Grid Partitioned Data Summary consider privacy preserving decision tree induction via ID3 case training data horizontally vertically distributed Furthermore consider problem case data horizontally vertically distributed situation refer grid partitioned data give algorithm privacy preserving ID3 horizontally partitioned data involving two party grid partitioned data discus two different evaluation method preserving privacy ID3 namely first merging horizontally developing vertically first merging vertically next developing horizontally Next introducing privacy preserving data mining gridpartitioned data main contribution paper show mean complexity analysis former evaluation method efficient Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.02186938188970089, 0.06465274840593338, -0.023896807804703712, 0.007932971231639385, -0.04124712198972702, -0.013055076822638512, 0.034486278891563416, -0.027087276801466942, 0.06703199446201324, 0.026384925469756126, -0.01684005744755268, 0.03257887810468674, 0.03094588965177536, 0.004504091572016478, -0.048734888434410095, -0.004831486381590366, 0.03155790641903877, -0.020675666630268097, -0.013700255192816257, -0.013693347573280334, -0.021404162049293518, -0.0369783490896225, 0.002125113271176815, -0.05120737850666046, -0.0009439994464628398, -0.03322243317961693, -0.02511237934231758, -0.022290799766778946, 0.0022427672520279884, -0.052830688655376434, 0.043139487504959106, 0.005883827805519104, -0.009936315007507801, 0.017634866759181023, 2.215550466644345e-06, -0.021981030702590942, -0.07044407725334167, 0.015608780086040497, 0.007486538030207157, 0.003152454737573862, -0.03269783407449722, 0.031108640134334564, 0.029993653297424316, -0.002176276408135891, -0.052069392055273056, 0.005140912719070911, -0.0017012846656143665, 0.07172196358442307, 0.05843565985560417, 0.013843754306435585, -0.002816074527800083, -0.056429725140333176, 0.030350016430020332, 0.002914849668741226, -0.009452151134610176, 0.0009215407771989703, 0.02994709275662899, -0.0011357226176187396, -0.07240283489227295, -0.029011819511651993, -0.023364603519439697, -0.020231934264302254, 0.005374974571168423, 0.012353870086371899, -0.003947154153138399, 0.02797805331647396, 0.007946099154651165, -0.02431345358490944, -0.038126301020383835, -0.003265789709985256, 0.010764525271952152, 0.014013325795531273, -0.008447340689599514, 0.008252162486314774, 0.029813043773174286, -0.028270505368709564, -0.003629318904131651, 0.014600268565118313, -0.06310158967971802, 0.007459744345396757, 0.010793118737637997, 0.05819473788142204, -0.02976970374584198, -0.00493683572858572, -0.017299311235547066, 0.0823671817779541, -0.021049080416560173, 0.011668963357806206, -0.0137917660176754, -0.049793411046266556, 0.000701749580912292, -0.03516703471541405, 0.010194549337029457, -0.005647793412208557, -0.0049443659372627735, 0.010498481802642345, 0.01925498992204666, -0.005285263527184725, 0.016611365601420403, -0.016257189214229584, -0.040849555283784866, -0.04241239279508591, 0.09423614293336868, 0.0012897772248834372, 0.032810285687446594, 0.01693260855972767, 0.0027464518789201975, 0.07369661331176758, 0.03310258314013481, 0.03348030149936676, -0.017805641517043114, 0.0004902192740701139, -0.03407249227166176, 0.10655006766319275, -0.03500506654381752, 0.046120572835206985, -0.03621133789420128, 0.03336084261536598, -0.04447302222251892, -0.007980015128850937, 0.0001799498568288982, 0.0062545305117964745, 0.04891566187143326, 0.026663888245821, -0.006485333200544119, -0.07272154092788696, -0.004936215002089739, 0.029722895473241806, -0.0074927625246346, 0.007612887769937515, 0.03410080820322037, -0.020737111568450928, -0.0050709606148302555, 0.021783458068966866, -0.012216748669743538, 0.0031591064762324095, 0.01753983087837696, 0.009104463271796703, -0.04720669239759445, -0.05256214365363121, 0.012610443867743015, 0.008911743760108948, -0.04230392724275589, -0.017867282032966614, 0.0431755967438221, -0.07800263911485672, 0.001205654814839363, -0.025190794840455055, -0.01967933215200901, 0.018269671127200127, 0.007669695187360048, 0.03754134848713875, -0.05686439201235771, 0.03230884298682213, 0.027365444228053093, 0.03781212866306305, 0.021929467096924782, -0.037356920540332794, 0.05584956333041191, 0.027431854978203773, 0.040695369243621826, -0.03449580818414688, 0.018946560099720955, -0.06948328763246536, 0.03533409535884857, 0.004979845602065325, 0.029244352132081985, 0.037152014672756195, -0.03819466009736061, -0.07657670974731445, -0.06542610377073288, 0.01095514465123415, 0.017033422365784645, -0.04650424048304558, 0.008290506899356842, 0.028723469004034996, -0.002118530450388789, 0.0016236728988587856, -0.10336887836456299, 0.03700673580169678, -0.03228631988167763, 0.025250354781746864, 0.017819199711084366, -0.011288749054074287, -0.030735688284039497, -0.059349432587623596, -0.03115392103791237, 0.015417498536407948, -0.007442292757332325, -0.034422047436237335, 0.03379250317811966, -0.009284011088311672, 0.01752563938498497, 0.007502998225390911, -0.03877069056034088, 0.02516941726207733, 0.04173193499445915, -0.004334860946983099, 0.010083219036459923, -0.027414308860898018, -0.06833634525537491, -0.04805062711238861, 0.06351371854543686, -0.011214441619813442, 0.010162965394556522, -0.006502409465610981, 0.006668501999229193, -0.005378089379519224, 0.049082864075899124, -0.09925127029418945, -0.022543691098690033, -0.04395437240600586, 0.01770266890525818, -0.0021717753261327744, -0.08281475305557251, 0.0803351029753685, -0.013980332762002945, -0.006181187927722931, 0.039495211094617844, -0.044607408344745636, -0.016048839315772057, -0.009955525398254395, 0.011576895602047443, 0.023730244487524033, 0.00468048918992281, 0.042509064078330994, 0.09099135547876358, 0.041500676423311234, 0.05103584751486778, 0.014834051951766014, 0.04495365545153618, -0.037783343344926834, 0.040684424340724945, 0.042973559349775314, -0.03389058634638786, 0.040882278233766556, 0.017734410241246223, -0.033664703369140625, -0.043624456971883774, 0.03308515623211861, 0.007814076729118824, 0.007279324810951948, -0.022927580401301384, -0.008187626488506794, -0.03646184504032135, -0.01087671797722578, -0.00899418443441391, -0.018036726862192154, 0.015579886734485626, -0.014308732002973557, -0.001657792367041111, -0.024030741304159164, 0.06648102402687073, -0.05297711491584778, -0.01851661130785942, -0.08195662498474121, -0.03634103387594223, 0.06831493228673935, 0.016188882291316986, 0.08842293173074722, -0.012303291819989681, -0.056615110486745834, 0.0017072015907615423, -0.00015674922906327993, 0.007995616644620895, 0.0003157386090606451, -0.01090710237622261, 0.024046022444963455, 0.04603015258908272, 0.023788047954440117, 0.060097064822912216, -0.03266015276312828, 0.01259914506226778, 0.013165395706892014, -0.0350726917386055, -0.05007106065750122, 0.02064545266330242, -0.033429790288209915, -0.016266632825136185, 0.009897441603243351, 0.03911931440234184, -0.04190966114401817, 0.08928540349006653, -0.03502599895000458, -0.03066355548799038, 0.02602882869541645, 0.02722105383872986, -0.06527964025735855, 0.00655557494610548, 0.005808670539408922, -0.02671559527516365, -0.010624757967889309, -0.011400992050766945, 0.03676886856555939, -0.03616560623049736, 0.024613693356513977, -0.0237488504499197, -0.03215773031115532, 0.02316739782691002, -0.022753721103072166, 0.011528688482940197, 0.027873776853084564, -0.004373521544039249, 0.0028640502132475376, 0.014356155879795551, 0.031609151512384415, 0.04479554295539856, -0.013868851587176323, 0.046010468155145645, -0.0398888885974884, 0.022953076288104057, -0.05251333862543106, 0.017830537632107735, 0.005171006545424461, 0.05690709128975868, 0.0030701656360179186, -0.04690221697092056, -0.04577173665165901, 0.028386954218149185, -0.004889911040663719, -0.045897237956523895, -0.0446745902299881, 0.04081445932388306, -0.012773212045431137, 0.025650041177868843, -0.0398007296025753, -0.02919478341937065, -0.012681301683187485, 0.023359131067991257, 0.0035111084580421448, 0.061305537819862366, -0.027259474620223045, -0.04782011732459068, 0.03040534444153309, 0.0003628599806688726, 0.03945322707295418, -0.031278058886528015, 0.02947915345430374, 0.028838610276579857, -0.0517590269446373, -0.011713710613548756, -0.041447095572948456, -0.04111838713288307, -0.05621662735939026, 0.07400808483362198, 0.008401818573474884, 0.038257088512182236, -0.0054063452407717705, 0.038060203194618225, 0.024383332580327988, 0.013887100853025913, 0.00863683596253395, 0.026249177753925323, -0.03717133030295372, 0.021262673661112785, -0.024886511266231537, -0.08517854660749435, -0.03175641596317291, -0.012301727198064327, 0.010226373560726643, 0.051762983202934265, 0.07294271141290665, 0.03220391646027565, 0.055532366037368774, 0.0030586442444473505, -0.007978660054504871, -0.012940151616930962, -0.028147613629698753, 0.012674684636294842, -0.007437250576913357, -0.013862601481378078, 0.0012837841641157866, 0.07121971249580383, -0.005757642909884453, 0.0377880297601223, -0.07424476742744446, -0.010705143213272095, 0.030447250232100487, -0.016193265095353127, 0.015711547806859016, -0.01335226185619831, -0.04456605389714241, 0.024493278935551643, -0.004984556697309017, 0.030767805874347687, -0.029787249863147736, -0.06857950240373611, -0.03091614320874214, -0.06789952516555786, 0.029565680772066116, 0.004644516855478287, 0.00662847189232707, -0.05157222971320152, -0.060620829463005066, 0.023089084774255753, 0.021932251751422882, -0.08583558350801468, -0.017628710716962814, -0.004699955694377422, -0.03152137249708176, -7.833291601855308e-05, -0.0595090426504612, -0.008919532410800457, -0.034680310636758804, -0.01667698845267296, -0.024352701380848885, 0.0026140413247048855, 0.036163512617349625, 0.016633734107017517, -0.058694690465927124, 0.022610360756516457, 0.015530112199485302, -0.02528313174843788, -0.033655907958745956, 0.06383058428764343, 0.021283118054270744, 0.04678501561284065, -0.016555842012166977, 0.002719005336984992, 0.03232930228114128, 0.016724757850170135, 0.056687138974666595, 0.046190738677978516, -0.01629689708352089, -0.0033032484352588654, 0.04096692055463791, -0.01369389332830906, 0.029375653713941574, 0.0015828970354050398, -0.023029549047350883, 0.0010565519332885742, 0.04468076676130295, 0.0015274652978405356, 0.06494709104299545, 0.02996937185525894, 0.07793740928173065, 0.07502896338701248, -0.03954869136214256, -0.05420104041695595, -0.03408866748213768, 0.015930987894535065, -0.0326555036008358, 0.027951834723353386, 0.03863763436675072, 0.002673465060070157, -0.0425991490483284, 0.025215357542037964, -0.057071056216955185, -0.08216936141252518, 0.01697612553834915, 0.027754735201597214, -0.006440125871449709, 0.039882924407720566, 0.0034270244650542736, 0.037034135311841965, -0.03645622730255127, -0.053026434034109116, 0.055538445711135864, -0.012720105238258839, -0.024392984807491302, 0.027139585465192795, 0.002241718815639615, 0.007817371748387814, -0.03337875008583069, 0.018541578203439713, 0.004617608152329922, 0.05644762143492699, 0.043552082031965256, -0.0222370196133852, -0.0006497983122244477, -0.029666868969798088, -0.005279518198221922, -0.003461961867287755, 0.012621716596186161, 0.01481107622385025, 0.012687482871115208, -0.10355881601572037, -0.06330133974552155, 0.026567736640572548, -0.0035879448987543583, 0.043591950088739395, 0.029736537486314774, 0.06098174303770065, -0.0038527916185557842, -0.03412376344203949, 0.08267766982316971, 0.008422644808888435, -0.013633458875119686, -0.02769428677856922, 0.0023889895528554916, 0.028454028069972992, 0.012856519781053066, 0.025721395388245583, 0.03321445360779762, 0.08367805927991867, -0.07401212304830551, -0.027432668954133987, 0.04204760119318962, 0.026786748319864273, 0.04073508828878403, -0.05295204371213913, 0.006722735241055489, -0.018349628895521164, -0.006466876715421677, 0.051262740045785904, 0.04704093188047409, 0.0103157889097929, -0.005839924328029156, 0.018168959766626358, -0.004438208881765604, 0.01379257719963789, 0.04524500295519829, -0.012957392260432243, 0.014196495525538921, 0.013744835741817951, 0.002280688611790538, -0.046320393681526184, 0.09415265172719955, -0.04270936921238899, 0.0064808581955730915, 0.003623825265094638, 0.015383290126919746, -0.029070697724819183, -0.033869169652462006, -0.04844919592142105, -0.017088666558265686, 0.008610575459897518, -0.01810407266020775, 0.036669548600912094, 0.031084338203072548, 0.020876802504062653, -0.04490036889910698, -0.049670543521642685, -0.07731588929891586, -0.038180332630872726, 0.0192631296813488, 0.021243872120976448, 0.03368973731994629, -0.0007387898513115942, 0.004636982921510935, -0.017218688502907753, 0.003874074900522828, -0.06290408968925476, 0.00500535499304533, 0.0705597922205925, 0.023431459441781044, -0.029024681076407433, -0.013681641779839993, 0.022911394014954567, -0.01908975839614868, -0.061556994915008545, -0.06531771272420883, -0.0487690195441246, -0.0162056814879179, -0.011419507674872875, -5.213995191858491e-33, -0.029721857979893684, -0.059838660061359406, -0.04170530289411545, 0.03520755469799042, -0.016257505863904953, -0.012171796523034573, -0.0024451331701129675, -0.0073338644579052925, 0.01971440576016903, -0.012965823523700237, -0.018053604289889336, 0.02778742089867592, 0.008776352740824223, -0.02226170338690281, -0.01977815106511116, 0.023316461592912674, 0.011770514771342278, -0.018632985651493073, -0.042813096195459366, 0.02346361055970192, 0.008821403607726097, 0.012552477419376373, -0.02592364512383938, -0.06239549070596695, 0.012832473032176495, 0.023375295102596283, -0.059282176196575165, 0.028092194348573685, -0.09573134034872055, 0.010875074192881584, 0.04756072163581848, -0.05048676207661629, 0.04114779829978943, -0.0023536798544228077, -0.035531073808670044, 0.03658697009086609, -0.08051463216543198, -0.003005120437592268, -0.03833162412047386, 0.020354965701699257, 0.016284670680761337, 0.0022792480885982513, 0.06245678663253784, -0.028753990307450294, 0.034976668655872345, 0.00844681728631258, 0.0011620372533798218, 0.004920417908579111, -0.03415992483496666, -0.04048214852809906, 0.09089454263448715, 0.02415342442691326, 0.005523543804883957, 0.0048493328504264355, 0.040677014738321304, 0.0021962819155305624, 0.01967482827603817, -0.02948623336851597, -0.02098112180829048, 0.033658698201179504, 0.045710239559412, -0.033992744982242584, -0.05590491369366646, -0.00785763468593359, 0.04269241541624069, 0.0022872984409332275, 0.07365558296442032, -0.01451279316097498, -0.007257742807269096, -0.03969139978289604, -0.04887185990810394, 0.014558958820998669, -0.02555948868393898, -3.595172984205419e-06, 0.023104943335056305, -0.043037012219429016, -0.04802698642015457, 0.0751577690243721, -0.02846533991396427, -0.05257599428296089, -0.01846236176788807, -0.021878518164157867, -0.07742871344089508, -0.02794763073325157, 0.053506843745708466, -0.042314670979976654, -0.013635102659463882, 0.026280630379915237, 0.012076708488166332, 0.02624315768480301, -0.03201666101813316, 0.014561988413333893, -0.0374608151614666, -0.04882638901472092, -0.034056369215250015, 0.0537295825779438, 0.06800258159637451, 0.018090253695845604, -0.039744067937135696, -0.03877165541052818, 0.030930155888199806, -0.023583026602864265, -0.0008462290279567242, -0.027640772983431816, 0.027013326063752174, -0.0027553346008062363, 0.044655103236436844, 0.028193537145853043, -0.05483260005712509, -0.015549927949905396, 0.051450520753860474, 0.009897607378661633, 0.006159384269267321, 0.0424606092274189, -0.003434564918279648, -0.03353988751769066, -0.005000441800802946, -0.026175159960985184, 0.030112003907561302, 0.04149818792939186, -0.021446198225021362, 0.023168427869677544, -0.08475469052791595, -0.0013521339278668165, 0.05857206881046295, 0.0007801776519045234, 0.02082928828895092, -0.04066707566380501, 0.026206782087683678, 0.03259625285863876, -0.016240421682596207, -0.019219664856791496, 2.7525757673174667e-07, -0.05182243138551712, -0.0415409654378891, -0.01964099518954754, -0.03759600594639778, 0.04201769083738327, 0.011186796240508556, 0.015574331395328045, 0.04858081415295601, -0.017278451472520828, -0.006919631734490395, 0.004323019180446863, -0.04652263596653938, 0.02327096462249756, 0.0618116594851017, -0.04912157356739044, -0.050946272909641266, 0.018765844404697418, 0.013205697759985924, -0.03194982558488846, 0.044931963086128235, 0.03769785910844803, 0.026351887732744217, 0.042328134179115295, -0.021632768213748932, 0.01671838015317917, -0.005992862395942211, -0.04009343311190605, -0.0005977805703878403, 0.011949347332119942, -0.013638067990541458, 0.06571890413761139, 0.005704104900360107, 0.0163862407207489, 0.06779602915048599, -0.021173937246203423, 0.02339744009077549, -0.049518875777721405, 0.06552363187074661, 0.003261438338086009, 0.06026800349354744, 0.03928373381495476, -0.03783867135643959, 0.007481331471353769, 0.021384017542004585, 0.017441775649785995, 0.006343609653413296, -0.043194111436605453, 0.05840511992573738, 0.056530971080064774, -0.04882027581334114, 0.028270047158002853, 0.07149635255336761, -0.004379323683679104, -0.00965100061148405, -0.03355192020535469, -0.02799648977816105, 0.060215216130018234, -0.007781856693327427, -0.006418474018573761, -0.026564041152596474, 0.0012883800081908703, -0.013459058478474617, 0.07614471763372421, 0.021546196192502975, 0.015300476923584938, 0.018542833626270294, 0.03436034917831421, 3.131258433668889e-34, -0.015864990651607513, -0.015223603695631027, -0.010992823168635368, -0.012810389511287212, 0.01843326911330223, -0.022599326446652412, 0.1127292588353157, -0.05241527408361435, 0.027418507263064384, -0.009637627750635147, 0.00463862344622612]

['Stefanie Jegelka', 'Suvrit Sra', 'Arindam Banerjee']

0812.0389v4

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor clustering [8,34]. Like k-means, these more general problems also suffer from the NP-hardness of the associated optimization. Researchers have developed approximation algorithms of varying degrees of sophistication for k-means, k-medians, and more recently also for Bregman clustering [2]. However, there seem to be no approximation algorithms for Bregman co- and tensor clustering. In this paper we derive the first (to our knowledge) guaranteed methods for these increasingly important clustering settings. Going beyond Bregman divergences, we also prove an approximation factor for tensor clustering with arbitrary separable metrics. Through extensive experiments we evaluate the characteristics of our method, and show that it also has practical impact.

Approximation Algorithms for Bregman Co-clustering and Tensor Clustering

http://arxiv.org/pdf/0812.0389v4

Title Approximation Algorithms Bregman Coclustering Tensor Clustering Summary past year powerful generalization Euclidean kmeans problem made Bregman clustering 7 coclustering ie simultaneous clustering row column input matrix 918 tensor clustering 834 Like kmeans general problem also suffer NPhardness associated optimization Researchers developed approximation algorithm varying degree sophistication kmeans kmedians recently also Bregman clustering 2 However seem approximation algorithm Bregman co tensor clustering paper derive first knowledge guaranteed method increasingly important clustering setting Going beyond Bregman divergence also prove approximation factor tensor clustering arbitrary separable metric extensive experiment evaluate characteristic method show also practical impact Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04563336446881294, -0.0635950043797493, -0.030383793637156487, 0.036995917558670044, -0.055590786039829254, 0.03852684795856476, 0.05106087774038315, 0.05158771201968193, 0.04719838500022888, 0.004513761028647423, 0.01976138725876808, -0.04889467731118202, -0.004500410985201597, 0.007881284691393375, -0.014739075675606728, -0.06304741650819778, 0.0037671122699975967, -0.036168262362480164, -0.001585524994879961, -0.04948244243860245, -0.004597298800945282, -0.0064948201179504395, -0.05939238518476486, -0.039015088230371475, -0.018934596329927444, -0.021829672157764435, 0.0018618215108290315, -0.05942661687731743, 0.012604479677975178, 0.011651118285953999, 0.038875777274370193, 0.016432886943221092, -0.015921391546726227, 0.04304346814751625, 1.8756841200229246e-06, -0.0025324453599750996, -0.04822222515940666, -0.009463775902986526, 0.05986722558736801, 0.0008424142724834383, 0.021505828946828842, -0.020239677280187607, 0.03385386988520622, -0.03099239617586136, -0.0158882737159729, -0.030402403324842453, -0.03503016009926796, 0.05157550051808357, 0.034640833735466, -0.005645018070936203, -0.024231698364019394, 0.023440629243850708, -0.029420359060168266, -0.004333957564085722, -0.03608924522995949, 0.018207335844635963, 0.01798495464026928, 0.010497440584003925, -0.004046616144478321, 0.010076995939016342, 0.002272042678669095, 0.040333591401576996, 0.004033261444419622, 0.024017509073019028, 0.036726828664541245, 0.05026881396770477, -0.031162632629275322, 0.011893585324287415, 0.001646595192141831, 0.06299055367708206, -0.00298264529556036, 0.009384578093886375, 0.05934599041938782, 0.02421512082219124, -0.030189592391252518, -0.005002100020647049, -0.02873370237648487, -0.0215674489736557, -0.007610772270709276, 0.00117694481741637, -0.068572998046875, -0.01627832092344761, -0.026160569861531258, -0.01086600124835968, 0.015058831311762333, 0.03819096460938454, 0.058505307883024216, -0.004714378621429205, -0.04135880991816521, 0.025195321068167686, -0.003211792791262269, 0.014779942110180855, 0.040338970720767975, -0.00854398775845766, -0.04564690962433815, -0.054687462747097015, 0.03857685253024101, -0.08047834783792496, -0.016963854432106018, -0.014417421072721481, 0.024823512881994247, -0.016355955973267555, 0.01483936421573162, 0.062194664031267166, -0.056044917553663254, -0.010893243364989758, -0.017415454611182213, -0.015452433377504349, 0.015607140958309174, -0.006995595525950193, -0.022418327629566193, 0.02240024134516716, -0.02224438451230526, 0.007577772717922926, 0.0010369648225605488, 0.019489392638206482, -0.04498208686709404, 0.04812464863061905, -0.022370291873812675, 0.014581487514078617, 0.01833156682550907, 0.010978545993566513, 0.07791388034820557, -0.025976458564400673, -0.023087123408913612, -0.0459502711892128, -0.04022800177335739, 0.03209913522005081, -0.0916876569390297, 0.0749584287405014, 0.012057220563292503, 0.05878685414791107, 0.04332905635237694, -0.04266935586929321, 0.0202458668500185, -0.01570599153637886, -0.03170181065797806, -0.023192571476101875, -0.010074958205223083, 0.03477753326296806, -0.025850601494312286, -0.01769716665148735, -0.05028533563017845, -0.05275075137615204, 0.061679765582084656, -0.03881783410906792, -0.028906002640724182, 0.04997972026467323, -0.030232785269618034, -0.09342538565397263, -0.0645337700843811, 0.052181269973516464, 0.0038937728386372328, 0.010533531196415424, 0.07829351723194122, 0.006732670124620199, 0.0060631027445197105, -0.007375803776085377, -0.005757550243288279, 0.019294925034046173, 0.03099728375673294, -0.01290256530046463, -0.044460151344537735, -0.015999164432287216, -0.015704268589615822, -0.03776390478014946, 0.007893388159573078, -0.017207982018589973, 0.026991447433829308, 0.035057369619607925, 0.04128854349255562, 0.016722634434700012, -0.049014244228601456, -0.008649265393614769, 0.031551674008369446, 0.030153391882777214, 0.05486651510000229, 0.018741777166724205, -0.013681476935744286, -0.00251455744728446, -0.05027784779667854, 0.0035195171367377043, -0.006208373233675957, 0.02549489215016365, -0.011760756373405457, -0.031083017587661743, 0.07993388921022415, 0.00905492901802063, -0.001820104313082993, -0.017231134697794914, 0.06958277523517609, -0.05198689550161362, 0.03833472728729248, -0.03263319656252861, 0.08020130544900894, -0.055803701281547546, -0.018299344927072525, 0.005464170593768358, 0.004073622636497021, 0.007720706518739462, 0.025306371971964836, 0.0389060340821743, 0.06181223690509796, -0.05877961963415146, 0.001323506236076355, -0.0759190171957016, -0.05658703297376633, 0.04817480221390724, 0.015808183699846268, -0.0917045995593071, -0.015902353450655937, 0.008650329895317554, 0.005450794473290443, -0.04196951910853386, 0.0025702319107949734, 0.031217288225889206, 0.009111270308494568, -0.06459704041481018, -0.07051066309213638, 0.04980577528476715, -0.009130467660725117, -0.027147160843014717, 0.0711003765463829, 0.025719234719872475, 0.0060133920051157475, 0.02092762291431427, 0.043023731559515, 0.03144471347332001, 0.017840584740042686, 0.04482350870966911, 0.025163907557725906, -0.06568606942892075, 0.059194114059209824, -0.05345536023378372, -0.013326194137334824, -0.029840894043445587, 0.04962167888879776, -0.008820993825793266, 0.04073576256632805, -0.035124290734529495, -0.008842045441269875, -0.042200252413749695, -0.010934999212622643, -0.05110285058617592, 0.08070671558380127, 0.016811883077025414, -0.006940467748790979, -0.038560524582862854, 0.04387522488832474, -0.019739847630262375, -0.009553398936986923, 0.021769003942608833, 0.024647856131196022, -0.002947181696072221, 0.05614129826426506, -0.010571052320301533, -0.07253822684288025, -0.0018282762030139565, -0.018801920115947723, 0.0025203099939972162, -0.006633390672504902, 0.04596919193863869, -0.012356191873550415, 0.0389086939394474, 0.003931933548301458, 0.04450315609574318, -0.04276430606842041, -0.06095708906650543, -0.020548537373542786, -0.013412886299192905, -0.016103770583868027, 0.01073300652205944, -0.02075977437198162, 0.0001701221044640988, 0.001239207573235035, 0.036957547068595886, 0.0206040907651186, 0.0014220158336684108, -0.07295145094394684, 0.07043764740228653, -0.027449805289506912, -0.005911494605243206, -0.007054738700389862, -0.01914764940738678, 0.01692383922636509, 0.025118298828601837, -0.024452095851302147, 0.020725691691040993, -0.02162068523466587, -0.03411197289824486, -0.05658639594912529, 0.03150920569896698, -0.010463587008416653, 0.016467660665512085, -0.0030583071056753397, -0.019938629120588303, 0.06560736894607544, 0.030630068853497505, 0.05851247161626816, -0.04101308062672615, 0.021313436329364777, 0.010461097583174706, 0.027749311178922653, -0.00363171030767262, -0.046606726944446564, 0.04339095950126648, 0.03279310092329979, -0.03980272263288498, 0.049867406487464905, 0.008837223052978516, 0.009345837868750095, -0.035111311823129654, 0.008170412853360176, -0.0393134206533432, -0.005982792470604181, 0.033102020621299744, -0.08750046789646149, -0.04182878136634827, 0.009984956122934818, 0.005531035829335451, 0.007812161929905415, 0.032703645527362823, 0.014903252013027668, -0.03236081451177597, -0.0034155722241848707, -0.02610996924340725, -0.051077645272016525, -0.0297547597438097, -0.05993447080254555, 0.003773120930418372, 0.05093350633978844, -0.08363793045282364, 0.026048971340060234, -0.01606374979019165, 0.06424236297607422, 0.035522423684597015, -0.006994959898293018, 0.01452302373945713, 0.04616610333323479, -0.010231727734208107, 0.025000134482979774, 0.02555157244205475, 0.0014292243868112564, 0.06587059050798416, 0.039126116782426834, -0.02826644293963909, 0.016692422330379486, -0.025536319240927696, 0.009004528634250164, 0.04384976252913475, 0.0016737827099859715, 0.006747536361217499, -0.007588468957692385, -0.009199608117341995, 0.014401652850210667, 0.07061909139156342, -0.009812586940824986, -0.014836050570011139, -0.049501240253448486, 0.01930299587547779, 0.0017029085429385304, 0.08911797404289246, 0.03128260374069214, -0.012332684360444546, -0.0476687029004097, -0.0019045154331251979, 0.012411560863256454, -0.009106237441301346, -0.020850321277976036, -0.020741023123264313, 0.03334464505314827, 0.04893436282873154, 0.0022186136338859797, 0.05179337039589882, 0.039091262966394424, -0.047542963176965714, -0.019988063722848892, 0.014415530487895012, -0.01148903090506792, 0.014322847127914429, 0.009330294094979763, 0.02393597923219204, 0.05009368434548378, -0.017888350412249565, 0.014936752617359161, 0.027924872934818268, -0.061878006905317307, 0.03704423829913139, 0.012499118223786354, 0.006292737554758787, 0.009022969752550125, 0.02810550294816494, -0.05251305177807808, -0.07370942831039429, 0.003599968971684575, -0.03042192943394184, -0.008925259113311768, 0.016214653849601746, 0.022252459079027176, -0.021495528519153595, 0.055523648858070374, -0.01444937288761139, -0.026943016797304153, -0.02430911362171173, -0.07157512754201889, 0.0037590276915580034, -0.10368671268224716, 0.057630207389593124, -0.04164193198084831, -0.058796226978302, 0.0010116196935996413, 0.01581747457385063, -0.008729394525289536, -0.0318962000310421, -0.006157816853374243, 0.040320634841918945, 0.02811671607196331, -0.005964223761111498, 0.05709867924451828, -0.03466769680380821, -0.008376694284379482, 0.026547281071543694, 0.04710238799452782, 0.041893839836120605, -0.05272169038653374, -0.033336054533720016, 0.0011642836034297943, -0.019194303080439568, -0.0019766101613640785, -0.00843854434788227, 0.0040078903548419476, 0.0032686516642570496, 0.043934013694524765, 0.06886203587055206, 0.06267629563808441, 0.022185245528817177, -0.041604574769735336, -0.015967143699526787, 0.004544623661786318, -0.08013392984867096, 0.06721672415733337, -0.016211137175559998, 0.0944986343383789, -0.05482883006334305, -0.009052546694874763, -0.00360044464468956, -0.08178219944238663, -0.02819843403995037, 0.014694632962346077, -0.0017655816627666354, -0.0033079085405915976, -0.03764684498310089, 0.03865012899041176, -0.01879473589360714, 0.004954103846102953, -0.04621176794171333, -0.048457372933626175, -0.0323982834815979, -0.05058470740914345, -0.032398272305727005, 0.01671605370938778, -0.009021447971463203, -0.01068644504994154, -0.05574691668152809, -0.06311269104480743, 0.08014939725399017, -0.010602708905935287, -0.019222404807806015, 0.06704919040203094, -0.00825110450387001, -0.09012477844953537, -0.03419431298971176, -0.0036831973120570183, 0.004202588927000761, 0.04293258860707283, 0.017178785055875778, -0.05309104174375534, -0.06195308640599251, 0.04819423705339432, -0.012983123771846294, 0.02234058454632759, 0.08510483056306839, 0.01801758073270321, 0.050368066877126694, -0.05750221759080887, -0.0047319731675088406, 0.009183930233120918, 0.017422040924429893, 0.013333716429769993, -0.014950762502849102, -0.025426728650927544, 0.030281979590654373, -0.05226384848356247, 0.023488638922572136, 0.02214263565838337, -0.005657276604324579, 0.013372529298067093, 0.005923525895923376, 0.06148558109998703, 0.0377502404153347, -0.00394664378836751, 0.004383249673992395, 0.0150389913469553, -0.03442980349063873, -0.019488057121634483, 0.060200050473213196, -0.004464719910174608, -0.005280727054923773, 0.012453804723918438, 0.05774610862135887, -0.02628927491605282, 0.0525055006146431, 0.0021565286442637444, 0.0029448759742081165, 0.01990743726491928, 0.0068376678973436356, 0.023394308984279633, 0.01668100617825985, -0.021148687228560448, -0.04356181249022484, -0.014296924695372581, -0.0006577202584594488, 0.05094428360462189, -0.019972417503595352, 0.023770617321133614, 0.006039635743945837, 0.01050126738846302, -0.016071317717432976, 0.08738158643245697, 0.0699969008564949, -0.07909731566905975, -0.004905536770820618, 0.002350721275433898, -0.05569615960121155, -0.055999767035245895, 0.02993927150964737, 0.0366092324256897, 0.06305839121341705, -0.03217301517724991, -0.018471594899892807, 0.028034839779138565, 0.005856362171471119, 0.03645399957895279, 0.0025288844481110573, -0.01162927970290184, -0.00800787191838026, 0.012295114807784557, 0.007296205963939428, 0.030772382393479347, 0.06611596792936325, -0.0030696846079081297, -0.03320619463920593, 0.004888591822236776, -0.048493292182683945, -0.008763556368649006, -5.9832041648900406e-33, 0.0025605326518416405, -0.034435465931892395, -0.05637409910559654, -0.07192890346050262, -0.021174468100070953, 0.0031397456768900156, 0.021808356046676636, 0.017564667388796806, 0.02587788738310337, -0.029935097321867943, 0.005982706788927317, -0.0097914794459939, -0.01907341182231903, -0.046450480818748474, 0.03020375408232212, 0.022305568680167198, -0.009964647702872753, -0.004415879026055336, -0.022829344496130943, 0.06277312338352203, 0.017075106501579285, 0.020700866356492043, -0.01934230700135231, -0.058611903339624405, -0.011188313364982605, 0.025791825726628304, -0.006429453380405903, 0.04652918130159378, 0.030660070478916168, 0.01451241783797741, -0.049889542162418365, 0.014610840938985348, 0.02218545787036419, 0.034078843891620636, 0.02325112745165825, -0.0624832808971405, -0.029895111918449402, 0.0013670617481693625, -0.014917355962097645, 0.032859526574611664, -0.001315812929533422, 0.028790855780243874, 0.026319751515984535, 0.03362196311354637, -0.003198356134817004, -0.03564382344484329, 0.051458653062582016, 0.018337899819016457, -0.04493628442287445, -0.006076468154788017, 0.06496086716651917, 0.027465615421533585, -0.05039972811937332, 0.04951270669698715, 0.019998425617814064, -0.010123062878847122, -0.020608477294445038, 0.017902441322803497, -0.058545418083667755, 0.032163091003894806, -0.009347151964902878, 0.014180540107190609, 0.010909443721175194, -0.03633676469326019, 0.03321722149848938, 0.04224288836121559, 0.04639775678515434, -0.029074804857373238, -0.0005050182808190584, -0.014827548526227474, 0.02168269082903862, 0.0006034888792783022, -0.010020117275416851, 0.020762061700224876, -0.025447197258472443, -0.024820655584335327, -0.029746485874056816, 0.01200090441852808, -0.030892428010702133, -0.022838959470391273, 0.0028002560138702393, 0.024325203150510788, -0.03792968764901161, -0.04835125058889389, 0.021445507183670998, -0.04664912819862366, -0.028470560908317566, -0.0092295678332448, -0.06464865058660507, -0.008419675752520561, -0.0892353281378746, -0.02992185391485691, -0.059280626475811005, 0.001921789487823844, 0.042207613587379456, -0.051149655133485794, 0.00022522997460328043, 0.056737080216407776, 0.05290819704532623, -0.00816468894481659, -0.008913547731935978, -0.06990650296211243, -0.021420201286673546, -0.1011580377817154, -0.007134674582630396, -0.02771439589560032, 0.0022658335510641336, 0.02307562343776226, -0.01973344199359417, -0.002936436329036951, 0.06037577986717224, -0.000961629266384989, 0.02002289518713951, 0.0007937708869576454, -0.013119371607899666, -0.013904226943850517, -0.004089294001460075, 0.06369396299123764, 0.07119984924793243, 0.029764989390969276, 0.018062707036733627, -0.027275441214442253, -0.009526949375867844, 0.004254522733390331, -0.005066532175987959, -0.023768411949276924, -0.01645723730325699, -0.03834622725844383, 0.054629966616630554, -0.02464628592133522, -0.03940312936902046, -0.05684276670217514, 2.636813292156148e-07, -0.009113016538321972, 0.047663118690252304, -0.04308594390749931, -0.049394480884075165, -0.008448930457234383, 0.008325302042067051, -0.006937121041119099, 0.03283485770225525, -0.023195795714855194, 0.01887303777039051, 0.07132101058959961, 0.011505837552249432, 0.010853159241378307, -0.02374603971838951, -0.006343374960124493, 0.024033185094594955, -0.06177355349063873, 0.016780035570263863, -0.039703305810689926, -0.049827709794044495, -0.02496299333870411, 0.021861908957362175, 0.043330296874046326, 0.019493181258440018, 0.02652731165289879, -0.03761684522032738, 0.01341920904815197, -0.04468692094087601, 0.025259792804718018, 0.010648522526025772, 0.058192551136016846, -0.03697587177157402, -0.014737799763679504, -0.012167368084192276, 0.021666143089532852, 0.0168150644749403, 0.01123772282153368, -0.01720399223268032, 0.027075253427028656, 0.0402304045855999, 0.041731588542461395, 0.03110574372112751, 0.004566885996609926, -0.04759342595934868, 0.05234261974692345, 0.035597946494817734, 0.004905122797936201, -0.031249867752194405, -0.03314533457159996, 0.0035560105461627245, 0.0008290210389532149, 0.018541822209954262, 0.015750762075185776, 0.043425753712654114, 0.028914907947182655, -0.040952835232019424, 0.1034575030207634, 0.01366922352463007, 0.051720667630434036, 0.06934266537427902, -0.008257954381406307, -0.015024510212242603, 0.07435765862464905, 0.058654654771089554, 0.03706071525812149, 0.05063535273075104, 0.013099065981805325, 2.0671015353799635e-34, -0.0031605775002390146, 0.03193572536110878, 0.0013162437826395035, 0.0001385009236400947, -0.03831494227051735, -0.026383547112345695, -0.06886972486972809, -0.017869019880890846, -0.007727844640612602, -0.037365786731243134, -0.02491675689816475]

['Adam Tauman Kalai', 'Shang-Hua Teng']

0812.0933v1

We consider the problem of PAC-learning decision trees, i.e., learning a decision tree over the n-dimensional hypercube from independent random labeled examples. Despite significant effort, no polynomial-time algorithm is known for learning polynomial-sized decision trees (even trees of any super-constant size), even when examples are assumed to be drawn from the uniform distribution on {0,1}^n. We give an algorithm that learns arbitrary polynomial-sized decision trees for {\em most product distributions}. In particular, consider a random product distribution where the bias of each bit is chosen independently and uniformly from, say, [.49,.51]. Then with high probability over the parameters of the product distribution and the random examples drawn from it, the algorithm will learn any tree. More generally, in the spirit of smoothed analysis, we consider an arbitrary product distribution whose parameters are specified only up to a [-c,c] accuracy (perturbation), for an arbitrarily small positive constant c.

Decision trees are PAC-learnable from most product distributions: a smoothed analysis

http://arxiv.org/pdf/0812.0933v1

Title Decision tree PAClearnable product distribution smoothed analysis Summary consider problem PAClearning decision tree ie learning decision tree ndimensional hypercube independent random labeled example Despite significant effort polynomialtime algorithm known learning polynomialsized decision tree even tree superconstant size even example assumed drawn uniform distribution 01n give algorithm learns arbitrary polynomialsized decision tree em product distribution particular consider random product distribution bias bit chosen independently uniformly say 4951 high probability parameter product distribution random example drawn algorithm learn tree generally spirit smoothed analysis consider arbitrary product distribution whose parameter specified cc accuracy perturbation arbitrarily small positive constant c Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.021885311231017113, -0.020260335877537727, -0.02572735957801342, 0.020465144887566566, -0.011316363699734211, -0.043275292962789536, -0.007310749031603336, 0.0009893638780340552, -0.05204666405916214, -0.025379491969943047, 0.06287685036659241, 0.028670815750956535, 0.025390159338712692, 0.022948650643229485, -0.013003816828131676, -0.03267828747630119, 0.00924144871532917, -0.019575804471969604, 0.03416501730680466, -0.020480308681726456, 0.010487323626875877, -0.03021976910531521, -0.008301906287670135, -0.01142739038914442, -0.09815552830696106, -0.05948016047477722, -0.005603258963674307, -0.001555846305564046, 0.0017277600709348917, -0.008734767325222492, 0.032470088452100754, 0.007697828114032745, -0.048967402428388596, -0.0032045263797044754, 2.27047894441057e-06, -0.028045520186424255, -0.029954614117741585, -0.008823649026453495, 0.0030348191503435373, 0.06197597086429596, 0.021557796746492386, 0.1019158735871315, -0.007755441125482321, -0.02438906393945217, -0.028910771012306213, -0.023487167432904243, 0.023910319432616234, 0.03502373397350311, -0.02513289637863636, 0.005651658400893211, -0.021081596612930298, -0.013059305027127266, 0.015562495216727257, -0.0075644636526703835, 0.04865841194987297, -0.05361253768205643, 0.02155807800590992, -0.043443188071250916, -0.023692920804023743, -0.028558356687426567, -0.03005056641995907, 0.018831493332982063, 0.015561303123831749, -0.015447879210114479, 0.023686446249485016, 0.042826030403375626, -0.014627589844167233, 0.033794041723012924, -0.04028653725981712, 0.06225714832544327, -0.0705590546131134, 0.00341601250693202, -0.02286895178258419, -0.03221682086586952, 0.01458755787461996, 0.03296450525522232, -0.03033832088112831, 0.03159335255622864, -0.0447915643453598, -0.008160029537975788, -0.02693861350417137, 0.027299590408802032, -0.010363592766225338, 0.008901654742658138, 0.00616467697545886, 0.11640142649412155, -0.01805141009390354, -0.010942908935248852, 0.03742288053035736, -0.039532292634248734, -0.022286389023065567, -0.04453454166650772, -0.011073979549109936, -0.007695084437727928, -0.01587410271167755, -0.008912945166230202, 0.05327301099896431, 0.019731344655156136, 0.0239400751888752, -0.026579806581139565, 0.009017137810587883, -0.03586486726999283, -0.0105277169495821, 0.01610242947936058, -0.017188839614391327, 0.012272000312805176, -0.009015968069434166, 0.04397460073232651, -0.01003335602581501, 0.08626354485750198, -0.0016269130865111947, 0.003391257720068097, -0.004190996754914522, 0.09771575033664703, -0.026947902515530586, -0.015993723645806313, -0.0708240494132042, 0.02975161001086235, -0.01829012669622898, -0.02771025523543358, 0.05913207679986954, 0.05742767080664635, 0.010025554336607456, 0.02201770804822445, -0.01766020618379116, 0.010199358686804771, -0.03260704129934311, 0.028565632179379463, -0.020679863169789314, 0.033367712050676346, 0.026051731780171394, 0.033755823969841, 0.005450642667710781, 0.01660880446434021, 0.007317954674363136, 0.033940766006708145, -0.006356514524668455, -0.015154565684497356, -0.06149709224700928, 0.022577442228794098, -0.05855796858668327, 0.03660953417420387, -0.02192126214504242, -0.056802570819854736, -0.027589894831180573, -0.0535123236477375, 0.00518333725631237, 0.017058907076716423, -0.022955024614930153, -0.043779365718364716, -0.031583596020936966, 0.04579232260584831, 0.029784075915813446, 0.011323409155011177, 0.0777718722820282, -0.01849280297756195, -0.01390532311052084, 0.0248431246727705, 0.03073856048285961, 0.03701154515147209, 0.015711260959506035, -0.01792353019118309, 0.023076552897691727, -0.01952262781560421, -0.03485291078686714, -0.046339504420757294, -0.017689332365989685, -0.03820177912712097, -0.04220737889409065, 0.005301595199853182, 0.0014908716548234224, -0.01624126359820366, -0.036308079957962036, -0.06919361650943756, 0.03644784539937973, 0.0187225304543972, -0.01191909983754158, -0.015459933318197727, -0.003643808187916875, 0.0006322393310256302, 0.00914109218865633, 0.028576966375112534, -0.006711467169225216, -0.005384301766753197, -0.05092950910329819, -0.018930891528725624, -0.04873330146074295, -0.020840682089328766, -0.030597830191254616, -0.051770925521850586, 0.01880880631506443, -0.02205604687333107, -0.026698589324951172, -0.03413340821862221, 0.013739054091274738, -0.01850058324635029, -0.005207414273172617, 0.02909880131483078, 0.04534117504954338, 0.02838416025042534, -0.05736982449889183, -0.011925174854695797, 0.07544577866792679, -0.04117664322257042, -0.0330570712685585, -0.08384661376476288, 0.04120798036456108, 0.030438845977187157, -0.010186259634792805, -0.041751738637685776, -0.012709042057394981, -0.03357073292136192, 0.03503941372036934, 0.0031487648375332355, -0.022664548829197884, -0.0023482670076191425, 0.035146865993738174, 0.06201405078172684, -0.028735779225826263, -0.03584597259759903, -0.007001839112490416, 0.00731309037655592, 0.011661514639854431, -0.027972698211669922, 0.04133027791976929, -0.012678493745625019, 0.1030273362994194, 0.007953974418342113, -0.009465363807976246, 0.014208126813173294, -0.00616829888895154, -0.02884499728679657, 0.03906704857945442, -0.012076827697455883, -0.07226332277059555, 0.0009876653784886003, 0.052425410598516464, -0.03436817601323128, 0.021557848900556564, -0.032751716673374176, 0.009484569542109966, 0.0021339531522244215, -0.012708750553429127, -0.02876961976289749, -0.020434606820344925, -0.017781607806682587, 0.027955830097198486, -0.02158512733876705, 0.036722827702760696, 0.0027940385043621063, -0.0005630523664876819, -0.030716240406036377, 0.040170542895793915, 0.0021675152238458395, 0.03273213282227516, -0.02547152154147625, -0.02970425970852375, 0.06995167583227158, -0.02171379141509533, 0.059001315385103226, 0.034020062536001205, -0.06777995079755783, -0.0031377600971609354, -0.00041162202251143754, 0.018409905955195427, 0.01928074285387993, -0.016276925802230835, 0.026588909327983856, 0.013081974349915981, 0.011648658663034439, 0.02122781239449978, -0.025985300540924072, 0.004997441545128822, -0.013868848793208599, -0.031130561605095863, -0.030497558414936066, 0.05205848813056946, -0.04901532456278801, -0.02836386300623417, 0.022360989823937416, -0.010957373306155205, -0.0044367508962750435, 0.0170315932482481, -0.03053593449294567, 0.018224036321043968, 0.03444387763738632, 0.03976383060216904, -0.04871171712875366, 0.010076777078211308, 0.02305278554558754, -0.02494431659579277, -0.02015295997262001, -0.003789575770497322, 0.022466395050287247, -0.056368906050920486, -0.01581656001508236, -0.007722211070358753, 0.0572330541908741, -0.008878081105649471, -0.029187968000769615, 0.0035854263696819544, 0.03465818986296654, -0.0345383957028389, -0.00872245617210865, -0.006939269602298737, -0.03235865384340286, 0.020289791747927666, 0.02589366026222706, 0.004629838280379772, 0.05953650176525116, -0.00531525444239378, -0.04544062539935112, 0.021679503843188286, -0.039715223014354706, -0.003713499289005995, -0.026734188199043274, -0.0281642135232687, -0.013031503185629845, -0.0006849413621239364, 0.022178493440151215, -0.015496736392378807, -0.09150255471467972, 0.03034910559654236, 0.0068353828974068165, 0.02452434040606022, -0.03782108798623085, -0.05567376688122749, -0.01352103240787983, -0.021892957389354706, 0.026243792846798897, 0.008456685580313206, -0.09444132447242737, -0.05765242874622345, -0.014809195883572102, 0.03960001841187477, 0.01652461104094982, -0.021521111950278282, -0.02747810259461403, 0.00024510995717719197, 0.01620187796652317, 0.01584632135927677, -0.02458827942609787, 0.03356029838323593, -0.0785544365644455, 0.0767669603228569, -0.011095752939581871, 0.07248497009277344, -0.021402794867753983, 0.011550706811249256, -0.015179533511400223, -0.02905731089413166, 0.04155349358916283, -0.033361151814460754, -0.05894577503204346, 0.007250444032251835, 0.05831572413444519, 0.025667183101177216, -0.0374683141708374, -0.03774337098002434, 0.009608287364244461, -0.008286883123219013, -0.011415509507060051, 0.02666042000055313, 0.08349582552909851, -0.018516715615987778, 0.05088634788990021, -0.007788457442075014, -0.02862352691590786, 0.0002916112425737083, 0.04502788931131363, -0.004980557598173618, 0.03772982209920883, 0.07613053917884827, 0.03143354505300522, 0.010472288355231285, -0.06493504345417023, -0.00047976727364584804, -0.001531612710095942, -0.008743532001972198, 0.003024882636964321, -0.031166594475507736, -0.0428600050508976, 0.0038755994755774736, -0.04336312785744667, 0.009998016059398651, -0.0031203744001686573, -0.045649006962776184, 0.03691964969038963, -0.10893154889345169, -0.009694980457425117, -0.018828222528100014, -0.026460692286491394, -0.0172907542437315, -0.0033242146018892527, -0.005194519646465778, -0.04771948978304863, -0.03082411363720894, -0.03336411342024803, -0.0027221287600696087, -0.026564594358205795, 0.05948652699589729, -0.030857114121317863, -0.044064924120903015, 0.009903522208333015, -0.048177678138017654, -0.047775108367204666, -0.03035249561071396, 0.013404246419668198, -0.05381548032164574, 0.00551873492076993, 0.008393530733883381, 0.014705040492117405, -0.0050127399154007435, -0.0022314724046736956, 0.06469449400901794, 0.034443870186805725, 0.024869641289114952, 0.025344284251332283, 0.019488254562020302, 0.04662412405014038, 0.05458354577422142, 0.05265360325574875, 0.06090163439512253, 0.051918450742959976, -0.06633966416120529, -0.014028306119143963, -0.04367056116461754, 0.03656550496816635, -0.022900518029928207, -0.025483056902885437, -0.0030006070155650377, -0.03621799126267433, -0.04814649373292923, -0.011721349321305752, 0.06325428187847137, 0.0367758683860302, 0.08647985011339188, -0.003878974821418524, -0.06271982192993164, -0.0929175615310669, 0.062196653336286545, -0.003200023900717497, 0.061221521347761154, 0.010551206767559052, -0.018105830997228622, -0.0114375539124012, 0.02946999855339527, 0.022522281855344772, -0.02041720040142536, 0.07046747207641602, 0.05006681755185127, 0.00855419971048832, 0.048365700989961624, 0.03773373365402222, 0.03293801099061966, -0.051179394125938416, -0.01863347738981247, 0.008455305360257626, -0.049131326377391815, -0.037972066551446915, 0.049379900097846985, 0.021739911288022995, -0.012423580512404442, -0.034364521503448486, -0.029650822281837463, 0.017828261479735374, 0.0759834498167038, -0.0044069369323551655, -0.002781463321298361, 0.0354086272418499, -0.027519162744283676, -0.02282118611037731, 0.014788190834224224, 0.0017070642206817865, 0.08216598629951477, 0.0019644538406282663, -0.025422394275665283, -0.024342751130461693, -0.11374460905790329, 0.022851407527923584, 0.006770196370780468, 0.014207364991307259, 0.05430486053228378, 0.008250522427260876, -0.024839144200086594, 0.10823758691549301, 0.047504622489213943, -0.016300642862915993, 0.010333684273064137, 0.0023852128069847822, 0.04711002856492996, -0.031839583069086075, 0.012279062531888485, -0.038066741079092026, 0.04552045464515686, -0.007195456884801388, 0.009277976118028164, -0.040516749024391174, 0.0013873931020498276, 0.010242721065878868, -0.030818555504083633, -0.021031808108091354, 0.03981737419962883, -0.038604479283094406, 0.012097323313355446, 0.0057794805616140366, 0.05808650702238083, 0.051993392407894135, -0.03307854384183884, -0.00829711277037859, -0.02834523469209671, -0.07002770900726318, -0.03990873321890831, -0.030177144333720207, -0.025258714333176613, -0.0012228924315422773, 0.02376982569694519, -0.020239999517798424, -0.00539798429235816, -0.027880653738975525, -0.03290647640824318, -0.023426784202456474, 0.008028619922697544, -0.00966616440564394, 0.0572863407433033, 0.023869797587394714, 0.01949421875178814, -0.03218866512179375, 0.009468823671340942, 0.05487445741891861, 0.05846482515335083, -0.015924982726573944, -0.06764945387840271, -0.02397049404680729, -0.010822655633091927, 0.008645564317703247, 0.016307411715388298, 0.07470420747995377, 0.007686746772378683, 0.017140133306384087, -0.03157925605773926, -0.01816083863377571, -0.010341332294046879, 0.02246248722076416, 0.1363276094198227, -0.00897061824798584, 0.00386103056371212, 0.04589797183871269, -0.037755709141492844, 0.026135943830013275, -0.01076264213770628, -0.01827956549823284, -0.03241484984755516, 0.05461868643760681, -0.08549881726503372, -5.629880685075601e-33, 0.012028349563479424, -0.003095003077760339, -0.06980395317077637, 0.048830993473529816, -2.4125194613588974e-05, 0.03119431436061859, 0.029864322394132614, 0.011832761578261852, 0.05353628471493721, 0.03277672454714775, -0.0016391129465773702, -0.0037132399156689644, -0.001261647674255073, 0.03457129746675491, 0.029340483248233795, -0.030724115669727325, -0.01707494631409645, 0.01119676697999239, -0.010497181676328182, 0.03379402682185173, 0.019685544073581696, 0.013409855775535107, -6.437343108700588e-05, -0.020400144159793854, -0.030371857807040215, 0.07028024643659592, 0.004104092717170715, 0.01838517002761364, -0.045321136713027954, 0.05447391793131828, 0.026662206277251244, 0.04642272740602493, 0.0027962508611381054, -0.015574117191135883, -0.012159843929111958, -0.02788427472114563, -0.0017544043948873878, -0.026568042114377022, -0.033017080277204514, -0.018868915736675262, -0.004900234751403332, 0.01838097721338272, 0.05606060102581978, 0.02146434225142002, -0.0003384395968168974, -0.030966587364673615, 0.06387589126825333, -0.03655250370502472, -0.06867518275976181, -0.07305474579334259, 0.053981486707925797, 0.0417504645884037, -0.029324514791369438, 0.04000401869416237, 0.0047732628881931305, 0.005395873449742794, -0.001218703924678266, 0.03482012078166008, 0.024251610040664673, 0.04996244236826897, 0.025786789134144783, 0.03029578924179077, -0.0025253731291741133, -0.0335734486579895, 0.02395370602607727, 0.015254952944815159, 0.01612023636698723, -0.004854234866797924, 0.014156751334667206, -0.07606835663318634, -0.05956422910094261, 0.04008500650525093, -0.0012465696781873703, 0.015494626946747303, 0.07884279638528824, -0.03205832466483116, -0.04672295227646828, 0.06558780372142792, 0.0273627620190382, -0.022635309025645256, -0.022771712392568588, -0.008447768166661263, -0.01828262209892273, -0.01957428641617298, 0.021538367494940758, 0.025046562775969505, 0.002937570447102189, 0.01374900434166193, 0.007198181003332138, 0.017329281195998192, 0.029825543984770775, 0.043268587440252304, -0.04951035976409912, -0.011877056211233139, -0.02870156057178974, -0.0026587743777781725, -0.005169258452951908, 0.07821134477853775, -0.008453065529465675, -0.04027518630027771, 0.01698366366326809, -0.03434979170560837, -0.059791237115859985, -0.022926002740859985, 0.010701064951717854, 0.018196936696767807, 0.01849513314664364, 0.012976855970919132, -0.03213360160589218, -0.005982577800750732, 0.042248159646987915, -0.06379591673612595, -0.007915711961686611, 0.056899990886449814, 0.03489052131772041, -0.04124064743518829, -0.026925530284643173, 0.010579266585409641, 0.003929427824914455, 0.05150290206074715, 0.004578208550810814, -0.002670680172741413, -0.04910968616604805, -0.022228512912988663, -0.03230351209640503, 0.02696753479540348, -0.015467342920601368, -0.02150445245206356, 0.004462356213480234, -0.053731877356767654, 0.0018216364551335573, -0.029672781005501747, 2.7562529680835723e-07, -0.0010589580051600933, 0.008243651129305363, -0.03904523700475693, 0.0026803412474691868, 0.0634334534406662, -0.02504643425345421, -0.028430437669157982, 0.002150688087567687, -0.011461094953119755, -0.07969047874212265, 0.029437463730573654, -0.06597208976745605, 0.0340244397521019, -0.026421552523970604, -0.09160389751195908, -0.05720019340515137, -0.014155978336930275, 0.059700530022382736, -0.04159081354737282, 0.003520563244819641, 0.014283232390880585, 0.0658041462302208, 0.04826189950108528, -0.04488396644592285, 0.016206979751586914, 0.013964426703751087, 0.00028528974507935345, -0.045500773936510086, 0.060181133449077606, 0.004892060533165932, 0.05117527022957802, -0.04435350373387337, 0.019074639305472374, 0.06387275457382202, 0.000395104376366362, 0.051882825791835785, 0.02695685625076294, 0.07550670206546783, 0.012712846510112286, 0.0675070509314537, 0.03431474789977074, -0.0008779592462815344, 0.02921600081026554, -0.029259691014885902, 0.05234312266111374, -0.050891563296318054, -0.02019253745675087, -0.014592473395168781, -0.001097348751500249, 0.0027390215545892715, 0.046253837645053864, 0.0008412220631726086, 0.023359572514891624, 0.024960847571492195, -0.05481317639350891, -0.019829630851745605, 0.08107160031795502, 0.029138119891285896, 0.03705678507685661, 0.08590061217546463, -0.01542934775352478, -0.06325063109397888, 0.016977306455373764, 0.04848174378275871, 0.029253829270601273, -0.031209228560328484, 0.011305487714707851, 2.6720545501737877e-34, 0.012717864476144314, 0.019479218870401382, 0.038886625319719315, -0.008691312745213509, -0.01381430309265852, -0.019611628726124763, 0.06774882972240448, -0.05181707441806793, 0.013322794809937477, -0.03931788355112076, -0.007251021917909384]

['Alaa Abi-Haidar', 'Jasleen Kaur', 'Ana G. Maguitman', 'Predrag Radivojac', 'Andreas Retchsteiner', 'Karin Verspoor', 'Zhiping Wang', 'Luis M. Rocha']

0812.1029v1

We participated in three of the protein-protein interaction subtasks of the Second BioCreative Challenge: classification of abstracts relevant for protein-protein interaction (IAS), discovery of protein pairs (IPS) and text passages characterizing protein interaction (ISS) in full text documents. We approached the abstract classification task with a novel, lightweight linear model inspired by spam-detection techniques, as well as an uncertainty-based integration scheme. We also used a Support Vector Machine and the Singular Value Decomposition on the same features for comparison purposes. Our approach to the full text subtasks (protein pair and passage identification) includes a feature expansion method based on word-proximity networks. Our approach to the abstract classification task (IAS) was among the top submissions for this task in terms of the measures of performance used in the challenge evaluation (accuracy, F-score and AUC). We also report on a web-tool we produced using our approach: the Protein Interaction Abstract Relevance Evaluator (PIARE). Our approach to the full text tasks resulted in one of the highest recall rates as well as mean reciprocal rank of correct passages. Our approach to abstract classification shows that a simple linear model, using relatively few features, is capable of generalizing and uncovering the conceptual nature of protein-protein interaction from the bibliome. Since the novel approach is based on a very lightweight linear model, it can be easily ported and applied to similar problems. In full text problems, the expansion of word features with word-proximity networks is shown to be useful, though the need for some improvements is discussed.

Uncovering protein interaction in abstracts and text using a novel linear model and word proximity networks

http://arxiv.org/pdf/0812.1029v1

Title Uncovering protein interaction abstract text using novel linear model word proximity network Summary participated three proteinprotein interaction subtasks Second BioCreative Challenge classification abstract relevant proteinprotein interaction IAS discovery protein pair IPS text passage characterizing protein interaction ISS full text document approached abstract classification task novel lightweight linear model inspired spamdetection technique well uncertaintybased integration scheme also used Support Vector Machine Singular Value Decomposition feature comparison purpose approach full text subtasks protein pair passage identification includes feature expansion method based wordproximity network approach abstract classification task IAS among top submission task term measure performance used challenge evaluation accuracy Fscore AUC also report webtool produced using approach Protein Interaction Abstract Relevance Evaluator PIARE approach full text task resulted one highest recall rate well mean reciprocal rank correct passage approach abstract classification show simple linear model using relatively feature capable generalizing uncovering conceptual nature proteinprotein interaction bibliome Since novel approach based lightweight linear model easily ported applied similar problem full text problem expansion word feature wordproximity network shown useful though need improvement discussed Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.05675117298960686, 0.002017195336520672, 0.0034536204766482115, -0.00861004926264286, -0.03156363591551781, -0.007500193081796169, 0.016156036406755447, 0.032721661031246185, 0.04132937639951706, -0.04392758756875992, -0.00853084959089756, 0.02153579704463482, 0.059303492307662964, 0.08648006618022919, -0.016322392970323563, 0.030540108680725098, 0.02319975756108761, 0.07246406376361847, 0.0023158988915383816, 0.019054222851991653, 0.02627340517938137, -0.0003157815954182297, 0.01830408163368702, 0.014858213253319263, 0.026499178260564804, -0.0056495824828743935, -0.011139445938169956, -0.058759771287441254, 0.0446447916328907, -0.03829954192042351, -0.009361072443425655, 0.03327926620841026, 0.023530131205916405, 0.008866175077855587, 2.3989191504369956e-06, -0.07429960370063782, -0.0301717109978199, 0.018572499975562096, 0.014267330057919025, 0.0010461326455697417, 0.006519692484289408, -0.006362768821418285, 0.035173848271369934, 0.024166977033019066, 0.017622267827391624, 0.01628980040550232, 0.07239749282598495, 0.05745643377304077, -0.016100209206342697, 0.00690231891348958, -0.01832979917526245, -0.0417073555290699, 0.04442931339144707, -0.015975894406437874, 0.06592239439487457, -0.017751410603523254, 0.057827915996313095, -0.004641411826014519, 0.0006448469939641654, -0.012075751088559628, 0.003819934092462063, 0.024265842512249947, -0.042713794857263565, -0.018043188378214836, 0.06337931752204895, 0.07795709371566772, 0.03162958100438118, -0.06246734410524368, 0.02498333714902401, 0.02657976560294628, -0.0018466153414919972, -0.020465809851884842, -0.024124158546328545, 0.0029242851305752993, -0.020068902522325516, 0.0621546134352684, 0.005420058965682983, -0.05273430049419403, -0.01769052818417549, 0.03491970896720886, -0.007174031808972359, 0.007060418836772442, 0.017982734367251396, 0.010037273168563843, 0.016835356131196022, -0.0045547871850430965, -0.024232208728790283, -0.01867865025997162, -0.02118287794291973, -0.04425540193915367, -0.01697140373289585, -0.022629739716649055, 0.05704732984304428, 0.0032802291680127382, 0.026155520230531693, -0.017591550946235657, 0.045555390417575836, -0.07456371933221817, 0.09386385232210159, -0.08737156540155411, -0.002579235006123781, -0.02112971432507038, 0.005175142083317041, 0.02320115827023983, 0.001203264924697578, -0.02850070223212242, 0.009161100722849369, -0.008050153963267803, 0.007550740148872137, 0.08460510522127151, -0.05494256690144539, -0.003674125764518976, -0.006887787953019142, 0.03301098197698593, 0.005842642858624458, -0.06146086007356644, -0.0392058789730072, 0.009918543510138988, 0.0013521291548386216, 0.007527658250182867, -0.010474867187440395, 0.05370476841926575, 0.0008042624103836715, 0.03496765345335007, -0.021541371941566467, 0.006539169233292341, -0.0015324619598686695, -0.0003247415297664702, -0.040334176272153854, 0.01113409735262394, 0.0054107061587274075, -0.016470281407237053, 0.03304242715239525, -0.004754263442009687, -0.005715549923479557, 0.12169333547353745, -0.03435083478689194, -0.036672238260507584, -0.012204036116600037, -0.027793556451797485, -0.014748157933354378, 0.001748688635416329, -0.06812572479248047, -0.03351960703730583, 0.07946313917636871, 0.006935652811080217, -0.04909296706318855, 0.010737267322838306, 0.014019845053553581, -0.01684741862118244, -0.05630424991250038, 0.09574169665575027, -0.04240412637591362, 0.014977297745645046, 0.060921452939510345, 0.015102541074156761, 0.04448328912258148, -0.07898183912038803, 0.012246747501194477, 0.006028651725500822, 0.013085013255476952, -0.020598609000444412, -0.009198087267577648, -0.04859652370214462, -0.014798558317124844, -0.05715738609433174, 0.017235079780220985, 0.018298262730240822, 0.058638595044612885, 0.006882925517857075, -0.056069515645504, -0.01984591595828533, 0.00012567138765007257, -0.014281139709055424, 0.059864941984415054, 0.09999928623437881, 0.0030280984938144684, 0.03874198719859123, -0.02769697830080986, 0.07249919325113297, 0.0002509324694983661, 0.02020266093313694, -0.003551746951416135, 0.015583807602524757, -0.07488229125738144, 0.0187600739300251, 0.03242170810699463, 0.00540507584810257, 0.027147989720106125, -0.048281699419021606, -0.025763843208551407, -0.01878713257610798, 0.050689946860075, -0.06933462619781494, 0.023519311100244522, -0.027497051283717155, -0.0384400300681591, -0.023223012685775757, 0.05153854563832283, -0.026702426373958588, -0.002765200799331069, 0.0030968603678047657, 0.011755134910345078, 0.0027476949617266655, 0.03488973155617714, -0.06327236443758011, 0.004383784253150225, -0.030398648232221603, -0.03160453587770462, 0.02789423055946827, -0.026437781751155853, -0.01129075326025486, -0.014213364571332932, -0.00942576676607132, 0.045029278844594955, 0.017589395865797997, 0.019305754452943802, 0.000977984513156116, -0.04725905880331993, 0.047572143375873566, 0.001544747850857675, 0.044761963188648224, -0.011175869032740593, 0.027130937203764915, 0.005630317609757185, -0.007403736002743244, -0.012175249867141247, 0.03809376806020737, 0.016653958708047867, 0.016001731157302856, 0.025754572823643684, 0.040403321385383606, 0.05821067467331886, -0.04430543631315231, -0.06955788284540176, -0.035538073629140854, 0.06727320700883865, 0.014891612343490124, -0.004507849458605051, 0.048238132148981094, 0.023588569834828377, -0.010799308307468891, -0.03800898417830467, -0.004484433680772781, 0.032922085374593735, -0.007490965072065592, 0.0552540048956871, 0.015259485691785812, 0.011265257373452187, -0.010453769937157631, 0.02435595914721489, -0.04650764912366867, 0.018334634602069855, 0.023241333663463593, 0.04171294718980789, -0.025542771443724632, -0.024075882509350777, 0.03758390620350838, -0.001234545256011188, 0.044874437153339386, -0.003169548697769642, -0.021287238225340843, 0.006687617395073175, 0.044566426426172256, -0.011579637415707111, -0.034928955137729645, -0.024501925334334373, 0.027380941435694695, -0.009810592979192734, 0.06567993015050888, 0.058941978961229324, -0.010277565568685532, -0.0304497629404068, 0.03399784862995148, 0.009521384723484516, -0.039169423282146454, 0.030146759003400803, -0.03501475602388382, -0.00650608679279685, 0.05203685909509659, 0.037847451865673065, -0.008851851336658001, -0.04600857198238373, -0.007980081252753735, -0.04257895052433014, 0.06994932144880295, 0.0704389438033104, -0.11466147750616074, 0.03935565799474716, 0.0477435439825058, -0.02467378042638302, 0.017447948455810547, 0.011255193501710892, -0.04360323026776314, 0.002653389470651746, 0.025230376049876213, -0.0080832839012146, 0.02082633040845394, 0.01851138472557068, -0.01164060179144144, 0.06538143754005432, 0.024369418621063232, 0.001596649643033743, -0.002537847962230444, -0.039365485310554504, 0.042067963629961014, -0.008557939901947975, -0.031831420958042145, -0.014956751838326454, 0.05524564906954765, 0.02146398462355137, -0.000776643049903214, -0.02986697480082512, 0.026532448828220367, 0.057852987200021744, 0.0221408624202013, -0.03187810257077217, -0.05879904702305794, -0.004372386261820793, -0.008099999278783798, 0.023274976760149002, -0.006355744320899248, 0.05176171287894249, -0.009226594120264053, 0.046371761709451675, -0.06336932629346848, -0.014961839653551579, 0.04073890671133995, 0.02581758238375187, 0.006330525502562523, 0.03414645045995712, -0.008013005368411541, -0.028445415198802948, 0.03316939249634743, -0.007493780460208654, 0.02992282062768936, -0.02950933203101158, 0.02733948640525341, 0.023433422669768333, -0.021017979830503464, -0.014678645879030228, -0.017281970009207726, -0.010316827334463596, 0.09934374690055847, 0.005734751001000404, -0.004759122617542744, 0.057351741939783096, -0.0509197898209095, -0.01210843026638031, 0.05940394103527069, -0.025436095893383026, -0.022705188021063805, -0.030215486884117126, 0.0013994135661050677, -0.013722519390285015, 0.0367540679872036, 0.012485609389841557, -0.07856415957212448, -0.03221004828810692, 0.02254549413919449, 0.04703853279352188, 0.033977165818214417, -0.07355839759111404, -0.0419313982129097, -0.00943481270223856, -0.025696812197566032, -0.01572633534669876, -0.021876944229006767, 0.0025476093869656324, -0.028001749888062477, -0.023194657638669014, -0.018198853358626366, 0.006919903215020895, 0.05371413379907608, 0.056683249771595, -0.07854107022285461, -0.007071675732731819, -0.04052402824163437, -0.09883300215005875, -0.018292509019374847, 0.04944369196891785, -0.005082224030047655, 0.012210042215883732, -0.030654849484562874, -0.03315051272511482, -0.048773109912872314, -0.05840488523244858, -0.02117072232067585, 0.014893796294927597, 0.008555491454899311, 0.004838036373257637, -0.07424123585224152, -0.029634572565555573, -0.1193709447979927, -0.018839022144675255, -0.039084747433662415, -0.022394053637981415, 0.0012316374341025949, 0.007715435698628426, 0.013586114160716534, -0.011382617056369781, -0.047037817537784576, -0.03664448857307434, 0.014079579152166843, -0.029901577159762383, -0.0024059410206973553, 0.004081741441041231, 0.07649437338113785, -0.00747688626870513, -0.007441076450049877, 0.03476138412952423, -0.02222461812198162, 0.012022220529615879, -0.06739751994609833, 0.095936119556427, 0.016301080584526062, 0.014620528556406498, -0.0519721582531929, 0.017208881676197052, -0.001075725071132183, -0.043541908264160156, -0.03669712319970131, 0.043766267597675323, -0.009578682482242584, -0.020711416378617287, -0.059464506804943085, 0.016355322673916817, -0.03531075641512871, 0.002896284218877554, 0.02250601537525654, -0.04108307138085365, -0.04119940474629402, 0.05109281837940216, 0.03185505419969559, 0.01974642463028431, 0.004789430648088455, -0.03935893625020981, -0.029370125383138657, -0.046206939965486526, -0.06873544305562973, -0.01667475327849388, 0.020984089002013206, -0.001770155387930572, 0.024032915011048317, 0.09215042740106583, -0.03256614878773689, -0.05157546326518059, -0.028922194615006447, 0.008303617127239704, 0.11658412963151932, 0.032836612313985825, 0.008284649811685085, 0.01958068273961544, 0.03876090422272682, 0.015367791056632996, -0.048901282250881195, -0.012225871905684471, -0.026029562577605247, -0.07372639328241348, -0.0637640431523323, -0.02612907439470291, 0.013341174460947514, 0.025245867669582367, -0.012180835008621216, -0.05692625045776367, -0.007607287727296352, 0.03921544924378395, 0.00896194763481617, -0.039857134222984314, -0.011759575456380844, -0.005187086760997772, -0.01270317193120718, -0.006563820876181126, 0.0010240798583254218, 0.021946905180811882, 0.018751567229628563, -0.04351314902305603, 0.021521219983696938, -0.05847356840968132, 0.0457659475505352, 0.0073693059384822845, 0.048622388392686844, 0.0412326417863369, -0.029226481914520264, -0.05173742026090622, 0.02057374268770218, -0.005410349927842617, -0.009134692139923573, -0.003981131594628096, -0.030394786968827248, 0.02962489053606987, 0.05790933966636658, -0.002422800986096263, -0.036479853093624115, -0.04015225172042847, 0.0004819845489691943, 0.010420096106827259, 0.04672139510512352, 0.008614655584096909, 0.0313110277056694, 0.03086879476904869, -0.016367271542549133, -0.030813800171017647, -0.06304856389760971, -0.010375984944403172, 0.009101788513362408, -0.02026439644396305, 0.006823277100920677, -0.0017903299303725362, 0.024320080876350403, -0.04003755375742912, 0.026819493621587753, -0.00403064489364624, 0.03170949965715408, -0.0463516004383564, -0.037179674953222275, -0.000729832798242569, -0.03875915706157684, 0.008376712910830975, 0.01201639324426651, 0.009225345216691494, -0.027009451761841774, 0.034114938229322433, -0.053552139550447464, 0.017573509365320206, 0.07085632532835007, 0.019330637529492378, -0.016301210969686508, -0.02239121124148369, 0.049703121185302734, -0.0004862699133809656, -0.015751583501696587, -0.023434922099113464, -0.09260726720094681, 0.03161090239882469, 0.019848711788654327, 0.03145904839038849, 0.05306766927242279, -0.0725356861948967, 0.0005702890339307487, -0.009108209051191807, -0.02536621503531933, 0.012748013250529766, 0.009819327853620052, 0.013474574312567711, 0.05163922533392906, -0.02936793491244316, 0.005749823525547981, 0.06670958548784256, -0.08500484377145767, 0.0063714622519910336, 0.017337016761302948, 0.002819432644173503, -0.0292852520942688, -0.015331885777413845, -6.398813784276692e-33, 0.04022155702114105, -0.09363038837909698, -0.025531284511089325, 0.029937785118818283, -0.005331925116479397, 0.03202090412378311, -0.05424872040748596, -0.013564690947532654, -0.009423069655895233, 0.050992850214242935, 0.009649357758462429, -0.00644916296005249, -0.001759205712005496, -0.059691812843084335, 0.015256124548614025, 0.010835722088813782, 0.002418356714770198, 0.0467086099088192, 0.046388402581214905, -0.0014175764517858624, 0.008859931491315365, 0.06864982098340988, 0.008056295104324818, -0.06738410890102386, -0.0011530056362971663, -0.011336099356412888, 0.006179978605359793, -0.013171899132430553, 0.0077211023308336735, 0.013576554134488106, -0.018052078783512115, -0.014008918777108192, 0.015901491045951843, 0.011452892795205116, 0.010854335501790047, 0.02582593262195587, -0.03663582354784012, -0.009172618389129639, -0.026107480749487877, -0.032787125557661057, -0.010502851568162441, 0.015721717849373817, 0.043128907680511475, -0.023087164387106895, -0.006904181558638811, 0.006385067477822304, 0.08880934864282608, -0.037620652467012405, -0.047308024019002914, 0.021616756916046143, -0.06709214299917221, 0.019346293061971664, 0.02276262454688549, 0.03594053536653519, 0.04231448099017143, 0.019550427794456482, 0.012384667061269283, -0.000372880109352991, -0.020926738157868385, 0.016956405714154243, 0.011537495069205761, 0.03669026866555214, 0.018265793099999428, 0.03381020575761795, 0.009363300167024136, 0.01614893041551113, -0.03291169926524162, -0.035183146595954895, 0.036081865429878235, -0.009120811708271503, -0.022367918863892555, 0.03065016306936741, 0.06660782545804977, -0.020738396793603897, 0.012382222339510918, -0.06484127044677734, -0.1099146232008934, 0.04922324791550636, -0.023676883429288864, -0.016649844124913216, -0.04816727340221405, -0.009473956190049648, 0.01672302931547165, -0.015177902765572071, 0.016119252890348434, 0.021259374916553497, -0.0507858544588089, -0.07434526085853577, -0.03904289752244949, -0.044617969542741776, 0.001238782424479723, 0.018075503408908844, -0.032015807926654816, -0.03138641268014908, -0.01253112405538559, 0.020439177751541138, -0.0037719702813774347, 0.0014714421704411507, -0.027467377483844757, -0.05989086255431175, -0.05194684490561485, -0.020705120638012886, -0.031243935227394104, -0.02452024258673191, 0.004307131748646498, -0.046312473714351654, 0.016671035438776016, -0.03431641682982445, 0.004021214321255684, -0.01045574713498354, -0.011145936325192451, -0.052696242928504944, 0.03303489834070206, 0.037681445479393005, -0.030494555830955505, 0.004210465122014284, 0.010403696447610855, 0.08430535346269608, 0.06871060281991959, 0.020165201276540756, 0.010058451443910599, 0.02150033973157406, 0.004957040771842003, -0.0030211086850613356, -0.0657762661576271, -0.015673579648137093, -0.006230372004210949, 0.0642789900302887, 0.03521110862493515, -0.0342949740588665, -0.026837365701794624, -0.033874478191137314, 3.0740014267394145e-07, 0.06943950057029724, 0.03922105208039284, -0.0016023705247789621, -0.007863529957830906, -0.0021279642824083567, 0.00924192275851965, 0.004614153411239386, 0.016541343182325363, -0.06924193352460861, 0.0048866309225559235, 0.06021648272871971, -0.04275413602590561, -0.01547178253531456, 0.021335801109671593, -0.029762886464595795, -0.0021048029884696007, -0.08981728553771973, -0.050529975444078445, -0.03578173369169235, 0.0053802072070539, 0.03326883539557457, 0.013264440931379795, 0.027660345658659935, 0.00696693966165185, 0.0013538931962102652, -0.029427748173475266, -0.011071371845901012, -0.015539140440523624, 0.02302812971174717, 0.05421127378940582, -0.03514711931347847, -0.022585522383451462, -0.014891826547682285, 0.032991211861371994, -0.0510261245071888, -0.0391453318297863, -0.007651515305042267, -0.02030060812830925, -0.0548112653195858, 0.04174194484949112, 0.05794581025838852, 0.004647761583328247, 0.03320525959134102, -0.029383623972535133, 0.0068236906081438065, -0.04581055790185928, -0.06156197190284729, 0.038227710872888565, 0.04811698943376541, -0.02142135426402092, 0.05123591423034668, 0.024201203137636185, 0.03323572501540184, 0.030953167006373405, -0.04299372062087059, 0.010387657210230827, 0.014431728050112724, -0.030492214486002922, -0.007938978262245655, 0.019279122352600098, 0.002020798856392503, 0.01704595424234867, -0.01600021868944168, -0.021241575479507446, 0.04038744419813156, -0.009946155361831188, -0.025204671546816826, 3.3184024148608264e-34, 0.0460638627409935, -0.028254274278879166, 8.681310282554477e-05, 0.02833392843604088, -0.01805213652551174, -0.00759227154776454, -0.008827051147818565, 0.030471952632069588, -0.03688563406467438, -0.05286099761724472, -0.017852671444416046]

['Fangwen Fu', 'Mihaela van der Schaar']

0812.1244v1

In this paper, we propose a general cross-layer optimization framework in which we explicitly consider both the heterogeneous and dynamically changing characteristics of delay-sensitive applications and the underlying time-varying network conditions. We consider both the independently decodable data units (DUs, e.g. packets) and the interdependent DUs whose dependencies are captured by a directed acyclic graph (DAG). We first formulate the cross-layer design as a non-linear constrained optimization problem by assuming complete knowledge of the application characteristics and the underlying network conditions. The constrained cross-layer optimization is decomposed into several cross-layer optimization subproblems for each DU and two master problems. The proposed decomposition method determines the necessary message exchanges between layers for achieving the optimal cross-layer solution. However, the attributes (e.g. distortion impact, delay deadline etc) of future DUs as well as the network conditions are often unknown in the considered real-time applications. The impact of current cross-layer actions on the future DUs can be characterized by a state-value function in the Markov decision process (MDP) framework. Based on the dynamic programming solution to the MDP, we develop a low-complexity cross-layer optimization algorithm using online learning for each DU transmission. This online algorithm can be implemented in real-time in order to cope with unknown source characteristics, network dynamics and resource constraints. Our numerical results demonstrate the efficiency of the proposed online algorithm.

Decomposition Principles and Online Learning in Cross-Layer Optimization for Delay-Sensitive Applications

http://arxiv.org/pdf/0812.1244v1

Title Decomposition Principles Online Learning CrossLayer Optimization DelaySensitive Applications Summary paper propose general crosslayer optimization framework explicitly consider heterogeneous dynamically changing characteristic delaysensitive application underlying timevarying network condition consider independently decodable data unit DUs eg packet interdependent DUs whose dependency captured directed acyclic graph DAG first formulate crosslayer design nonlinear constrained optimization problem assuming complete knowledge application characteristic underlying network condition constrained crosslayer optimization decomposed several crosslayer optimization subproblems DU two master problem proposed decomposition method determines necessary message exchange layer achieving optimal crosslayer solution However attribute eg distortion impact delay deadline etc future DUs well network condition often unknown considered realtime application impact current crosslayer action future DUs characterized statevalue function Markov decision process MDP framework Based dynamic programming solution MDP develop lowcomplexity crosslayer optimization algorithm using online learning DU transmission online algorithm implemented realtime order cope unknown source characteristic network dynamic resource constraint numerical result demonstrate efficiency proposed online algorithm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.03431332856416702, -0.010286958888173103, -0.041254714131355286, -0.017111582681536674, -0.03525286167860031, -0.03422529250383377, 0.04044858366250992, 0.004746971186250448, -0.015864964574575424, -0.0011924250284209847, 0.035946257412433624, 0.02861829288303852, -0.004508437588810921, 0.04083919897675514, -0.027276745066046715, 0.0008438802906312048, -0.004795354325324297, 0.004869451280683279, 0.0001603852433618158, 0.005748827010393143, 0.04328364133834839, -0.041993558406829834, 0.02880694903433323, 0.008297215215861797, 0.024324310943484306, -0.03687756881117821, -0.03426622226834297, 0.00049735011998564, 0.00779137434437871, -2.1143752746866085e-05, 0.024810323491692543, -0.007693362422287464, 0.03291362151503563, 0.013077433221042156, 2.426374521746766e-06, 0.06086820363998413, -0.01441456563770771, -0.006787269841879606, -0.018513033166527748, 0.030537376180291176, -0.040325697511434555, -0.04922671988606453, -0.014824118465185165, 0.036130502820014954, -0.0018043190939351916, -0.01269526407122612, 0.04935621842741966, 0.03961372375488281, 0.030014952644705772, 0.015683121979236603, -0.007447874639183283, 0.0269529577344656, 0.025112148374319077, -0.0013942166697233915, 0.00430825212970376, -0.04210328310728073, -0.0003421632864046842, 0.02713875286281109, -0.012536304071545601, -0.025096502155065536, -0.06085807830095291, 0.0033471211791038513, 0.007431516423821449, -0.017202097922563553, 0.023952942341566086, -0.044335559010505676, 0.023443667218089104, -0.007025400176644325, -0.06622681021690369, 0.01935373991727829, -0.044450923800468445, 0.03601723164319992, 0.031980179250240326, -0.0158686526119709, -0.05253220722079277, 0.004979965277016163, 0.0034299995750188828, -0.07551645487546921, -0.050560299307107925, 0.006964073982089758, -0.09026821702718735, 0.0660182535648346, 0.007328025531023741, 0.04611789062619209, 0.022187232971191406, 0.05934467911720276, -0.008757244795560837, -0.0015652163419872522, -0.009007355198264122, -0.031727369874715805, 0.052204083651304245, -0.027518823742866516, 0.02382589504122734, -0.03161944821476936, -0.020564835518598557, -0.039266087114810944, -0.011587681248784065, -0.05279184877872467, -0.05340474471449852, -0.01768236793577671, 0.09904100745916367, -0.010402380488812923, 0.03450900316238403, -0.010796867311000824, 0.014857875183224678, 0.011205539107322693, -0.08209188282489777, -0.02746504731476307, -0.01878044754266739, -0.001633590436540544, 0.010833289474248886, -0.023719215765595436, -0.016462067142128944, 0.07245189696550369, -0.011781969107687473, 0.021776793524622917, -0.06420797109603882, 0.024979770183563232, -0.04889338091015816, -0.036692626774311066, -0.0020949707832187414, -0.006083966698497534, -0.005456286948174238, -0.016444697976112366, -0.026189247146248817, -0.018366781994700432, 0.046099334955215454, 0.039644595235586166, -0.0033634700812399387, 0.009343035519123077, 0.0318153016269207, -0.011726276949048042, -0.014216979965567589, 0.012711474671959877, -0.008899716660380363, 0.11841628700494766, -0.028713347390294075, 0.013801085762679577, 0.019570987671613693, -0.037450242787599564, 0.03635498508810997, 0.003518712939694524, -0.02192608267068863, -0.008081537671387196, -0.0009436444961465895, -0.058547813445329666, -0.04851415753364563, 0.05999806150794029, -0.026771750301122665, -0.006837711203843355, -0.007411304395645857, 0.06633206456899643, 0.0548931322991848, 0.0037790106143802404, 0.07280733436346054, -0.0016089276177808642, 0.014548631384968758, 0.025658398866653442, 4.8336718464270234e-05, -0.002698864322155714, -0.01703541912138462, -0.061729900538921356, -0.024225905537605286, -0.0017184013267979026, 0.10784468799829483, -0.016061192378401756, -0.05357307568192482, -0.05349021032452583, 0.002986053703352809, 0.01505027525126934, -0.036198779940605164, -0.002338316524401307, -0.018349260091781616, -0.0004045485402457416, 0.02255144715309143, -0.05093255639076233, 0.07538723945617676, 0.007006315514445305, -0.012808824889361858, 0.09748823195695877, -0.0743158832192421, 0.012301282957196236, 0.021942615509033203, 0.09581610560417175, -0.0013663278659805655, -0.026932811364531517, 0.017799198627471924, 0.049561403691768646, -0.03800845518708229, -0.011736792512238026, 0.02159894071519375, -0.03526385501027107, 0.014351564459502697, 0.03189420327544212, -0.0014565420569851995, -0.0046265400014817715, -0.06423144042491913, 0.06307146698236465, -0.0023885644041001797, -0.026842648163437843, -0.01781974732875824, -0.02429124526679516, -0.008846479468047619, 0.006020704284310341, 0.001274998765438795, 0.021904924884438515, -0.062196604907512665, -0.016065359115600586, 0.019141048192977905, -0.030784601345658302, 0.009153553284704685, -0.008493938483297825, 0.041509080678224564, -0.02294129692018032, 0.01274059247225523, 0.057755108922719955, 0.024700922891497612, -0.023115796968340874, -0.03234827145934105, 0.006045521702617407, -0.027256904169917107, 0.03021421656012535, -0.0010897674364969134, 0.00512783695012331, 0.008534595370292664, 0.02903180569410324, 0.04398435726761818, 0.07118166983127594, 0.0665067806839943, 0.004421519115567207, 0.024522580206394196, -0.043567001819610596, -0.009419821202754974, -0.024486245587468147, -0.05031910911202431, 0.0021553721744567156, -0.03563639521598816, -0.001225504674948752, -0.0017025336856022477, -0.05862203240394592, 0.06285343319177628, 0.06667841225862503, -0.021678579971194267, -0.041448090225458145, 0.03751629963517189, -0.011031762696802616, -0.007269502617418766, -0.025290770456194878, -0.04425249248743057, -0.0049125864170491695, 0.05265313386917114, -0.016246028244495392, -0.0010828308295458555, 0.02978905476629734, -0.017838751897215843, -0.010546273551881313, 0.02553809992969036, 0.04322340711951256, 0.01062016375362873, 0.0687575414776802, -0.008689108304679394, -0.0519508421421051, 0.032096896320581436, -0.01412577461451292, 0.02142590656876564, 0.0738503560423851, -0.023475145921111107, 0.020916897803544998, -0.01587802916765213, 0.022580718621611595, -0.00984256248921156, -0.011851855553686619, 0.0663096010684967, 0.02387060411274433, 0.0006338602397590876, -0.003906929399818182, 0.07595836371183395, 0.021958399564027786, -0.07481715083122253, -0.008158345706760883, 0.048297636210918427, -0.014092285186052322, 0.022219328209757805, -0.043188467621803284, 0.02737553045153618, 0.026397641748189926, -0.012507821433246136, -0.06772011518478394, -0.018006756901741028, -0.03431957960128784, 0.016842443495988846, 0.016834555193781853, -0.006469725631177425, -0.050706010311841965, -0.03076278045773506, 0.05036865919828415, -0.040929362177848816, -0.006180611439049244, 0.027065467089414597, 0.00898405909538269, -0.0012694071047008038, 0.002477683825418353, -0.05174712836742401, 0.025810973718762398, -0.04814666137099266, 0.030879341065883636, -0.010348405689001083, 0.046359289437532425, -0.008336846716701984, 0.07922942191362381, 0.01862146332859993, -0.030949732288718224, -0.059491463005542755, -0.0372689887881279, 0.012131963856518269, -0.04087816923856735, -0.04669810086488724, -0.02875935658812523, 0.013919214718043804, -0.016314595937728882, 0.004650721792131662, -0.004432112444192171, 0.05428924784064293, 0.02469857782125473, -0.014852648600935936, -0.007663100957870483, -0.06539678573608398, -0.015351706184446812, -0.008695608004927635, -0.05483689159154892, 0.0639803484082222, -0.034813087433576584, -0.007973532192409039, -0.03456723317503929, 0.047818854451179504, 0.05611862242221832, -0.02558092214167118, -0.07446611672639847, 0.07087673991918564, 0.01779836043715477, -0.016905933618545532, 0.003953864332288504, 0.024954184889793396, 0.04021057114005089, 0.024684952571988106, -0.02202863059937954, -0.021523157134652138, 0.021329648792743683, 0.018893733620643616, 0.04297603294253349, -0.031007515266537666, 2.7023097572964616e-05, -0.027845028787851334, -0.014111180789768696, 0.00791530217975378, 0.02104290947318077, -0.016786910593509674, -0.023432165384292603, -0.011586506851017475, 0.059633392840623856, 0.12675108015537262, -0.03593608736991882, 0.001378153101541102, 0.03794990852475166, -0.02975478582084179, 0.006665582302957773, 0.01367666944861412, -0.00953549426048994, -0.013104149140417576, 0.04043237864971161, -0.012576275505125523, -0.0653301253914833, 0.03119756281375885, -0.007457543630152941, -0.0011742764618247747, -0.12798678874969482, -0.023688718676567078, -0.016786998137831688, -0.05022849887609482, -0.016109269112348557, 0.023648623377084732, -0.052539851516485214, -0.009324612095952034, -0.03170117363333702, -0.0030607194639742374, -0.013758569024503231, 0.005840492434799671, -0.031245240941643715, -0.03663129732012749, 0.029162205755710602, -0.01908181980252266, 0.01258808746933937, -0.01193923782557249, -0.04086847975850105, -0.06464239954948425, 0.0021955983247607946, 0.06450838595628738, -0.02004065178334713, 0.06686979532241821, -0.021787064149975777, 0.003004928585141897, -0.025456076487898827, -0.04657287895679474, 0.010341104120016098, 0.004039573948830366, -0.005782790947705507, 0.016996940597891808, 0.0356656014919281, 0.011940992437303066, -0.05627131089568138, 0.06008244678378105, -0.05479811877012253, -0.033606965094804764, -0.04387437552213669, 0.020527321845293045, 0.0032758961897343397, 0.007581259589642286, -0.05849310755729675, 0.0464911162853241, 0.043001119047403336, 0.05401112884283066, -0.03439990431070328, 0.0671934261918068, -0.009002854116261005, 0.018952634185552597, -0.0488482229411602, -0.014916499145328999, 0.048918288201093674, -0.04680309444665909, -0.062097784131765366, -0.048249851912260056, -0.054670412093400955, 0.026812594383955002, 0.013992711901664734, -0.04853629320859909, -0.01804032176733017, 0.03414203226566315, 0.01082457322627306, 0.021994248032569885, 0.0030929376371204853, 0.058442968875169754, -0.07850728183984756, 0.047846097499132156, 0.013499819673597813, 0.05794907733798027, 0.050840314477682114, 0.047055210918188095, -0.08359722048044205, -0.09490367025136948, 0.06620612740516663, -0.005355521105229855, -0.0031089377589523792, 0.035474419593811035, 0.03633631393313408, -0.037003420293331146, -0.0023822090588510036, -0.045092154294252396, -0.031182441860437393, -0.044163916260004044, 0.007788412272930145, -0.023353835567831993, 0.002845609560608864, 0.022852454334497452, 0.004987443797290325, -0.060564879328012466, 0.06792160123586655, -0.037796150892972946, -0.014682861976325512, -0.027855275198817253, 0.049956247210502625, -0.03604139760136604, -0.016808990389108658, 0.03635985776782036, -0.03891947120428085, 0.044363200664520264, 0.016038088127970695, -0.055640608072280884, -0.006899552885442972, 0.029800403863191605, -0.010131278075277805, 0.016565099358558655, 0.03809259459376335, 0.029269244521856308, -0.025057196617126465, 0.010184136219322681, 0.07486642152070999, 0.009639586322009563, 0.015535075217485428, -0.026020817458629608, 0.0010253333020955324, -0.016979198902845383, -0.0018345998832955956, 0.07893335074186325, 0.014159820042550564, 0.12950116395950317, -0.08680994063615799, 0.03537760302424431, 0.039135243743658066, -0.03677431493997574, 0.0157144907861948, 0.007801641710102558, 0.04362121969461441, 0.048523422330617905, 0.020252643153071404, 0.01856541819870472, -0.021292895078659058, -0.04054192453622818, -0.014185368083417416, 0.0063549792394042015, 0.03969680890440941, -0.05542949214577675, -0.01367779728025198, 0.03949127718806267, -0.04905858635902405, 0.023779910057783127, -0.0180199071764946, 0.018863726407289505, 0.025972070172429085, -0.033995985984802246, 0.008129339665174484, 0.0500282384455204, 0.021790487691760063, 0.05987982824444771, -0.04232481122016907, 0.01453645434230566, 0.04357985034584999, -0.006061690393835306, -0.007221181411296129, 0.015641985461115837, 0.017139697447419167, 0.056398216634988785, -0.004178378731012344, -0.07674770057201385, -0.019492657855153084, 0.0011878011282533407, 0.05249805003404617, 0.03903374448418617, 0.006443163845688105, -0.030239082872867584, 0.00828117597848177, 0.019821519032120705, 0.013860621489584446, 0.036547064781188965, -0.0008860123343765736, 0.07695448398590088, -0.01710636541247368, 0.022029448300600052, -0.0021578462328761816, 0.0156561192125082, 0.03985559195280075, -0.011594328097999096, -0.0388219840824604, 0.020362919196486473, 0.022534793242812157, 0.05873376131057739, -6.773001554134258e-33, 0.008508557453751564, -0.018489770591259003, -0.03322453424334526, -0.018605681136250496, -0.053289227187633514, 0.04229043796658516, 0.0077352081425487995, -0.027469631284475327, 0.03706563636660576, -0.06117621064186096, -0.006999057251960039, 0.026792848482728004, 0.031516171991825104, 0.02477545663714409, 0.028291884809732437, 0.010874866507947445, -0.0024441462010145187, -0.05081510916352272, -0.009302371181547642, 0.026269925758242607, -0.0026409269776195288, 0.02591199055314064, -0.024112196639180183, 0.01409987173974514, -0.049588292837142944, 0.033566590398550034, 0.010469234548509121, -0.025438645854592323, -0.032112278044223785, 0.032364193350076675, -0.0672987774014473, -0.029636768624186516, -0.03396471217274666, -0.03986192122101784, -0.0017435146728530526, 0.08162938058376312, 0.003190178656950593, 0.02273642085492611, -0.047338493168354034, 0.029248787090182304, -0.03326743468642235, -0.027179338037967682, 0.018443305045366287, 0.049656521528959274, -0.07868584245443344, -0.013776647858321667, 0.034247539937496185, 0.040797360241413116, -0.03383517265319824, -0.02592056430876255, 0.003052013460546732, -0.011923044919967651, 0.012590264901518822, 0.02708866447210312, 0.07851652055978775, -0.004341950174421072, -0.050313275307416916, 0.012526510283350945, -0.046730633825063705, 0.031310997903347015, -0.0686086043715477, 0.017371514812111855, 0.014654829166829586, -0.010126841254532337, 0.031008213758468628, 0.020225659012794495, 0.013220209628343582, 0.021151937544345856, 0.011140087619423866, -0.0013915274757891893, 0.027016976848244667, 0.009715509600937366, -0.017926396802067757, 0.0004114683251827955, 0.021255087107419968, -0.09097591787576675, -0.041622571647167206, -0.005393579136580229, 0.0027759179938584566, -0.02672659233212471, 0.013395622372627258, 0.023562565445899963, 0.017871756106615067, -0.004066728986799717, 0.019190872088074684, 0.005492758005857468, 0.030417190864682198, -0.03519488126039505, -0.01428520493209362, 0.03362754359841347, -0.030122270807623863, -0.04895545169711113, 0.011093582026660442, -0.024557998403906822, 0.03962293639779091, -0.04244120046496391, 0.02267666719853878, 0.01048101857304573, 0.020751861855387688, -0.028172781690955162, -0.06360825896263123, -0.03255191445350647, -0.04649459570646286, -0.04849850386381149, -0.011373888701200485, -0.0151205537840724, 0.004232469946146011, 0.05959153547883034, -0.017102137207984924, 0.014501289464533329, 0.013776908628642559, -0.013928035274147987, 0.0483706034719944, 0.036398809403181076, 0.030064009130001068, -0.04926211014389992, -0.0351288728415966, 0.005915661342442036, -0.01736917532980442, -0.029769744724035263, -0.0011411434970796108, 0.009691622108221054, 0.04808495193719864, 0.03056482970714569, -0.03798563405871391, -0.0075733233243227005, -0.050367482006549835, -0.017520414665341377, -0.01817530207335949, -0.03354280814528465, -0.03070654347538948, 0.0016128377756103873, 3.1731482863506244e-07, -0.06305143237113953, 0.048830799758434296, 0.03849153220653534, 0.022647075355052948, -0.0037128464318811893, -0.034853387624025345, -0.008789166808128357, 0.015605316497385502, -0.033121805638074875, 0.04354959353804588, 0.014004508964717388, -0.07137355953454971, 0.03231973201036453, -0.021486399695277214, -0.02551286481320858, 0.001130423741415143, 0.014340878464281559, 0.06185148283839226, -0.006442156154662371, -0.003225066466256976, -0.024993104860186577, -0.012690848670899868, -0.0009268889552913606, 0.016857175156474113, 0.03121935948729515, 0.05747660994529724, 0.0017689639935269952, 0.0368061438202858, 0.025543538853526115, -0.03395998105406761, -0.01245870441198349, -0.0075025130063295364, -0.08453111350536346, -0.011148842051625252, -0.016600163653492928, 0.04040038585662842, -0.004660327918827534, -0.011714083142578602, 0.006850093137472868, -0.030813077464699745, 0.023056304082274437, 0.013565802946686745, -0.013083156198263168, 0.024555029347538948, -0.007731411140412092, 0.007461769971996546, -0.08543874323368073, -0.051892854273319244, 0.012354779057204723, 0.009759613312780857, -0.0007301354198716581, 0.0070291198790073395, 0.05404915660619736, -0.05509980022907257, -0.021592488512396812, 0.004429810214787722, 0.05386990308761597, -0.009672963060438633, 0.033940959721803665, 0.06207507848739624, 0.02142622135579586, -0.020335661247372627, -0.030234884470701218, 0.012711002491414547, 0.10445953160524368, 0.012608610093593597, 0.0010675331577658653, 3.1678280170052225e-34, -0.007112910505384207, -0.020033281296491623, 0.02633075602352619, 0.054702263325452805, -0.07986133545637131, -0.03019629418849945, 0.005734611302614212, -8.157839329214767e-05, 0.0013501733774319291, -0.010838812217116356, -0.006120186299085617]

['Erik M. Boczko', 'Todd Young', 'Minhui Zie', 'Di Wu']

0812.3147v1

We investigate the performance of a simple signed distance function (SDF) based method by direct comparison with standard SVM packages, as well as K-nearest neighbor and RBFN methods. We present experimental results comparing the SDF approach with other classifiers on both synthetic geometric problems and five benchmark clinical microarray data sets. On both geometric problems and microarray data sets, the non-optimized SDF based classifiers perform just as well or slightly better than well-developed, standard SVM methods. These results demonstrate the potential accuracy of SDF-based methods on some types of problems.

Comparison of Binary Classification Based on Signed Distance Functions with Support Vector Machines

http://arxiv.org/pdf/0812.3147v1

Title Comparison Binary Classification Based Signed Distance Functions Support Vector Machines Summary investigate performance simple signed distance function SDF based method direct comparison standard SVM package well Knearest neighbor RBFN method present experimental result comparing SDF approach classifier synthetic geometric problem five benchmark clinical microarray data set geometric problem microarray data set nonoptimized SDF based classifier perform well slightly better welldeveloped standard SVM method result demonstrate potential accuracy SDFbased method type problem Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.004720108583569527, -0.047239091247320175, -0.026977790519595146, -0.026590265333652496, -0.013421121053397655, 0.009956044144928455, 0.09744065254926682, 0.059920988976955414, 0.05282741039991379, 0.0209205225110054, 0.07673874497413635, -0.0033408498857170343, 0.05467444285750389, 0.05597274750471115, -0.023656338453292847, -0.012117170728743076, 0.002087801229208708, 0.02586013823747635, -0.045945171266794205, -0.03711654245853424, 0.0030745898839086294, -0.02868052013218403, 0.021444058045744896, 0.04675816744565964, -0.020672276616096497, 0.017587415874004364, 0.01757034845650196, -0.042575087398290634, 0.03576350212097168, -0.0418701171875, 0.027589473873376846, 0.005378055851906538, -0.0016353866085410118, 0.018118886277079582, 1.9371905182197224e-06, -0.06546586006879807, 0.004590893164277077, 0.008972074836492538, 0.04975767806172371, -0.021599985659122467, 0.004819998051971197, -0.05205399915575981, 0.03830333054065704, -0.031200304627418518, 0.0006665497785434127, -0.049295421689748764, 0.04226800426840782, 0.07843616604804993, 0.012907756492495537, 0.0026924738194793463, -0.013169646263122559, -0.019369997084140778, 0.03247048705816269, -0.020173855125904083, 0.016025623306632042, 0.07323385775089264, 0.02364792488515377, 0.016603348776698112, -0.048396237194538116, 0.007207395043224096, 0.020905353128910065, 0.06466257572174072, 0.006471078842878342, 0.004235696047544479, 0.0648760199546814, 0.04770822450518608, -0.05251608416438103, 0.04031190648674965, 0.03754935413599014, 0.030806703492999077, -0.05908579006791115, -0.02988255023956299, 0.024332961067557335, -0.021459052339196205, -0.02699507586658001, 0.03700121119618416, -0.007338486146181822, -0.03633576259016991, -0.01729714125394821, 0.013753280974924564, -0.05907290801405907, 0.03193267062306404, -0.013375130482017994, -0.05876399949193001, 0.013049193657934666, -0.014883381314575672, -0.013574647717177868, -0.021505074575543404, 0.013496771454811096, -0.009026742540299892, -0.019512344151735306, -0.00199696933850646, 0.02581789530813694, -0.007073570974171162, -0.030240260064601898, -0.04061112552881241, 0.04198668524622917, -0.02991129457950592, 0.09705649316310883, -0.07728022336959839, 0.04155955836176872, -0.03964229300618172, -0.007505720015615225, 0.017515482380986214, -0.08100508153438568, -0.02371455356478691, -0.020982230082154274, 0.09619233012199402, -0.017801037058234215, 0.10737194120883942, -0.026052620261907578, 0.029910149052739143, 0.019115649163722992, 0.018351631239056587, 0.0425909161567688, 0.0038085607811808586, -0.05862786993384361, -0.00036658375756815076, 0.01677071675658226, -0.008774551562964916, 0.05898146703839302, 0.024564342573285103, 0.056943804025650024, 0.04147094860672951, -0.01927275024354458, -0.016138752922415733, -0.05150701850652695, 0.0049064988270401955, -0.10435058176517487, 0.0413493886590004, 0.023747026920318604, 0.02050803415477276, 0.0023899031803011894, 0.014280839823186398, -0.0026634775567799807, -0.005501115694642067, -0.010827704332768917, -0.00043011803063564, 0.012709537521004677, -0.02718484215438366, -0.0360509492456913, -0.01560705155134201, -0.010021128691732883, -0.030939938500523567, 0.016615889966487885, 0.029046490788459778, -0.03353693708777428, 0.03148529678583145, 0.03304225206375122, -0.031001606956124306, 0.005484588909894228, 0.03976612910628319, -0.04616707190871239, -0.004298545885831118, 0.04805174842476845, -0.012774680741131306, -0.005528239533305168, -0.010445245541632175, -0.013630308210849762, -0.02012534625828266, 0.006722153630107641, -0.03260793164372444, -0.03769078850746155, -0.04906238242983818, -0.03924828767776489, -0.05896957591176033, -0.023546554148197174, 0.021551944315433502, 0.027212299406528473, 0.022549010813236237, -0.04206453263759613, -0.018053455278277397, -0.012143753468990326, -0.05923845246434212, -0.020467018708586693, 0.054810140281915665, 0.03141453117132187, 0.00950424000620842, -0.040392205119132996, 0.033960532397031784, -0.005880145821720362, -0.0503782294690609, 0.05597677826881409, -0.00020607792248483747, -0.05248754099011421, -0.004520602058619261, -0.05520271509885788, -0.04690927267074585, -0.00509497569873929, -0.015022789128124714, -0.013115056790411472, -0.040643010288476944, 0.01701228693127632, -0.052700966596603394, 0.030570736154913902, -0.08013938367366791, 0.0013494141167029738, -0.005671102087944746, 0.016257796436548233, 0.00263308547437191, -0.09164516627788544, -0.012068363837897778, 0.030659979209303856, -0.07408589124679565, -0.03356389328837395, -0.07210803776979446, -0.03136320784687996, -0.0078027378767728806, -0.021449267864227295, -0.04944504797458649, -0.013028076849877834, 0.010512401349842548, 0.011388574726879597, 0.004027710296213627, 0.01356662530452013, 0.058326222002506256, 0.011881456710398197, -0.018684925511479378, 0.012034229002892971, 0.0458243191242218, 0.00967993400990963, -0.017902545630931854, 0.003495030803605914, 0.030659480020403862, 0.023792969062924385, 0.02205304242670536, 0.03649070858955383, 0.03610027953982353, -0.004067116416990757, -0.03247790411114693, 0.03304564952850342, -0.045146722346544266, 0.051023632287979126, -0.0411238819360733, -0.052601158618927, -0.03131292387843132, 0.03104289621114731, -0.05429771542549133, 0.04093644767999649, -0.005543896928429604, 0.025307435542345047, 0.005976422224193811, -0.017578016966581345, -0.006885211449116468, -0.011504987254738808, -0.012421387247741222, -0.03705717995762825, -0.014505450613796711, 0.06096254289150238, -0.02722909115254879, -0.0050783902406692505, -0.041847147047519684, 0.051183246076107025, 0.003941622097045183, 0.02825874090194702, -0.07048305869102478, -0.060767874121665955, 0.06378492712974548, -0.00016585111734457314, 0.019505999982357025, -0.0016818270087242126, -0.05726296082139015, -0.030407574027776718, -0.013432065956294537, 0.038179878145456314, 0.00626779580488801, -0.007958879694342613, -0.021723687648773193, -0.04800979420542717, 0.03411993384361267, -0.011317724362015724, -0.013431654311716557, -0.03937104716897011, 0.03109375387430191, -0.01515540387481451, -0.03674089536070824, 0.019643383100628853, 0.003952360711991787, -0.04566774517297745, 0.06520654261112213, 0.0011875081108883023, -0.025174053385853767, -0.037671346217393875, -0.025966018438339233, 0.0028146635740995407, -0.005989455617964268, 0.013675390742719173, -0.04425319284200668, -0.004135103430598974, 0.06888855993747711, -0.01563420705497265, 0.006818324327468872, -0.008313920348882675, -0.0009569465182721615, 0.025502193719148636, -0.05185280367732048, -0.05719524994492531, 0.043765101581811905, 0.025933334603905678, -0.02566785365343094, 0.001509601715952158, 0.07066846638917923, -0.017194218933582306, -0.007942475378513336, -0.05837474390864372, 0.030555106699466705, 0.043811947107315063, -0.0032893267925828695, -0.0018226578831672668, -0.01708253100514412, -0.013819132931530476, -0.010977433063089848, -0.00890511553734541, -0.020998602733016014, 0.02984706312417984, 0.00224540987983346, -0.06093470752239227, 0.019424105063080788, -0.01644318737089634, -0.006531938444823027, 0.010259805247187614, -0.017928440123796463, 0.054470546543598175, -0.015565207228064537, 0.041307561099529266, -0.013233424164354801, -0.033066537231206894, -0.0009069731459021568, -0.06943275034427643, -0.0008023899281397462, 0.04095631465315819, -0.08426078408956528, 0.03783071041107178, 0.026869092136621475, 0.008877112530171871, 0.026745369657874107, -0.06724068522453308, -0.005680155474692583, 0.04008753225207329, -0.0053294068202376366, 0.007722063455730677, -0.0011072477791458368, -0.03788582235574722, 0.0013590379385277629, 0.03655340149998665, -0.05495000630617142, -0.015763748437166214, -0.004949336871504784, 0.010190031491219997, 0.07796113193035126, -0.06651603430509567, 0.030099228024482727, -0.035742294043302536, -0.006859597750008106, -0.01300770603120327, -0.005562741309404373, -0.02702225185930729, -0.04544379934668541, -0.046500448137521744, 0.01763109117746353, 0.040923506021499634, 0.00809469074010849, -0.04612727835774422, 0.02723044343292713, -0.01899922825396061, 0.010694696567952633, 0.014523947611451149, 0.007814041338860989, -0.07103659212589264, -0.041444331407547, 0.0640145093202591, 0.015905136242508888, -0.005408523604273796, 0.053984496742486954, 0.05211709439754486, -0.05924138054251671, -0.02707809954881668, -0.047241270542144775, -0.019631672650575638, 0.017636718228459358, 0.008377280086278915, 0.023584263399243355, -0.0005425940034911036, -0.009777462109923363, -0.005821791477501392, -0.025730732828378677, -0.05877339467406273, 0.04330861195921898, -0.025390181690454483, 0.009028279222548008, 0.03598454222083092, -0.10605356097221375, -0.05146767944097519, -0.03940799832344055, -0.021850725635886192, 0.009503742679953575, -0.10794008523225784, -0.014814568683505058, -0.024438194930553436, -0.01100863702595234, 0.014253425411880016, -0.03774305060505867, 0.011904805898666382, 0.005425342358648777, -0.05653788149356842, -0.02310912497341633, -0.011219896376132965, 0.0001898320479085669, 0.006667634006589651, -0.020957868546247482, -0.01722455769777298, -0.006431050132960081, 0.03544749692082405, -0.06693141162395477, 0.05889293551445007, 0.06700767576694489, -0.005014696624130011, -0.011315069161355495, 0.01647873967885971, -0.019376102834939957, 0.020550226792693138, 0.004585111979395151, 0.05175330117344856, -0.02545803040266037, -0.020279180258512497, -0.042137909680604935, 0.021414680406451225, 0.012168931774795055, -0.003532532835379243, -0.003985120449215174, -0.001124444417655468, -0.04637886583805084, 0.043059106916189194, 0.07154570519924164, 0.06545892357826233, 0.05355668067932129, -0.016938524320721626, -0.034727487713098526, -0.0355941466987133, -0.0485067144036293, 0.020193716511130333, -0.005268212873488665, 0.06345730274915695, 0.016759784892201424, 0.008530141785740852, -0.013453982770442963, -0.010221694596111774, -0.05430750176310539, -0.0009483695030212402, 0.06858567148447037, 0.0761701688170433, 0.006078606471419334, 0.01682385802268982, 0.012026862241327763, 0.019228177145123482, -0.019104819744825363, -0.07217592746019363, -0.0315404050052166, -0.005436532665044069, -0.029356729239225388, 0.032230064272880554, 0.008113956078886986, -0.060890354216098785, -0.0486094206571579, -0.012982956133782864, 0.027016693726181984, 0.04112355411052704, 0.05237962678074837, -0.010323718190193176, 0.0011466924333944917, -0.06900773197412491, 0.00262585561722517, -0.022122059017419815, 0.014276521280407906, 0.03760267794132233, 0.008612941950559616, -0.022520730271935463, -0.06777020543813705, -0.00826149620115757, -0.02571054734289646, 0.048886001110076904, 0.11020094901323318, 0.04962301626801491, -0.04863177612423897, -0.011701459065079689, 0.055636145174503326, 0.032385241240262985, 0.04739522188901901, 0.009977013804018497, -0.003703106427565217, 0.029988067224621773, 0.040453679859638214, -0.055152323096990585, 0.023222459480166435, -0.03172546997666359, -0.014051907695829868, 0.012253903783857822, 0.027487333863973618, 0.042506180703639984, 0.05798039957880974, -0.0069676474668085575, 0.042619626969099045, -0.0286371111869812, -0.02687726728618145, 0.054213013499975204, 0.0054473066702485085, 0.0018352731131017208, 0.030333541333675385, 0.0014920210232958198, 0.09458103775978088, -0.031159237027168274, 0.01269031036645174, 0.01771162636578083, 0.0509696826338768, -0.02502882108092308, -0.024494212120771408, -0.022687608376145363, -0.0034178791102021933, -0.006854407023638487, 0.008891061879694462, -0.016683954745531082, -0.059020306915044785, 0.02563120424747467, -0.03494611009955406, 0.023450303822755814, 0.07210659235715866, -0.0004006647795904428, -0.033220503479242325, 0.02661951817572117, 0.018709339201450348, -0.030792996287345886, -0.04128088429570198, -0.07962541282176971, -0.05606551840901375, -0.030378570780158043, 0.034310005605220795, 0.04380930960178375, 0.02925610914826393, 0.005328270606696606, -0.02080109529197216, -0.03669426590204239, -0.004871855955570936, 0.04783010482788086, -0.05989450961351395, 0.05085662752389908, 0.05027484521269798, -0.024222584441304207, -0.05248066037893295, 0.014236215502023697, -0.03496928885579109, -0.007973017171025276, -0.009864839725196362, -0.020116813480854034, -0.04479970037937164, -0.03651461750268936, -5.3270634220701945e-33, 0.02111351303756237, -0.02609000727534294, -0.07227921485900879, -0.014942212961614132, -0.054260216653347015, 0.013845602050423622, -0.001776528311893344, 0.02507328800857067, 0.02212061919271946, -0.006153319962322712, 0.00874225702136755, -0.023324113339185715, 0.011766950599849224, -0.016762929037213326, 0.018559947609901428, -0.04738239198923111, -0.011012353003025055, 0.005434020422399044, 0.03187110275030136, -0.00921577401459217, 0.035903509706258774, 0.028606420382857323, -0.028971515595912933, -0.09679270535707474, -0.03824440762400627, 0.01163829118013382, 0.016815634444355965, -0.005052634049206972, -0.02004695124924183, -0.005592815577983856, 0.0165338683873415, -0.005086027551442385, -0.029966995120048523, 0.035524882376194, 0.030095847323536873, -0.041780319064855576, 0.009159168228507042, 0.023910945281386375, -0.01022108644247055, 0.04697592929005623, -0.013021159917116165, 0.028521301224827766, 0.03080095164477825, -0.021855756640434265, -0.037378277629613876, 0.03497444465756416, 0.06920216232538223, -0.0251755528151989, -0.039275817573070526, -0.05941189080476761, 0.017663678154349327, 0.025191886350512505, 0.0075961872935295105, 0.011053659953176975, 0.014738375321030617, 0.016045141965150833, -0.011380059644579887, 0.025754472240805626, 0.0223211832344532, 0.029325710609555244, 0.033571574836969376, 0.012293578125536442, -0.003373048035427928, -0.001202789368107915, 0.043782301247119904, 0.04141390323638916, 0.06042587757110596, -0.104831263422966, 0.028466248884797096, -0.0021130286622792482, -0.0054368190467357635, 0.01248242799192667, 0.025983108207583427, -0.0015672643203288317, 0.05511138215661049, -0.03585467115044594, -0.06440049409866333, 0.04646025225520134, -0.0321187786757946, -0.0034770623315125704, -0.05548065900802612, -0.01271746028214693, 0.010487162508070469, 0.0038545115385204554, 0.02454141341149807, -0.049468837678432465, 0.0005713725695386529, -0.028776800259947777, 0.03557455539703369, -0.022405443713068962, -0.05383481830358505, 0.06647744029760361, -0.02497166022658348, -0.022086437791585922, 0.014862701296806335, -0.034593090415000916, 0.036289993673563004, 0.03153802827000618, 0.03074457123875618, -0.04811139777302742, 0.00800039991736412, -0.048662517219781876, 0.056042712181806564, -0.04059891030192375, 0.05296342819929123, -0.031015848740935326, 0.026411408558487892, -0.010573284700512886, -0.03404565528035164, 0.006010342855006456, 0.07272119075059891, -0.04734740033745766, -0.025822294875979424, 0.0453144796192646, 0.011389268562197685, -0.06603448837995529, -0.005593500565737486, 0.1142975464463234, 0.02513597346842289, -0.005192632786929607, -0.01308506540954113, -0.027487268671393394, 0.012480705976486206, -8.655367855681106e-05, -0.012074902653694153, 0.0013593926560133696, -0.004810047801584005, -0.03326389193534851, 0.014137811958789825, -0.015918366611003876, -0.007077433168888092, -0.05304528772830963, 2.549381861172151e-07, 0.028186755254864693, 0.06831158697605133, -0.0073479050770401955, -0.004229502286761999, 0.005250143818557262, -0.00900251604616642, -0.006437298841774464, -0.006144610699266195, -0.0420536994934082, 0.034950077533721924, 0.06486696749925613, -0.03232273831963539, 0.024393614381551743, -0.028168298304080963, 0.006847916636615992, 0.04076475650072098, -0.014401587657630444, 0.03189116716384888, -0.004004204645752907, 0.0393897108733654, 0.07303735613822937, 0.013306032866239548, 0.018446773290634155, -0.05033471807837486, 0.04496214911341667, 0.0012429992202669382, 0.007127619814127684, -0.042696379125118256, 0.06701285392045975, -0.02360042743384838, 0.020481647923588753, -0.04821697995066643, 0.04487094655632973, 0.03433069959282875, 0.04558743163943291, 0.0011754840379580855, 0.013670369051396847, 0.04408213123679161, 0.0039015179499983788, 0.010878188535571098, 0.028567032888531685, 0.04937758296728134, 0.07672935724258423, -0.015420298092067242, 0.03841029480099678, -0.0017419432988390326, -0.003159445011988282, -0.010309525765478611, 0.0005137429689057171, -0.010656175203621387, 0.0901670828461647, -0.01915343664586544, -0.005750385113060474, 0.01898498646914959, -0.00725628761574626, -0.022178802639245987, 0.008839540183544159, 0.006513018161058426, -0.010175101459026337, 0.0356636568903923, 0.0027141019236296415, 0.022894810885190964, 0.0583578422665596, 0.07120366394519806, 0.03697308152914047, 0.005341622978448868, -0.017395729199051857, 2.7371989777284203e-34, 0.01240792777389288, 0.03372420743107796, 0.013148797675967216, -0.0047960830852389336, -0.05444049462676048, 0.014182929880917072, 0.03442762792110443, -0.011321833357214928, -0.021179508417844772, -0.010577758774161339, 0.045431677252054214]

['Dmitry Gavinsky']

0812.3429v3

We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate a relational concept class that is efficiently learnable in PQ, while in any "reasonable" classical model exponential amount of training data would be required. This is the first unconditional separation between quantum and classical learning. We show that our separation is the best possible in several ways; in particular, there is no analogous result for a functional class, as well as for several weaker versions of quantum learning. In order to demonstrate tightness of our separation we consider a special case of one-way communication that we call single-input mode, where Bob receives no input. Somewhat surprisingly, this setting becomes nontrivial when relational communication tasks are considered. In particular, any problem with two-sided input can be transformed into a single-input relational problem of equal classical one-way cost. We show that the situation is different in the quantum case, where the same transformation can make the communication complexity exponentially larger. This happens if and only if the original problem has exponential gap between quantum and classical one-way communication costs. We believe that these auxiliary results might be of independent interest.

Quantum Predictive Learning and Communication Complexity with Single Input

http://arxiv.org/pdf/0812.3429v3

Title Quantum Predictive Learning Communication Complexity Single Input Summary define new model quantum learning call Predictive Quantum PQ quantum analogue PAC testing phase student required answer polynomial number testing query demonstrate relational concept class efficiently learnable PQ reasonable classical model exponential amount training data would required first unconditional separation quantum classical learning show separation best possible several way particular analogous result functional class well several weaker version quantum learning order demonstrate tightness separation consider special case oneway communication call singleinput mode Bob receives input Somewhat surprisingly setting becomes nontrivial relational communication task considered particular problem twosided input transformed singleinput relational problem equal classical oneway cost show situation different quantum case transformation make communication complexity exponentially larger happens original problem exponential gap quantum classical oneway communication cost believe auxiliary result might independent interest Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.007448494900017977, 0.0799742043018341, -0.023016447201371193, 0.02546311914920807, -0.056692346930503845, -0.018815843388438225, -0.02638181857764721, 0.04658270254731178, 0.01739286072552204, -0.00336903496645391, 0.01261874195188284, -0.0198733638972044, -0.011286262422800064, 0.061075083911418915, 0.0063226306810975075, -0.029666785150766373, 0.03795292228460312, 0.006109052803367376, -0.09616293758153915, -0.06327763199806213, -0.038879286497831345, -0.09225272387266159, -0.023502331227064133, -0.023817643523216248, 0.05924014374613762, -0.03738406300544739, -0.035027019679546356, -0.013221562840044498, -0.016941821202635765, 0.0019655206706374884, -0.015040930360555649, 0.04465101286768913, -0.011870462447404861, 0.003945714794099331, 1.8916392718892894e-06, 0.004878642503172159, -0.0233328677713871, -0.001113693811930716, -0.017992209643125534, -0.019016684964299202, -0.11140702664852142, -0.020953139290213585, 0.0014284085482358932, 0.017280559986829758, -0.0239357128739357, 0.02864278480410576, 0.053217023611068726, 0.03152827173471451, -0.00931638851761818, 0.0738951712846756, -5.854288974660449e-05, -0.02414463460445404, 0.03213644400238991, 0.00021708862914238125, 0.024661965668201447, -0.03589694947004318, 0.029680946841835976, -0.014140984043478966, -0.02640729583799839, -0.02458794042468071, -0.059045594185590744, 0.0021900939755141735, 0.053286951035261154, -0.028887415304780006, 0.024065107107162476, 0.0014631785452365875, 0.06120496988296509, 0.034223522990942, -0.06627944856882095, 0.04569645971059799, -0.021028777584433556, -0.0039732810109853745, -0.016893871128559113, 0.01878977380692959, -0.04342767223715782, 0.008110578171908855, 0.015215367078781128, -0.01613258570432663, -0.028390830382704735, 0.03243408724665642, -0.021686267107725143, 0.03165660426020622, 0.009068403393030167, -0.025102872401475906, 0.013955967500805855, 0.0704885795712471, 0.027000300586223602, -0.04138089343905449, 0.013773760758340359, 0.009927558712661266, -0.008879887871444225, 0.06000668928027153, -0.012374144978821278, -0.045040398836135864, -0.03286832943558693, 0.0007768679643049836, 0.009928638115525246, 0.02049483172595501, -0.03174975514411926, -0.018831264227628708, 0.02003224566578865, 0.03717682510614395, 0.06033489480614662, -0.005830500274896622, 0.03609355539083481, 0.0058362120762467384, 0.01327711995691061, -0.003963681403547525, -0.02801055647432804, 0.07990814000368118, -0.07500667124986649, 0.0068226223811507225, 0.0015205935342237353, 0.08299212902784348, -0.016372596845030785, -0.04124528542160988, -0.09861524403095245, -0.008121069520711899, 0.011499886400997639, 0.02900201827287674, 0.0017821021610870957, -0.00823182798922062, 0.017135847359895706, 0.01928277313709259, -0.01877918466925621, 0.04866171255707741, -0.01862851344048977, 0.01370853092521429, -0.04712597280740738, -0.03866496682167053, -0.0022931101266294718, 0.031964223831892014, -0.004871544893831015, 0.010337145067751408, -0.07833408564329147, 0.07730677723884583, -0.02415282279253006, -0.02128511294722557, 0.04009353369474411, 0.038936588913202286, 0.003247571876272559, 0.014674181118607521, 0.013620235957205296, 0.014447472989559174, 0.02188262902200222, 0.009782678447663784, 0.004233912099152803, -0.010950259864330292, 0.010483921505510807, -0.08130518347024918, -0.0030070424545556307, 0.06977050751447678, 0.025061460211873055, -0.013009265996515751, 0.05753104388713837, 0.04939799755811691, 0.03593574836850166, 0.05856750160455704, -0.016374871134757996, -0.03644997626543045, 0.048103880137205124, -0.05316467210650444, 0.05370273441076279, -0.02205732837319374, 0.049687352031469345, -0.04407791420817375, -0.03932758793234825, -0.03727950528264046, -0.00045403154217638075, 0.01797659695148468, -0.0439312644302845, 0.06312605738639832, -0.03169724717736244, -0.02753318101167679, 0.0033182655461132526, 0.038805995136499405, 0.05851288139820099, 0.01775139570236206, -0.06354880332946777, 0.054639846086502075, 0.006565979681909084, 0.03720640391111374, -0.03640766069293022, 0.057771384716033936, -0.06661026924848557, -0.0033359068911522627, 0.01883295364677906, -0.08559173345565796, -0.03693900257349014, -0.07586769014596939, 0.006688508205115795, -0.01983887329697609, -0.013700510375201702, -0.06311217695474625, 0.07390095293521881, 0.008014697581529617, -0.05971192941069603, -0.01436229981482029, 0.025316227227449417, -0.01838182471692562, 0.025313839316368103, -0.02596662938594818, 0.038101982325315475, 0.017545785754919052, -0.003575892187654972, -0.044221069663763046, 0.08518751710653305, 0.02989150583744049, -0.07950720936059952, 0.02172473818063736, 0.02975650504231453, -0.0024425589945167303, 0.04854029789566994, 0.003915910143405199, -0.029600609093904495, -0.003186238231137395, 0.004720812663435936, -0.031110230833292007, 0.03183736652135849, -0.03415093198418617, -0.027416883036494255, 0.05432335287332535, 0.0013296784600242972, 0.010785700753331184, 0.00045614063856191933, -0.04613685607910156, 0.0018888353370130062, 0.046734023839235306, 0.03036956675350666, 0.020570216700434685, -0.025302164256572723, 0.04237429425120354, 0.00034527439856901765, -0.03126200661063194, -0.04798160120844841, -0.07365162670612335, 0.0005777609767392278, -0.00445398036390543, -0.008872441947460175, -0.03897373378276825, 0.08427194505929947, 0.003986076917499304, 0.005393204744905233, -0.04143141955137253, 0.058826904743909836, 0.036770839244127274, 0.06093563139438629, -0.013502798043191433, -0.01845814473927021, 0.02391938678920269, 0.011515943333506584, -0.012014931067824364, 0.044235337525606155, 0.005798895377665758, 0.058992281556129456, -0.04279763624072075, -0.06509418040513992, -0.03581971675157547, -0.018418462947010994, -0.008941940031945705, -0.008036131039261818, 0.0048532020300626755, 0.04037397354841232, 0.0019696541130542755, -0.028910743072628975, 0.011595245450735092, -0.010921153239905834, 0.003523928113281727, -0.019413646310567856, -0.012415623292326927, 0.031990740448236465, 0.005361542571336031, 0.015170726925134659, 0.05021771788597107, -0.01950645074248314, -0.02980343997478485, -0.023406045511364937, -0.030980084091424942, -0.04074006527662277, -0.007384153548628092, 0.04268920049071312, 0.0009278321522288024, -0.030817514285445213, -0.016188833862543106, -0.009787766262888908, 0.030103687196969986, -0.021281303837895393, -0.03128724917769432, -0.027382230386137962, -0.0017669391818344593, -0.00030059131677262485, 0.022802600637078285, -0.023509863764047623, -0.007266492582857609, -0.02149561233818531, -0.029725603759288788, -0.009924110025167465, 0.03358002007007599, 0.043982818722724915, 0.037588465958833694, 0.05145871639251709, 0.08844679594039917, 0.004768948070704937, 0.0036498832050710917, -0.0855080857872963, -0.018528912216424942, 0.014513099566102028, 0.01569237746298313, 0.02462400309741497, 0.05467737093567848, -0.007278194651007652, -0.0020475469063967466, -0.024680092930793762, 0.00046668705181218684, -0.012910176068544388, -0.053272541612386703, -0.07213670015335083, 0.015880677849054337, 0.005995746236294508, -0.008686522021889687, -0.01350069884210825, -0.0070142061449587345, 0.07613372057676315, 0.03612823411822319, 0.03357316181063652, 0.025132542476058006, -0.04776235669851303, 0.049499671906232834, 0.032856401056051254, 0.017672603949904442, 0.04070034623146057, -0.09326846897602081, 0.009947342798113823, -0.009831001982092857, -0.03976631537079811, 0.04531882330775261, -0.004284801427274942, -0.030930250883102417, -0.010335154831409454, 0.0008996377582661808, -0.022555802017450333, -0.046104300767183304, -0.001006874954327941, 0.06241629272699356, 0.017974449321627617, -0.0030495449900627136, -0.05722857639193535, -0.020728716626763344, 0.04691247642040253, 0.02527460642158985, -0.015202264301478863, 0.024294491857290268, -0.022091185674071312, -0.02501671388745308, -0.006135894916951656, -0.007270712871104479, 0.0011702465126290917, -0.031160691753029823, -0.003725929418578744, -0.03508520871400833, 0.06315632909536362, 0.016263147816061974, -0.006327350158244371, 0.05365387722849846, 0.01065062079578638, -0.019071809947490692, 0.015651220455765724, -0.006070840172469616, -0.015829766169190407, 0.018146010115742683, 0.012162236496806145, 0.008806128054857254, 0.011393079534173012, -0.010453855618834496, -0.006364722270518541, -0.01200499851256609, -0.015988638624548912, -0.011386175639927387, -0.04291044548153877, -0.018088217824697495, 0.02620754763484001, -0.07815361022949219, 0.011092189699411392, -0.045368921011686325, 0.023457610979676247, 0.014148017391562462, -0.03527674078941345, -0.020341936498880386, -0.018077494576573372, -0.08202730119228363, 0.0168902724981308, 0.019050266593694687, -0.06409517675638199, -0.016106409952044487, -0.010119276121258736, -0.013021359220147133, 0.006359546445310116, 0.016831284388899803, -0.005686597898602486, 0.002113916678354144, 0.02253671921789646, 0.013860656879842281, 0.06015242263674736, -0.02808544784784317, 0.00507302675396204, -0.025032049044966698, 0.02098611742258072, 0.024520285427570343, -0.04068591445684433, -0.05901576578617096, -0.039504274725914, -0.06798861920833588, -0.014546344056725502, -0.007372016552835703, 0.006947311107069254, 0.04417817294597626, -0.027566131204366684, -0.009009850211441517, 0.02934390865266323, 0.021048936992883682, 0.026535367593169212, 0.05085371062159538, 0.008606517687439919, -0.009120597504079342, -0.028355779126286507, 0.0319930724799633, 0.01639033481478691, 0.007379250600934029, 0.055892180651426315, -0.053714342415332794, -0.026141133159399033, -0.06243676692247391, 0.014050433412194252, 0.04989127442240715, 0.010146667249500751, -0.003364371368661523, -0.04062294960021973, -0.023214949294924736, -0.04584779962897301, -0.09732771664857864, 0.05313904210925102, -0.043111033737659454, 0.030281912535429, 0.002295025158673525, 0.01697353459894657, 0.055507563054561615, 0.01397362258285284, 0.005769506562501192, -0.07260936498641968, 0.03941897302865982, -0.009824528358876705, -0.06034156307578087, -0.00477136904373765, -0.002953446237370372, -0.01674220897257328, 0.003129042685031891, -0.12429128587245941, 0.03856964409351349, -0.03675266355276108, 0.004404112230986357, -0.008019047789275646, 0.010985429398715496, -0.025041978806257248, 0.04203634336590767, -0.02814318984746933, -0.002089977264404297, 0.03222741559147835, 0.021838322281837463, 0.018158920109272003, 0.03866881877183914, 0.04454465210437775, -0.028654195368289948, 0.042130760848522186, 0.0040704961866140366, -0.0011323553044348955, -0.0038682364393025637, 0.014368758536875248, -0.09618114680051804, -0.05240434408187866, -0.02620391547679901, 0.003272325498983264, 0.06497742235660553, 0.0690726488828659, 0.0346398688852787, 0.0034133142326027155, 0.03502526506781578, -0.017825614660978317, 0.055254481732845306, -0.10171695798635483, 0.004552007187157869, 0.04751526564359665, 0.053141407668590546, 0.03834220767021179, -0.0031845830380916595, 0.09215591847896576, -0.045470405369997025, 0.005931446794420481, 0.004523747134953737, 0.01825425960123539, 0.008364828303456306, 0.0171032827347517, -0.0023029129952192307, -0.015550069510936737, 0.01969865895807743, 0.04814364016056061, 0.0390290804207325, 0.0018030469072982669, 0.059491995722055435, 0.020210647955536842, 0.01670023798942566, -0.03234788402915001, -0.03543348237872124, -0.04543966054916382, -0.0815233662724495, 0.028740867972373962, 0.10012208670377731, -0.02443329617381096, 0.07415672391653061, -0.023028815165162086, -0.021484659984707832, -0.0196769330650568, -0.008343777619302273, 0.0876396968960762, 0.007605980150401592, 0.016316622495651245, 0.049408867955207825, 0.039198748767375946, -0.01299369614571333, -0.013979933224618435, 0.02376721240580082, 0.01936066895723343, 0.03306151553988457, -0.05521510913968086, -0.004515016917139292, -0.04520512744784355, 0.012004271149635315, 0.05031584948301315, 0.023047953844070435, 0.009656587615609169, 0.026037372648715973, -0.003584649646654725, -7.783109322190285e-05, -0.002027168869972229, 0.03717593476176262, 0.029616491869091988, -0.0224281195551157, 0.03922527655959129, 0.022306716069579124, 0.003822898492217064, -0.08431617170572281, -0.0439567007124424, -0.062087077647447586, 0.10038070380687714, 0.012000730261206627, 0.02285139262676239, -5.637109607991173e-33, -0.05178888514637947, -0.02564549446105957, -0.00916440412402153, 0.01267725508660078, 0.01947932317852974, 0.028301898390054703, 0.010064088739454746, -0.027150042355060577, -0.012630943208932877, -0.03584242984652519, 0.019267160445451736, 0.04287843033671379, 0.019859833642840385, -0.019003992900252342, 0.010187423788011074, 0.003052252344787121, 0.051029887050390244, 0.0019976207986474037, -0.007359068375080824, 0.00612935284152627, 0.019269337877631187, -0.015508447773754597, 0.022280950099229813, 0.0263983067125082, 0.005404071882367134, -2.0314473658800125e-05, -0.006139818578958511, 0.06906988471746445, -0.03561461716890335, -0.0273831095546484, -0.03275927156209946, -0.02204926870763302, -0.04196210578083992, -0.0013304604217410088, 0.06622076779603958, -0.019867394119501114, -0.022418761625885963, -0.020794441923499107, -0.001163544598966837, -0.03643493354320526, -0.01709124818444252, 0.014071912504732609, 0.01625060848891735, 0.011817233636975288, -0.014579180628061295, -0.03598752245306969, -0.0013925122329965234, 0.019376888871192932, -0.020878728479146957, -0.04002481326460838, -0.009660538285970688, 0.005650731269270182, -0.00863153487443924, 0.03136827424168587, 0.0356668196618557, 0.01137703750282526, -0.03847425803542137, -0.06884212046861649, -0.02744981087744236, 0.04856892675161362, 0.032894495874643326, 0.04309886693954468, -0.01471678912639618, 0.020744688808918, 0.022633176296949387, -0.006884556729346514, 0.09122800081968307, -0.0675945058465004, 0.006059200968593359, -0.031640585511922836, -0.040304459631443024, 0.009853977710008621, 0.01203244924545288, -0.005399202462285757, 0.05430278182029724, -0.05186210945248604, -0.06950905174016953, -0.0245153047144413, 0.10205928236246109, -0.03709951415657997, 0.006702179089188576, -0.0029704677872359753, -0.0397578626871109, -0.08354809880256653, 0.022703032940626144, 0.020614899694919586, 0.009015016257762909, -0.002433326793834567, -0.02260558307170868, 0.02620445005595684, -0.014473442919552326, -0.006730637513101101, 0.01366503443568945, -0.03715146332979202, 0.003947266843169928, -0.030527856200933456, 0.032930146902799606, -0.015187093056738377, -0.010358266532421112, -0.04886733740568161, -0.013596519827842712, -0.021630138158798218, 0.0041857194155454636, -0.04949602484703064, -0.00010467263200553134, 0.033280398696660995, 0.024980641901493073, 0.009964020922780037, -0.04173192381858826, -0.001741609419696033, 0.007474089507013559, -0.04121575132012367, 0.04707763344049454, -0.0037863771431148052, 0.021897269412875175, -0.025578448548913002, -0.015037165023386478, 0.04997820407152176, -0.01128128170967102, 0.0516781322658062, -0.010430865921080112, 0.0048018633387982845, -0.0019237026572227478, 0.08704442530870438, -0.01208979170769453, -0.03760950267314911, -0.06663935631513596, 0.011215757578611374, 0.013438848778605461, -0.0776340514421463, -0.03754211589694023, -0.014034201391041279, 2.571774473381083e-07, 0.020123476162552834, -0.026298779994249344, -0.04027188569307327, -0.003888198174536228, 0.017650391906499863, -0.018320834264159203, 0.020776094868779182, 0.023379873484373093, -0.024970946833491325, 0.034719228744506836, 0.04387342929840088, -0.003027996513992548, 0.010335220023989677, -0.03000393696129322, -0.028077775612473488, -0.0721341073513031, -0.0775485560297966, -0.037476446479558945, -0.012765621766448021, 0.022283783182501793, 0.06062176451086998, 0.02316444180905819, 0.053963448852300644, 0.042791835963726044, 0.023298095911741257, 0.035816773772239685, 0.03913182020187378, 0.010883847251534462, 0.01125981193035841, 0.014418059028685093, 0.016507018357515335, -0.05700058490037918, 0.029779989272356033, -0.005812355317175388, 0.009940164163708687, 0.00104669074062258, -0.0055902996100485325, 0.009885002858936787, 0.02371952123939991, -0.006398105528205633, -0.05046573281288147, -0.0017807672265917063, 0.01324328314512968, 0.049667298793792725, 0.023574795573949814, -0.019201897084712982, -0.019829532131552696, 0.01924273930490017, -0.005166457034647465, 0.00993362907320261, 0.042885180562734604, 0.04815909266471863, 0.022772110998630524, -0.031013527885079384, -0.039744555950164795, 0.011869382113218307, 0.07374072819948196, 0.017458122223615646, 7.331417873501778e-05, 0.05176717787981033, 0.029853839427232742, -0.05351393297314644, 0.009182971902191639, -0.07558200508356094, -0.019401928409934044, -0.030486950650811195, -0.019795900210738182, 2.5497179602655833e-34, 0.00831291638314724, 0.02246473915874958, 0.0555674210190773, -0.003676596563309431, -0.00899315532296896, -0.04124896600842476, 0.01595008745789528, -0.04456532001495361, 0.018236583098769188, -0.011428323574364185, 0.0071473694406449795]

['Ke Zhang', 'Marcus Hutter', 'Huidong Jin']

0903.3257v1

Detecting outliers which are grossly different from or inconsistent with the remaining dataset is a major challenge in real-world KDD applications. Existing outlier detection methods are ineffective on scattered real-world datasets due to implicit data patterns and parameter setting issues. We define a novel "Local Distance-based Outlier Factor" (LDOF) to measure the {outlier-ness} of objects in scattered datasets which addresses these issues. LDOF uses the relative location of an object to its neighbours to determine the degree to which the object deviates from its neighbourhood. Properties of LDOF are theoretically analysed including LDOF's lower bound and its false-detection probability, as well as parameter settings. In order to facilitate parameter settings in real-world applications, we employ a top-n technique in our outlier detection approach, where only the objects with the highest LDOF values are regarded as outliers. Compared to conventional approaches (such as top-n KNN and top-n LOF), our method top-n LDOF is more effective at detecting outliers in scattered data. It is also easier to set parameters, since its performance is relatively stable over a large range of parameter values, as illustrated by experimental results on both real-world and synthetic datasets.

A New Local Distance-Based Outlier Detection Approach for Scattered Real-World Data

http://arxiv.org/pdf/0903.3257v1

Title New Local DistanceBased Outlier Detection Approach Scattered RealWorld Data Summary Detecting outlier grossly different inconsistent remaining dataset major challenge realworld KDD application Existing outlier detection method ineffective scattered realworld datasets due implicit data pattern parameter setting issue define novel Local Distancebased Outlier Factor LDOF measure outlierness object scattered datasets address issue LDOF us relative location object neighbour determine degree object deviate neighbourhood Properties LDOF theoretically analysed including LDOFs lower bound falsedetection probability well parameter setting order facilitate parameter setting realworld application employ topn technique outlier detection approach object highest LDOF value regarded outlier Compared conventional approach topn KNN topn LOF method topn LDOF effective detecting outlier scattered data also easier set parameter since performance relatively stable large range parameter value illustrated experimental result realworld synthetic datasets Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0020571411587297916, -0.027081776410341263, -0.025228314101696014, 0.03515364229679108, -0.03641258552670479, 0.0019385142950341105, 0.028102371841669083, 0.012422272004187107, -0.04271591082215309, 0.04300258681178093, 0.055509358644485474, 0.05129341036081314, 0.012499885633587837, 0.0433410219848156, -0.035082802176475525, -0.012251491658389568, 0.01873517967760563, -0.023398954421281815, 0.03246317058801651, -0.007156794425100088, 0.02645202912390232, -0.0397876538336277, 0.025028498843312263, -0.02418356202542782, -0.019197888672351837, -0.010095835663378239, -0.008682513609528542, -0.02125898003578186, 0.0688943937420845, -0.02965199202299118, 0.0740412026643753, 0.0013472442515194416, -0.01597670093178749, 0.042104147374629974, 2.2681983864458743e-06, -0.013749680481851101, -0.019608277827501297, -0.012513060122728348, 0.0601455420255661, -0.0006320143584161997, -0.0026980664115399122, 0.023217501118779182, 0.012447582557797432, -0.014247981831431389, -0.0027527224738150835, 0.03476245328783989, -0.0030532837845385075, 0.03825296461582184, 0.023622794076800346, 0.006704478990286589, -0.005306032951921225, 0.007008826360106468, -0.022976428270339966, 0.04834164306521416, 0.029795896261930466, 0.09630715101957321, 0.021510571241378784, 0.006656595505774021, -0.02738969214260578, 0.02744363434612751, -0.014144192449748516, -0.0203496515750885, 0.002587816910818219, 0.020757531747221947, 0.033128246665000916, 0.04460245743393898, -0.04656337574124336, 0.023790068924427032, 0.008788511157035828, 0.058378707617521286, -0.08632751554250717, -0.018028421327471733, 0.051601752638816833, -0.03056865744292736, -0.03853321075439453, 0.014399482868611813, -0.005360105074942112, 0.026368094608187675, -0.010756455361843109, 0.0007249513873830438, -0.029443129897117615, 0.05750054866075516, -0.04073047265410423, 0.005896293558180332, -0.029912814497947693, -0.004539042711257935, 0.0033967671915888786, -0.017222560942173004, -0.0684892013669014, -0.03492715209722519, -0.03004435822367668, -0.04456556588411331, 0.023730549961328506, 0.0120093934237957, -0.027314499020576477, -0.060171157121658325, 0.0022595487534999847, 0.005798031575977802, 0.09009960293769836, -0.010934827849268913, 0.052840013056993484, -0.010181942954659462, -0.06974400579929352, 0.02070286124944687, 0.02432037517428398, 0.01881089061498642, -0.0055890390649437904, 0.013473906554281712, 0.027115879580378532, 0.0055479807779192924, 0.03429262712597847, 0.020437318831682205, 0.043631937354803085, 0.0319606177508831, -0.06245534121990204, 0.014798790216445923, 0.02401130460202694, -0.004726476036012173, -0.006543582770973444, -0.026805082336068153, 0.01207662932574749, 0.03256691247224808, 0.008828509598970413, -0.02536209486424923, 0.032169584184885025, -0.026749949902296066, -0.07095625251531601, 0.005332248751074076, 0.01184995286166668, 0.022227782756090164, 0.005998173728585243, 0.03508930280804634, 0.04466554522514343, 0.02145267464220524, 0.021540412679314613, -0.042262159287929535, 0.0526130385696888, 0.022502927109599113, 0.011210543103516102, 0.00584384985268116, -0.021497642621397972, -0.007036522030830383, -0.03280654922127724, -0.0946408212184906, -0.036860886961221695, -0.05651253089308739, -0.02533285692334175, 0.030014518648386, -0.02337409183382988, -0.002122788690030575, 0.009328056126832962, 0.010412543080747128, -0.09890653192996979, 0.04581679403781891, 0.040035802870988846, -0.00135617156047374, 0.007009901572018862, -0.01972944289445877, -0.050946660339832306, 0.01827680878341198, 0.04179668426513672, -0.02338283695280552, 0.043154727667570114, -0.034128185361623764, -0.012843317352235317, 0.006981395184993744, -0.0227991733700037, 0.060997504740953445, -0.028191840276122093, -0.04084128886461258, -0.019472738727927208, -0.05206749588251114, 0.0012099762680009007, -0.01918032579123974, 0.008374184370040894, -0.008392573334276676, -0.044530920684337616, -0.06360390037298203, -0.048791319131851196, 0.06088373810052872, -0.07683605700731277, -0.01744925044476986, 0.022412296384572983, 0.010274630039930344, -0.061006929725408554, -0.04475225508213043, -0.03508393093943596, 0.03574560955166817, -0.03024246357381344, -0.031053833663463593, -0.03451060131192207, -0.03275427222251892, -0.013920688070356846, -0.028234878554940224, 0.006059602834284306, -0.013182925991714, 0.02954835630953312, -0.06348562985658646, 0.008042645640671253, 0.012981429696083069, -0.03644191101193428, -0.011541117914021015, 0.07638238370418549, -0.0010070821736007929, -0.027645079419016838, -0.050409432500600815, 0.004774431232362986, 0.005262613296508789, 0.051460299640893936, -0.025599487125873566, -0.05574634298682213, -0.018382111564278603, 0.02139100432395935, -0.02584812603890896, -0.009778372943401337, 0.0485360361635685, 0.03790298476815224, -0.005646479316055775, 0.017365092411637306, 0.04222409799695015, 0.013362441211938858, -0.06264619529247284, -0.001997019164264202, 0.010295123793184757, 0.03643297404050827, 0.023482760414481163, 0.017237890511751175, 0.03710446134209633, -0.008981874212622643, -0.02064550295472145, 0.030291607603430748, -0.05642031133174896, 0.027694929391145706, 0.026550257578492165, -0.008497496135532856, 0.002660819562152028, 0.044313982129096985, -0.005610013380646706, 0.029335010796785355, -0.03220140561461449, -0.01311560720205307, 0.029526568949222565, -0.017109612002968788, 0.004004269372671843, -0.017924634739756584, -0.045942097902297974, -0.05129094049334526, -0.03248133882880211, 0.015537545084953308, -0.023293597623705864, 0.035719189792871475, -0.013422196730971336, 0.07611097395420074, -0.02350245974957943, 0.024740826338529587, -0.03490922227501869, -0.010036931373178959, 0.06699004769325256, -0.0028228554874658585, 0.04522471874952316, -0.0799916610121727, -0.07492414861917496, -0.0005641723400913179, -0.012703665532171726, 0.04778409004211426, -0.008714946918189526, 0.01729700155556202, 0.0664559081196785, -0.027897661551833153, -0.015705600380897522, -0.032615527510643005, 0.037090372294187546, 0.009765279479324818, -0.012102825567126274, -0.025110293179750443, 0.03642778843641281, 0.010241135954856873, 0.031171245500445366, -0.025377660989761353, 0.08458856493234634, -0.030225764960050583, -0.06393325328826904, 0.010307036340236664, 0.016087161377072334, 0.023435458540916443, 0.004498077090829611, 0.006057289429008961, -0.028016727417707443, -0.0438036248087883, -0.005740027409046888, -0.0477469377219677, -0.014304072596132755, 0.0003023339668288827, -0.03598260506987572, 0.003447318682447076, -0.039730001240968704, 0.007269908208400011, 0.004308630712330341, 0.01816204935312271, -0.04953286051750183, 0.029995160177350044, 0.006481310352683067, -0.02163773588836193, 0.008680556900799274, -0.017222348600625992, 0.0925818607211113, 0.030804578214883804, -0.015419489704072475, 0.02002154104411602, -0.046697892248630524, 0.005345705430954695, -0.02386731468141079, 0.03591417893767357, 0.08366365730762482, 0.050260547548532486, -0.005156760569661856, -0.038877349346876144, 0.016996804624795914, -0.012762466445565224, 0.013626857660710812, -0.010075964033603668, -0.01846352033317089, -0.01831916719675064, 0.016519539058208466, 0.03437191992998123, 0.009932278655469418, -0.027031822130084038, 0.02966281585395336, -0.04927445203065872, -0.006639434490352869, 0.03345198556780815, -0.08036895841360092, -0.050660811364650726, 0.06398504972457886, -0.026604948565363884, 0.02457844838500023, 0.0028964357916265726, -0.03858835995197296, -0.0018004156881943345, -0.02625815011560917, 0.023637309670448303, 0.004506029654294252, -0.0481005497276783, -0.029031075537204742, 0.048477932810783386, -0.06848932057619095, -0.03383798897266388, -0.044791072607040405, 0.09087298810482025, 2.2033897039364092e-05, -0.039067137986421585, 0.07021970301866531, -0.026324963197112083, 0.021843060851097107, -0.010837226174771786, 0.014965713955461979, 0.0051835672929883, -0.021580372005701065, 0.014437435194849968, 0.011544600129127502, -0.001187964458949864, 0.03904715180397034, -0.032960742712020874, -0.03717418387532234, -0.02331431955099106, 0.012582579627633095, -0.022396167740225792, -0.023648828268051147, 0.015748566016554832, 0.005990324541926384, 0.09919524937868118, 0.012763083912432194, -0.05663793534040451, 0.06384999305009842, 0.03422916680574417, 0.013086975552141666, 0.01999259553849697, -0.07631539553403854, -0.00834436621516943, 0.033335279673337936, -0.012199901044368744, 0.028443461284041405, 0.03597917780280113, 0.017026055604219437, 0.009790252894163132, -0.04584557190537453, -0.08672984689474106, 0.039095714688301086, -0.07676978409290314, 0.04357411339879036, -0.005208489950746298, -0.10147061944007874, -0.11620515584945679, -0.03394751250743866, -0.02432159148156643, 0.0534200444817543, -0.006291136611253023, 0.01105745043605566, 0.04227667674422264, -0.010381023399531841, 0.0001168160088127479, -0.07872986793518066, -0.005794464610517025, 0.01799170672893524, -0.052127473056316376, 0.016953391954302788, -0.023974880576133728, 0.027955902740359306, 0.0001998996885959059, -0.018597275018692017, -0.02525145746767521, 0.020857591181993484, 0.03444492444396019, -0.025453923270106316, 0.05217187479138374, 0.08535655587911606, -0.013694610446691513, -0.036043595522642136, 0.010553243570029736, -0.058962382376194, 0.00958611536771059, 0.00925347302109003, 0.04174918308854103, -0.04457016661763191, 0.04781074821949005, -0.02698281779885292, -0.004143310245126486, 0.05725304037332535, -0.014814035035669804, -0.004627433605492115, -0.00928144995123148, -0.023269260302186012, 0.0013204308925196528, -0.020077193155884743, 0.0752430260181427, 0.03801153600215912, 0.05631053447723389, 0.015172010287642479, -0.05909109115600586, -0.09128934144973755, -0.04908030107617378, -0.014058255590498447, 0.02168380469083786, 0.015355104580521584, -0.00245941081084311, -0.10204074531793594, -0.008637779392302036, -0.016897566616535187, -0.05801010876893997, 0.01342704426497221, -0.011890840716660023, 0.04862651973962784, 0.0982309877872467, -0.002523384988307953, 0.02508830651640892, -0.049935683608055115, -0.05870150402188301, -0.035889603197574615, 0.009212487377226353, 0.0359346903860569, 0.03000880405306816, 0.005913327913731337, 0.014508525840938091, -0.0807349681854248, -0.0122001301497221, 0.005852335598319769, 0.019676165655255318, 0.0074363755993545055, -0.03351686894893646, 0.022809451445937157, -0.07597312331199646, 0.042384982109069824, 0.009596618823707104, 0.007099025882780552, 0.06677339971065521, 0.052158843725919724, -0.05383744463324547, -0.06037009879946709, 0.05507601425051689, 0.005540008656680584, 0.04421595484018326, 0.09212338179349899, 0.03408970683813095, -0.02518698200583458, -0.011176535859704018, 0.020700467750430107, -0.04598170518875122, 0.009040910750627518, 0.014495712704956532, 0.004996058996766806, -0.0005888859741389751, 0.058339446783065796, -0.03215519338846207, 0.05220504477620125, 0.009694002568721771, -0.006976217497140169, -0.007306497078388929, -0.007613919675350189, 0.025543415918946266, 0.04200875759124756, -0.03277552127838135, 0.003017372451722622, 0.01863284967839718, -0.02989180199801922, 0.028038453310728073, 0.046314459294080734, -0.0034441768657416105, -0.03540072217583656, 0.0322723314166069, 0.005809364840388298, -0.03383202850818634, -0.01724081300199032, -0.015308275818824768, 0.0056673805229365826, -0.030974198132753372, 0.0264279842376709, 0.010503769852221012, 0.02461235597729683, -0.03272180259227753, 0.005523748695850372, 0.013024836778640747, -0.018402880057692528, 0.035006649792194366, -0.00522083742544055, 0.009469951502978802, -0.027749713510274887, 0.0091878492385149, -0.04355460777878761, 0.057313479483127594, -0.01828577183187008, -0.010519499890506268, -0.014515494927763939, 0.006537233013659716, -0.009981993585824966, -0.011592503637075424, 0.10121103376150131, -0.019375065341591835, -0.0008279826142825186, -0.00043238551006652415, -0.0077810571528971195, 0.028946207836270332, -0.004357292316854, -0.00807566475123167, 0.01817101053893566, 0.0073595792055130005, 0.07794339954853058, -0.01536251325160265, 0.0391242578625679, -0.08075415343046188, -0.01707838848233223, -0.011705947108566761, -0.029022207483649254, 0.0020573122892528772, -0.03334682807326317, -0.004242794122546911, -5.892758690801897e-33, 0.00976546946913004, -0.06637492775917053, -0.03804837912321091, -0.06156431511044502, -0.0004659799160435796, -0.0025169304572045803, 0.011721492744982243, -0.026545843109488487, 0.026414060965180397, 0.011829322203993797, -0.038793157786130905, 0.023538334295153618, 0.00470674829557538, -0.01792805828154087, 0.022793957963585854, -0.010800912976264954, 0.014405567198991776, 0.015113506466150284, 0.018802806735038757, -0.0327761285007, 0.02663271315395832, 0.016067972406744957, 0.03706878051161766, -0.06782535463571548, -0.04844028502702713, -0.02575180120766163, -0.02240104228258133, 0.015924669802188873, -0.008276010863482952, -0.01794463023543358, 0.03441666439175606, 0.030683007091283798, -0.01098229456692934, 0.03087669610977173, -0.07250009477138519, -0.08226656913757324, -0.03498443588614464, -0.051925159990787506, -0.06921179592609406, 0.014083776623010635, 0.07796106487512589, -0.032330043613910675, 0.045843806117773056, -0.009246937930583954, -0.025173643603920937, -0.0010665666777640581, 0.056349582970142365, -0.03355350345373154, -0.020930424332618713, 0.09259645640850067, 0.04374486953020096, 0.009423919953405857, -0.02841823734343052, 0.03694977983832359, -0.06398593634366989, 0.004168019164353609, -0.00596356438472867, 0.033417537808418274, -0.06464304774999619, 0.05448276922106743, 0.06615112721920013, -0.017510544508695602, -0.028294432908296585, -0.00949301291257143, 0.04478338360786438, 0.02718603052198887, 0.07296290248632431, -0.030322162434458733, 0.01721116341650486, 0.0155578488484025, -0.003396049840375781, 0.06529083102941513, -0.005012229084968567, 0.05853968858718872, 0.06414473056793213, -0.020567916333675385, -0.05682303011417389, 0.04301274195313454, -0.05256565660238266, -0.050055380910634995, -0.026378005743026733, -0.03942806273698807, -0.05467914417386055, -0.009945644997060299, 0.09603171795606613, -0.040818314999341965, 0.03445826843380928, -0.01278185099363327, 0.021409353241324425, 0.002796619664877653, -0.0488736517727375, 0.013052072376012802, -0.024935493245720863, -0.039946962147951126, 0.015784509479999542, -0.02862553298473358, -0.001306399586610496, 0.012266434729099274, 0.03385329246520996, 0.005140877328813076, 0.028134744614362717, -0.015187420882284641, -0.011985682882368565, -0.0021082551684230566, -0.010652691125869751, 0.01631583832204342, 0.021819211542606354, 0.04621182382106781, -0.04992929473519325, 0.02560846135020256, 0.037496741861104965, -0.03362269327044487, -0.03165499120950699, 0.0504104308784008, -0.01423119567334652, -0.06043562293052673, -0.0086157051846385, 0.06800244748592377, 0.014952206052839756, 0.019147630780935287, -0.015865202993154526, -0.016833025962114334, -0.05015179142355919, -0.04502357169985771, -0.026779236271977425, -0.006019310560077429, -0.01725872978568077, -0.03677957132458687, 0.041441068053245544, -0.0069315447472035885, -0.010625462047755718, -0.043713439255952835, 2.9385918765001406e-07, -0.04554179310798645, 0.06284688413143158, 0.02234756201505661, 0.002863098867237568, 0.008099098689854145, -0.026809416711330414, 0.01737561635673046, 0.03612286224961281, -0.020224163308739662, -0.020069394260644913, 0.06880848109722137, -0.038361866027116776, -0.03683779016137123, 0.00650325370952487, -0.027736656367778778, 0.0366850383579731, -0.016929281875491142, -0.03680815547704697, -0.05604297295212746, 0.007397625595331192, -0.025390660390257835, 0.031597111374139786, 0.033175885677337646, -0.038460128009319305, 0.05569374933838844, 0.0038247897755354643, -0.029426611959934235, -0.04458240792155266, -0.007328559644520283, -0.022645870223641396, 0.029025234282016754, -0.034307464957237244, 0.053501907736063004, -0.0034917863085865974, 0.0023406618274748325, 0.028777670115232468, -0.0017363640945404768, 0.03016415797173977, -0.03332821652293205, 0.0015548324445262551, 0.009771661832928658, 0.0041451300494372845, -0.002319257240742445, -0.042019154876470566, 0.025904785841703415, 0.041261833161115646, 0.007892322726547718, 0.033478621393442154, -0.015579870902001858, 0.0004379695456009358, 0.03969745337963104, -0.009051577188074589, 0.037874024361371994, -0.011922129429876804, 0.015144714154303074, -0.014409784227609634, 0.0644308403134346, 0.034117117524147034, 0.0014826629776507616, -0.014508925378322601, -0.01282849907875061, -0.02847267873585224, 0.04610186815261841, 0.032861754298210144, 0.027036894112825394, 0.05373600870370865, -0.04045623913407326, 2.627904405807093e-34, 0.017197731882333755, 0.043515924364328384, -0.009666426107287407, -0.028282536193728447, -0.038748182356357574, 0.028527826070785522, 0.0005046982550993562, -0.020167695358395576, 0.03079231269657612, 0.018684115260839462, -0.0011499623069539666]

['Thomas Bréhard', 'Emmanuel Duflos', 'Philippe Vanheeghe', 'Pierre-Arnaud Coquelin']

0903.3329v1

This paper introduces a new approach to solve sensor management problems. Classically sensor management problems can be well formalized as Partially-Observed Markov Decision Processes (POMPD). The original approach developped here consists in deriving the optimal parameterized policy based on a stochastic gradient estimation. We assume in this work that it is possible to learn the optimal policy off-line (in simulation) using models of the environement and of the sensor(s). The learned policy can then be used to manage the sensor(s). In order to approximate the gradient in a stochastic context, we introduce a new method to approximate the gradient, based on Infinitesimal Perturbation Approximation (IPA). The effectiveness of this general framework is illustrated by the managing of an Electronically Scanned Array Radar. First simulations results are finally proposed.

Optimal Policies Search for Sensor Management

http://arxiv.org/pdf/0903.3329v1

Title Optimal Policies Search Sensor Management Summary paper introduces new approach solve sensor management problem Classically sensor management problem well formalized PartiallyObserved Markov Decision Processes POMPD original approach developped consists deriving optimal parameterized policy based stochastic gradient estimation assume work possible learn optimal policy offline simulation using model environement sensor learned policy used manage sensor order approximate gradient stochastic context introduce new method approximate gradient based Infinitesimal Perturbation Approximation IPA effectiveness general framework illustrated managing Electronically Scanned Array Radar First simulation result finally proposed Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.004011965822428465, 0.020912781357765198, 0.009859351441264153, -0.03279445692896843, 0.017989538609981537, -0.012120665982365608, 0.06442099064588547, -0.053652361035346985, -0.002512391423806548, -0.011414512060582638, 0.034598637372255325, 0.04922235757112503, 0.004305312409996986, 0.019498711451888084, -0.03124280646443367, 0.009405672550201416, 0.030909670516848564, -0.042419061064720154, 0.007848820649087429, 0.014886647462844849, 0.007852090522646904, -0.05566120147705078, -0.019851254299283028, -0.0023071193136274815, -0.018304381519556046, -0.01016976498067379, -0.0028776456601917744, -0.016244638711214066, 0.05393677577376366, -0.054613348096609116, 0.04506361111998558, -0.06555070728063583, 0.014074545353651047, 0.022900449112057686, 2.061978648271179e-06, 0.022463755682110786, -0.019835006445646286, -0.020733704790472984, 0.06336959451436996, -0.033424846827983856, 0.057901233434677124, -0.046852633357048035, 0.0069155641831457615, 0.024951737374067307, -9.235485777026042e-05, -0.02271019108593464, 0.05630878731608391, 0.004714825190603733, -0.011663660407066345, 0.030015001073479652, 0.013025983236730099, -0.05337408185005188, -5.600354779744521e-05, -0.03893879055976868, -0.010760931298136711, -0.05199407413601875, 0.028563907369971275, -0.03021000139415264, -0.002035835525020957, -0.010592670179903507, -0.020553497597575188, 0.03739027678966522, -0.00664445711299777, -0.027381595224142075, 0.06702616810798645, 0.005267196334898472, 0.015780547633767128, 0.02790076658129692, -0.020856531336903572, -0.01672525703907013, -0.03810298442840576, -0.011010042391717434, 0.08133448660373688, -0.018124496564269066, -0.044507015496492386, -0.016980258747935295, 0.0022963262163102627, -0.060261476784944534, -0.018152285367250443, 0.007827754132449627, -0.03944705054163933, 0.004641276318579912, -0.04704558476805687, 0.008410170674324036, -0.060419097542762756, 0.09558999538421631, -0.05342018976807594, -0.02182311750948429, -0.008100856095552444, -0.020514527335762978, 0.019972560927271843, -0.029515542089939117, -0.005792419891804457, 0.03150015324354172, -0.09548851102590561, 0.019536569714546204, -0.030995426699519157, -0.02661524899303913, -0.013331189751625061, 0.006028950214385986, 0.005405297037214041, 0.028128724545240402, 0.035987649112939835, 0.026263993233442307, 0.00033251947024837136, 0.021849364042282104, -0.04170697182416916, -0.012627063319087029, -0.034598372876644135, -0.037909988313913345, -0.03745158761739731, -0.008478772826492786, 0.042769789695739746, 0.09175393730401993, 0.05154222249984741, -0.005772818345576525, -0.004036987666040659, -0.02018425241112709, 0.0018298361683264375, -0.0024021416902542114, -0.007248143665492535, 0.01021620724350214, -0.023386765271425247, 0.008381728082895279, -0.025056492537260056, -0.009058571420609951, 0.001913759857416153, 0.029912566766142845, 0.005098981782793999, 0.04148058593273163, 0.021047644317150116, 0.02059619128704071, 0.01519403699785471, 0.02274247072637081, -0.03853929415345192, 0.04235834628343582, 0.012096394784748554, 0.02217104844748974, -0.04452553763985634, 0.01183699257671833, 0.052990421652793884, -0.0016266065649688244, 0.0038123633712530136, -0.007164062466472387, 0.03003622777760029, -0.03910326212644577, -0.025581208989024162, 0.009057903662323952, 0.0031852812971919775, 0.014458549208939075, 0.004292030818760395, 0.048282917588949203, 0.020260978490114212, -0.015929779037833214, 0.048971887677907944, -0.04030837118625641, -0.04068458825349808, 0.03056810423731804, 0.043542344123125076, -0.0169485155493021, -0.019376203417778015, -0.012206274084746838, -0.02345443144440651, -0.011161496862769127, -0.004994706250727177, -0.01605156436562538, 0.014250954613089561, 0.006406662054359913, -0.06800560653209686, 0.059446703642606735, 0.011775786988437176, -0.05886191129684448, 0.03004326857626438, 0.041186608374118805, 0.0014868100406602025, 0.029865020886063576, -0.028811292722821236, -0.011175896972417831, 0.01261311024427414, 0.08963432908058167, -0.02278308756649494, -0.02765851654112339, 0.02115403115749359, 0.05571633204817772, -0.04145962744951248, -0.07730240374803543, -0.046245306730270386, -0.020703503862023354, -0.008269325830042362, -0.03453433886170387, 0.006192253902554512, -0.014469234272837639, -0.07532641291618347, 0.002096188720315695, 0.025828633457422256, -0.08010292798280716, -0.005600643809884787, -0.07641532272100449, 0.029853180050849915, 0.08602258563041687, -0.018844811245799065, -0.03654050827026367, 0.033536408096551895, -0.06171560287475586, 0.0028535015881061554, -0.07337133586406708, -0.07196861505508423, -0.06488926708698273, 0.01829206943511963, -0.06477881222963333, -0.02774636074900627, 0.034975823014974594, -0.0025088477414101362, -0.019700951874256134, -0.050173867493867874, 0.021565398201346397, 0.0010951190488412976, 0.0671980157494545, -0.07622275501489639, 0.04296581819653511, -0.03666604310274124, 0.03003975749015808, -0.003768750000745058, 0.028786567971110344, 0.03978617861866951, -0.028679857030510902, 0.017238108441233635, 0.05081116408109665, 0.039453811943531036, -0.04533956199884415, 0.0038484055548906326, -0.0013841185718774796, -0.007754620164632797, -0.017973434180021286, 0.007736142724752426, 0.01071820966899395, -0.013203410431742668, -0.05382820963859558, 0.0204219538718462, -0.011430720798671246, 0.02717622183263302, 0.024165553972125053, -0.03690749779343605, -0.06918167322874069, 0.012498489581048489, -0.00044169402099214494, 0.025691719725728035, 0.030436992645263672, -0.03576261177659035, -0.0018594497814774513, -0.034176331013441086, 0.0050095561891794205, 0.026408156380057335, 0.0006070849485695362, -0.00814410112798214, -0.008334946818649769, 0.01292085275053978, 0.08563787490129471, -0.03383832797408104, 0.05844409763813019, 0.019325541332364082, -0.0029205225873738527, -0.03644028306007385, 0.012611852958798409, 0.05812077224254608, 0.09633633494377136, -0.023942574858665466, 0.05157892405986786, -0.04352016746997833, -0.007730753626674414, 0.01144458632916212, 0.0074697695672512054, -0.01849844865500927, 0.013098577968776226, 0.007772535551339388, 0.02232169918715954, 0.03475717455148697, -0.0532865971326828, -0.06952162832021713, -0.019588815048336983, 0.02091378904879093, -0.02688034065067768, -0.006478512194007635, -0.023324856534600258, 0.027664342895150185, 0.014217518270015717, 0.01747620850801468, -0.0032379906624555588, -0.03483635559678078, -0.034999970346689224, -0.011793645098805428, 0.003578725503757596, -0.010077964514493942, -0.030016200616955757, -0.0010923051740974188, -0.04670478403568268, 0.007068244740366936, 0.03157893568277359, -0.014645259827375412, 0.008802060969173908, 0.020454471930861473, 0.03280636668205261, -0.06324291229248047, 0.03638368472456932, 0.008696606382727623, 0.006556397769600153, -0.014367948286235332, 0.07638707756996155, 0.008912715129554272, -0.007423363626003265, 0.0032901037484407425, 0.0002784786920528859, 0.034092653542757034, 0.006324188318103552, -0.03462941572070122, -0.05879414081573486, -0.11010676622390747, 0.03421606123447418, -0.019308200106024742, -0.016756482422351837, 0.014482472091913223, 0.02589741349220276, 0.051851145923137665, 0.019965482875704765, 0.01081586442887783, -0.06109115853905678, -0.0484507754445076, 0.01850247010588646, -0.09130056947469711, 0.013004718348383904, 0.013268053531646729, -0.025033190846443176, 0.023623026907444, -0.01309118326753378, -0.06220681220293045, 0.025583861395716667, -0.018226465210318565, -0.09154792875051498, 0.0710105374455452, 0.05835516005754471, 0.0291056577116251, 0.0371776707470417, -0.007582397200167179, 0.03152228891849518, -0.0006909903604537249, -0.06586336344480515, -0.06022533029317856, -0.008103976957499981, -0.030271833762526512, -0.010657229460775852, 0.042837247252464294, 0.04406321793794632, 0.0034743843134492636, -0.019833482801914215, -0.03333812579512596, 0.013091960921883583, 0.05650670826435089, -0.08582782000303268, -0.009610097855329514, 0.01807270757853985, 0.026162076741456985, -0.006802144460380077, 0.047183990478515625, -0.01867905631661415, -0.0907723605632782, -0.021066395565867424, 0.013719323091208935, 0.012711143121123314, 0.02021370455622673, 0.014597629196941853, -0.004486287944018841, -0.041238412261009216, 0.011250793002545834, 0.014117173850536346, -0.03380218520760536, -0.048776138573884964, -0.0136208925396204, -0.05352666229009628, 0.008880237117409706, -0.025006573647260666, 0.019491463899612427, 0.054821573197841644, 0.003535874653607607, 0.027147924527525902, 0.06974614411592484, -0.017547035589814186, -0.019558610394597054, 0.02378232777118683, -0.03027145005762577, 0.03853536397218704, -0.053335223346948624, -0.03418680652976036, -0.09303242713212967, -0.03719744458794594, -0.0019643716514110565, -0.041637737303972244, 0.02201126143336296, 0.028621042147278786, 0.040565527975559235, 0.006523523014038801, 0.037059396505355835, -0.040580037981271744, -0.009647661820054054, -0.06355056166648865, -0.05150929093360901, 0.025298554450273514, 0.06285561621189117, 0.026377517729997635, -0.011463313363492489, -0.00933604221791029, 0.0286359004676342, 0.005316396709531546, -0.004139395896345377, -0.025556519627571106, -0.07527852058410645, 0.024734223261475563, -0.0012552998960018158, -0.01055366825312376, 0.05516200140118599, 0.008592519909143448, 0.026898227632045746, 0.006877145264297724, 0.04806336760520935, -0.07510390877723694, 0.0343935452401638, -0.030033333227038383, -0.04339633136987686, 0.09741302579641342, -0.011806276626884937, -0.024911217391490936, 0.012745564803481102, -0.03437071666121483, 0.01935207098722458, -0.015875739976763725, -0.0039055445231497288, 0.022013355046510696, -0.028487563133239746, -0.007609798572957516, 0.012057551182806492, -0.02681760862469673, -0.04234425351023674, -0.023942576721310616, 0.03856140002608299, 0.008649864234030247, 0.046132467687129974, 0.07089431583881378, 0.01410763431340456, 0.01314142532646656, -0.06498625874519348, 0.03910693898797035, 0.005311104469001293, 0.024902336299419403, 0.058986846357584, 0.027534646913409233, -0.006771572399884462, -0.04495807737112045, -0.10298974066972733, -0.0373212955892086, -0.008184734731912613, 0.02367652952671051, 0.06530635803937912, 0.0027174954302608967, -0.009198811836540699, -0.03992406651377678, -0.03324459120631218, 0.0423310324549675, -0.02390052191913128, 0.039405081421136856, -0.004810338839888573, 0.015671156346797943, 0.008356614969670773, 0.013527411967515945, 0.015534646809101105, -0.0023054187186062336, 0.055312417447566986, 0.004118380136787891, -0.0023269280791282654, 0.04952266812324524, 0.0175093375146389, 0.002499910304322839, 0.010195471346378326, 0.006107613444328308, 0.011799534782767296, -0.061386458575725555, -0.03450370579957962, 0.012857208959758282, -0.022348254919052124, 0.019513169303536415, -0.018053779378533363, 0.09915650635957718, 0.00584378931671381, 0.0027877772226929665, -0.003862474113702774, -0.005635416600853205, 0.0643240436911583, -0.061567146331071854, 0.018757343292236328, 0.04266580566763878, -0.006369347218424082, -0.014820685610175133, 0.010747307911515236, -0.008754882030189037, 0.059181805700063705, -0.0107734939083457, 0.05703768506646156, -0.012710223905742168, -0.004978615790605545, -0.034654419869184494, 0.04861875995993614, -0.01666574366390705, -0.009343032725155354, -0.040209151804447174, 0.0020071014296263456, -0.05524611100554466, 0.04086793586611748, 0.0765557736158371, 0.09627129882574081, 0.04262581467628479, -0.0535435751080513, -0.009162106551229954, 0.026104649528861046, 0.03791847825050354, 0.01899394392967224, 0.03745586797595024, 0.11493591219186783, 0.05264994129538536, 0.015051797032356262, 0.004609622992575169, 0.013124331831932068, 0.01982158236205578, 0.018662016838788986, 0.060359805822372437, -0.019592847675085068, 0.025218576192855835, -0.023116808384656906, 0.07599330693483353, -0.0015406922902911901, 0.06967818737030029, -0.020608199760317802, 0.01715659722685814, 0.05690242350101471, 0.007322898134589195, -0.02652621641755104, -0.0013598896330222487, -0.013726072385907173, -0.04822014272212982, 0.018794767558574677, -0.0033111865632236004, -0.027246644720435143, 0.10804713517427444, -0.007391601800918579, -0.01985125243663788, -0.018354445695877075, -0.016444213688373566, -0.01414995826780796, -5.1670903958667894e-33, 0.0017495236825197935, -0.011920151300728321, -0.04832473024725914, -0.007018525619059801, -0.04822098836302757, -0.033657658845186234, 0.03624391555786133, -0.043860260397195816, 0.04141650348901749, -0.02952759712934494, -0.035515058785676956, 0.02138105221092701, 0.03302253037691116, -0.02797512710094452, 0.009396862238645554, -0.003589560743421316, 0.007459001615643501, -0.03577733039855957, -0.0044601005502045155, -0.007340629119426012, 0.03035045973956585, 0.020217398181557655, -0.036292124539613724, -0.036825958639383316, -0.051849592477083206, 0.005553882103413343, -0.011618481948971748, -0.01757620833814144, -0.032479770481586456, 0.03252261504530907, -0.027015995234251022, -0.008296270854771137, -0.030152613297104836, 0.01340081263333559, -0.022592071443796158, 0.041540052741765976, -0.027913548052310944, -0.04434478282928467, -0.06734068691730499, 0.04104668274521828, 0.012328793294727802, -0.04209534078836441, 0.025408392772078514, 0.008190366439521313, -0.038515496999025345, 0.07450052350759506, 0.04787495732307434, 0.026535477489233017, 0.0019240688998252153, -0.01935935579240322, 0.007556697819381952, 0.016042843461036682, -0.03210059553384781, 0.018869822844862938, 0.02167818322777748, 0.0051514930091798306, -0.029462585225701332, -0.01207488588988781, -0.054393526166677475, -0.017632262781262398, -0.01501726545393467, 0.08123283833265305, -0.016086211428046227, 0.04064583033323288, 0.041266679763793945, 0.06690485030412674, 0.017129311338067055, 0.00843823328614235, 0.04515038803219795, -0.024494701996445656, -0.019081512466073036, -0.0381762832403183, -0.05298278108239174, 0.04442277550697327, 0.06130820885300636, -0.04171239212155342, -0.03982918709516525, 0.032532699406147, 0.010996664874255657, 0.1100088581442833, 0.005381474737077951, -0.005741257220506668, -0.022724971175193787, 0.02781369537115097, 0.06615077704191208, 0.001840903889387846, 0.012882738374173641, 0.003036349546164274, 0.002894133795052767, 0.028441432863473892, -0.043855857104063034, 0.007730236742645502, 0.006282643880695105, -0.03963218629360199, 0.032233286648988724, 0.004605147987604141, 0.039837200194597244, -0.015377523377537727, 0.034470587968826294, 0.025603769347071648, -0.05592883378267288, -0.06111309677362442, 0.0004185487050563097, -0.03664762154221535, -0.006942850071936846, -0.006240831688046455, -0.023184768855571747, 0.02671820856630802, -0.006318862549960613, 0.002366448752582073, 0.023689115419983864, 0.03927977383136749, -0.01846517063677311, -0.00010302272858098149, 0.02422570437192917, -0.049130234867334366, -0.005997788161039352, 0.054709821939468384, 0.025991950184106827, -0.0887996256351471, 0.0198927354067564, 0.03938543051481247, -0.002083373488858342, -0.04391786456108093, -0.024815503507852554, 0.016307568177580833, -0.06977437436580658, -0.03603615611791611, -0.04075697809457779, 0.015611667186021805, -0.0168477613478899, -0.028515253216028214, 2.7696916049535503e-07, -0.0479821115732193, 0.011890660971403122, 0.019577939063310623, 0.0282609760761261, 0.019323404878377914, -0.0020426970440894365, -0.023841893300414085, 0.012447456829249859, -0.015901681035757065, 0.0035003821831196547, 0.027659086510539055, -0.0744672566652298, 0.028312986716628075, -0.039510373026132584, -0.015197045169770718, -0.047141578048467636, 0.06106070801615715, 0.07684139162302017, -0.039521895349025726, -0.0052574011497199535, 0.04437761753797531, -0.02696777693927288, -0.00976958591490984, -0.006260622292757034, 0.016196466982364655, 0.008915096521377563, 0.01841440238058567, 0.03392023220658302, 0.019374428316950798, -0.03505462408065796, 0.06019360199570656, 0.03136226162314415, -0.031846508383750916, -0.04072639346122742, 0.031460851430892944, 0.05253475904464722, -0.015969572588801384, 0.034027453511953354, 0.007988576777279377, -0.046573132276535034, 0.04570610821247101, -0.0010217669187113643, 0.02217697910964489, -0.026621395722031593, 0.038507744669914246, -0.00506835849955678, -0.01815715990960598, 0.017672674730420113, 0.02085679955780506, 0.04641261696815491, -0.02331894263625145, -0.004805495496839285, 0.008303085342049599, -0.05801299214363098, -0.013732966035604477, -0.009150036610662937, 0.0020116360392421484, 0.024454403668642044, 0.013638889417052269, 0.03994777053594589, -0.007972896099090576, -0.042118895798921585, 0.03119993768632412, 0.024057162925601006, 0.06966428458690643, -0.018207775428891182, -0.047276780009269714, 2.3147951846650087e-34, 0.016357045620679855, -0.0385531410574913, -0.042357221245765686, -0.00592047767713666, -0.07981114834547043, 0.035431768745183945, -0.003930260427296162, 0.002564414404332638, 0.02751089632511139, -0.03100470080971718, -0.012762457132339478]

['Yusuke Watanabe', 'Kenji Fukumizu']

0903.4527v2

The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labeled by subgraphs called generalized loops. In our recent paper, we derive the loop series expansion in form of a polynomial with coefficients positive integers, and extend the result to the expansion of marginals. In this paper, we give more clear derivation for the results and discuss the properties of the polynomial which is introduced in the paper.

Graph polynomials and approximation of partition functions with Loopy Belief Propagation

http://arxiv.org/pdf/0903.4527v2

Title Graph polynomial approximation partition function Loopy Belief Propagation Summary Bethe approximation loopy belief propagation algorithm successful method approximating partition function probabilistic model associated graph Chertkov Chernyak derived interesting formula called Loop Series Expansion expansion partition function main term series Bethe approximation term labeled subgraphs called generalized loop recent paper derive loop series expansion form polynomial coefficient positive integer extend result expansion marginals paper give clear derivation result discus property polynomial introduced paper Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0672140121459961, -0.0003894760156981647, 1.8580265077616787e-06, 0.018500754609704018, -0.04627486318349838, -0.03394502401351929, -0.005249932873994112, -0.08961576968431473, 0.09308241307735443, 0.025672605261206627, 0.06450536102056503, 0.003210430033504963, -0.0008278469904325902, 0.08980850875377655, 0.001037871465086937, -0.04729620739817619, 0.019569437950849533, -0.04359334334731102, -0.0029799379408359528, -0.06552499532699585, 0.01497858576476574, -0.03256291151046753, -0.027899684384465218, -0.023478761315345764, -0.034062013030052185, -0.043458305299282074, -0.02151656709611416, -0.014853596687316895, -0.02331443876028061, -0.02458183839917183, -0.036612361669540405, -0.019260859116911888, -0.008300875313580036, 0.014294151216745377, 1.8857998611565563e-06, -0.01616028882563114, -0.02592320926487446, -0.009829796850681305, 0.007358549162745476, -0.03028692491352558, 0.055732280015945435, 0.04981767758727074, 0.036164335906505585, 0.0015376376686617732, -0.025558631867170334, -0.017847225069999695, 0.037789877504110336, 0.06490200757980347, -0.022815659642219543, 0.0014343976508826017, 0.006966875866055489, -0.013247033581137657, 0.039436038583517075, 0.009041049517691135, 0.041671544313430786, -0.03574896603822708, 0.0563211590051651, 0.02629069611430168, 0.013743521645665169, -0.08333255350589752, -0.03494485467672348, 0.011526097543537617, 0.01325268018990755, -0.014342302456498146, -0.007328279782086611, 0.022385068237781525, 0.052153442054986954, -0.0002953789080493152, -0.019353246316313744, 0.005719813983887434, 0.012769790366292, -0.029193995520472527, -0.02671065554022789, 0.017450859770178795, -0.016354160383343697, 0.08005382865667343, -0.04434684291481972, -0.04788645729422569, -0.06926797330379486, 0.012502124533057213, -0.025816932320594788, -0.016068078577518463, 0.044257521629333496, -0.013676566071808338, -0.017248718068003654, 0.11298556625843048, 0.02018010802567005, 0.021062111482024193, 0.01996842958033085, 0.0009145177318714559, -0.03492256999015808, -0.04286151006817818, 0.001555019523948431, -0.005463108420372009, -0.02794046886265278, -0.028721049427986145, -0.01629268378019333, 0.08390042185783386, -0.047794755548238754, 0.004027091432362795, -0.04688062146306038, -0.02628638967871666, 0.03472723066806793, 0.002699005650356412, -0.023086700588464737, -0.0270973090082407, -0.0658816546201706, -0.005056282039731741, -0.016455965116620064, 0.052357207983732224, -0.04855494946241379, 0.006259840447455645, -0.004639300983399153, 0.0814601480960846, 0.01104622520506382, -0.029161840677261353, -0.054410818964242935, 0.08739271014928818, -0.04247196391224861, -0.039411962032318115, 0.034358344972133636, 0.0422036349773407, 0.04909420758485794, 0.023732054978609085, -0.010630718432366848, 0.0457325205206871, -0.007311852183192968, 0.019222479313611984, -0.021637892350554466, -0.018476609140634537, 0.014862698502838612, -0.004461496137082577, 0.01871258206665516, 0.05451119691133499, -0.015381606295704842, 0.017408525571227074, 0.039913177490234375, -0.009382188320159912, 0.0019535846076905727, 0.0027516393456608057, -0.04673679545521736, -0.02798589877784252, -0.04153507947921753, -0.11872696876525879, 0.002849502954632044, -0.0230450127273798, 0.002222126815468073, 0.015369266271591187, -0.006824766751378775, -0.053812120109796524, -0.03933624178171158, 0.05128529667854309, -0.04335575923323631, -0.03463702276349068, 0.06192757934331894, -0.024174699559807777, -0.03962896019220352, 0.0010454388102516532, 0.008466710336506367, 0.028460223227739334, 0.008578197099268436, 0.013440090231597424, 0.02670869417488575, -0.050473544746637344, -0.027419518679380417, -0.002553456462919712, 0.011296592652797699, -0.0248771570622921, -0.005281203892081976, -0.013144711032509804, -0.03154834732413292, 0.024178048595786095, -0.0013351606903597713, -0.008190969936549664, -0.011580850929021835, -0.00039244318031705916, 0.01168630737811327, -0.00909490417689085, 0.0060186805203557014, 0.010844308882951736, 0.029948977753520012, 0.026861270889639854, -0.06745088845491409, -0.0005835505435243249, -0.0518442764878273, -0.01042194478213787, 0.027329271659255028, -0.03633742779493332, -0.023336678743362427, 0.01830541342496872, 0.03670027107000351, -0.024255122989416122, 0.007064324337989092, -0.03188324347138405, 0.029499288648366928, -0.05491723120212555, -0.012989376671612263, -0.02990352176129818, 0.019986098632216454, 0.020583638921380043, -0.037417590618133545, -0.013491420075297356, 0.02620665170252323, 0.04829584062099457, -0.006659688428044319, -0.06283710896968842, 0.0011809773277491331, 0.05304553359746933, 0.007289493922144175, -0.12409931421279907, 0.02310706302523613, -0.0014274651184678078, -0.0006549209356307983, 0.028330780565738678, -0.019416851922869682, 0.06243357062339783, 0.04408062621951103, 0.04397546872496605, -0.005474373232573271, -0.0031763690058141947, -0.01246069185435772, -0.034613966941833496, 0.005044752266258001, -0.04065558686852455, 0.05213029682636261, 0.05993373319506645, 0.0013032857095822692, 0.002445633988827467, 0.025645190849900246, 0.038507383316755295, -0.0019680301193147898, -0.002845571842044592, 0.0424499437212944, -0.021184120327234268, -0.03377914056181908, 0.029049960896372795, 0.00820169597864151, -0.08387424051761627, 0.03324757516384125, -0.10149892419576645, 0.05076880753040314, -0.027596300467848778, 0.02487250417470932, -0.003962496295571327, 0.08591855317354202, -0.019549239426851273, -0.0009942820761352777, -0.030492592602968216, 0.022523170337080956, -0.007873146794736385, -0.01621132157742977, 0.021252671256661415, -0.014473987743258476, -0.01528246235102415, 0.05371610075235367, -0.052874524146318436, -0.03025779500603676, 0.003608081955462694, -0.04569318890571594, 0.0418841727077961, -0.030734609812498093, 0.009604756720364094, -0.017270948737859726, 0.028996579349040985, -0.011213217861950397, 0.031167494133114815, -0.015274332836270332, -0.04799492284655571, -0.021800683811306953, 0.00466017983853817, 0.014933713711798191, -0.0028268015012145042, 0.018643591552972794, 0.002686085645109415, 0.013807245530188084, -0.017115408554673195, 0.05367389693856239, 0.003965443465858698, -0.03352680057287216, -0.051681824028491974, -0.06780242174863815, -0.039785392582416534, -0.023843465372920036, -0.03105592168867588, -0.018762942403554916, 0.025954846292734146, 0.021708469837903976, -0.0891859382390976, -0.027574891224503517, -0.044973332434892654, -0.0263739675283432, 0.002903483808040619, -0.015725625678896904, 0.006724422797560692, -0.019708797335624695, -0.04773528128862381, 0.011953042820096016, -0.019638394936919212, 0.008556565269827843, -0.04233156889677048, -0.001632017781957984, 0.018454257398843765, 0.02049805410206318, -0.006972112227231264, -0.056888148188591, -0.02276124246418476, 0.02041543275117874, -0.028798190876841545, -0.031125808134675026, -0.0538872592151165, 0.034229256212711334, -0.038512181490659714, 0.009457351639866829, -0.07310476154088974, 0.01225320715457201, -0.019532237201929092, -0.01707235909998417, -0.028243064880371094, 0.03691842406988144, -0.0044940379448235035, -0.035204652696847916, -0.026716182008385658, 0.011652818880975246, -0.03771406412124634, 0.045479852706193924, 0.018454477190971375, -0.043080735951662064, 0.0374707356095314, -0.05949104204773903, 0.10657326132059097, 0.04879050329327583, -0.05926357954740524, 0.0031569304410368204, -0.01698308438062668, 0.03887791186571121, -0.0171823650598526, -0.04863269627094269, -0.0039843847043812275, 0.01986927166581154, 0.014972486533224583, 0.03621137514710426, 0.0675649344921112, 0.032995302230119705, -0.05202101543545723, 0.03143799677491188, -0.008467642590403557, -0.033021245151758194, 0.03785504028201103, 0.04760584607720375, 0.01809057779610157, 0.04572638124227524, 0.017131773754954338, -0.0344947949051857, -0.021008038893342018, 0.00496956892311573, -0.019421841949224472, 0.0028172607999294996, -0.07662197947502136, 0.02050236240029335, -0.04507019370794296, 0.057666294276714325, -0.019972041249275208, 0.056189823895692825, 0.11846549063920975, -0.032646544277668, 0.019599752500653267, -0.026247747242450714, -0.04226116091012955, -0.032879579812288284, 0.0385349877178669, 0.04068179801106453, 0.02662568911910057, 0.060376450419425964, 0.01664726249873638, -0.021959176287055016, -0.056180689483881, -0.007523419335484505, 0.057089805603027344, -0.001932164654135704, 0.03606358543038368, -0.01315944455564022, -0.06360824406147003, 0.015737656503915787, 0.010793673805892467, 0.025921374559402466, -0.024155452847480774, -0.05243004858493805, -0.0018530836096033454, -0.03763828054070473, -0.012177309021353722, 0.03624013438820839, 0.043416719883680344, -0.03520425409078598, -0.08583206683397293, 0.009775160811841488, -0.00816460233181715, -0.06687687337398529, 0.028767801821231842, -0.00027265268727205694, 0.01422437559813261, 0.062381915748119354, -0.0035293633118271828, 0.01437963917851448, -0.03241429477930069, -0.05865807458758354, -0.02488214150071144, -0.03698018193244934, -0.01413857564330101, -0.03147222101688385, -0.009555203840136528, -0.0422237366437912, 0.0536101870238781, 0.0032030504662543535, -0.008822253905236721, 0.027149762958288193, 0.028928721323609352, 0.03251286596059799, 0.046224772930145264, 0.023748649284243584, -0.047901351004838943, 0.03351685404777527, 0.04519880935549736, 0.07099180668592453, 0.01964365504682064, -0.021602481603622437, 0.027974192053079605, 0.012274731881916523, 0.02187700942158699, -0.0012080767191946507, 0.00380092766135931, 0.023643262684345245, -0.03849461302161217, -0.06351885944604874, 0.05821722373366356, 0.015436708927154541, 0.02437538653612137, -0.009222973138093948, -0.03770756348967552, -0.01339968852698803, -0.04618491232395172, 0.05944468826055527, -0.024950869381427765, 0.07464965432882309, -0.023276537656784058, -0.02670236863195896, -0.014207563363015652, -0.053083278238773346, -0.05977647751569748, -0.050457973033189774, 0.017667308449745178, 0.028614258393645287, -0.024527085945010185, 0.05311286449432373, -0.028546283021569252, -0.04120922461152077, -0.011954124085605145, -0.0461965836584568, -0.05368698760867119, -0.02794494293630123, 0.0748051255941391, -0.0032565738074481487, 0.014945789240300655, -0.0011065809521824121, -0.052030302584171295, 0.04363102838397026, 0.016709808260202408, 0.01065034605562687, -0.00671900762245059, 0.017552705481648445, 0.01282593421638012, 0.033955082297325134, 0.0006899636937305331, 0.05033962056040764, -0.041504424065351486, 0.03137624263763428, -0.008038712665438652, -0.010822782292962074, -0.04041189327836037, -0.07598229497671127, 0.020383192226290703, 0.03034103289246559, 0.030460355803370476, 0.07752702385187149, -0.011876667849719524, -0.054521992802619934, 0.026106618344783783, 0.017714601010084152, -0.027074189856648445, -0.04946047067642212, 0.025236519053578377, 0.03409893065690994, 0.03655397519469261, 0.021509390324354172, -0.06435596942901611, 0.03971250727772713, -0.005977085325866938, 0.0044209701009094715, -0.02411852404475212, 0.015519277192652225, 0.030650513246655464, 0.0030555082485079765, -0.02230350486934185, -0.00558729562908411, -0.0031601053196936846, 0.01406140811741352, -0.013134101405739784, 0.013357793912291527, -0.00354304863139987, -0.03572027012705803, -0.03386097773909569, -0.02731059119105339, -0.037571754306554794, -0.0581522136926651, -0.05078712850809097, -0.0070605045184493065, 0.08981479704380035, 0.01176456082612276, 0.0769144743680954, -0.010913293808698654, -0.013155392371118069, 0.0026934053748846054, -0.06145394966006279, 0.03239956498146057, 0.04432377964258194, 0.009622848592698574, 0.017094722017645836, 0.04461514204740524, -0.017630377784371376, 0.01831233687698841, 0.021471772342920303, 0.032975196838378906, 0.0009666613768786192, -0.03768309950828552, -0.03776799142360687, -0.009633885696530342, 0.004862954840064049, -0.06675075739622116, 0.10683738440275192, 0.014270707033574581, 0.04642369970679283, 0.00835675559937954, 0.004643655847758055, -0.01036253571510315, 0.022664615884423256, 0.054773930460214615, -0.01845879852771759, -0.017757145687937737, 0.013180562295019627, -0.0163564532995224, 0.04552670195698738, -0.03582734987139702, -0.004319968167692423, 0.05398179590702057, -0.0033625331707298756, 0.0009381102863699198, -5.247792491154555e-33, -0.012042216025292873, -0.03450702130794525, -0.06405998766422272, 0.05045498535037041, -0.029874319210648537, -0.009491395205259323, 0.022214805707335472, 0.015070728026330471, 0.01766185648739338, -0.01486177183687687, 0.03244113177061081, 0.05405411496758461, 0.0009929381776601076, 0.015191151760518551, -0.007347326260060072, 0.008917990140616894, 0.0246827844530344, 0.04172511026263237, 0.004898243583738804, -0.0018453532829880714, 0.04170331731438637, 0.014092523604631424, 0.020783979445695877, 0.025974247604608536, 0.045001786202192307, 0.0580071285367012, -0.018673131242394447, 0.043351735919713974, 0.006988522596657276, -0.013001141138374805, 0.012784070335328579, 0.010518086142838001, -0.006594981532543898, -0.005215270910412073, 0.012120956555008888, -0.028956716880202293, 0.015458588488399982, -0.034558024257421494, -0.0033779896330088377, 0.00041988593875430524, -0.013129857368767262, -0.008212156593799591, 0.0731385350227356, 0.012685396708548069, -0.0039833360351622105, -0.008524583652615547, 0.043295249342918396, 0.013799288310110569, -0.019295349717140198, 0.0253219585865736, 0.059546928852796555, 0.03285505250096321, -0.010213294066488743, 0.05064748227596283, -0.013086121529340744, -0.060826994478702545, -0.04452535882592201, -0.012284341268241405, 0.023227179422974586, 0.027029315009713173, 0.043066490441560745, 0.034265775233507156, -0.021431144326925278, -0.021592052653431892, 0.031127244234085083, 0.020534679293632507, 0.10262536257505417, -0.06641725450754166, -0.03387419134378433, -0.055215463042259216, -0.04696667194366455, -0.010788634419441223, 0.019445493817329407, 0.03426926210522652, 0.0385892391204834, -0.004374391864985228, -0.059671323746442795, 0.023844333365559578, -0.04614678770303726, 0.028381161391735077, 0.024388423189520836, -0.01272576954215765, -0.00012335277278907597, -0.015637343749403954, 0.01313907653093338, -0.010015311650931835, -0.013209991157054901, -0.011166511103510857, -0.03488379716873169, -0.007258499041199684, -0.022021548822522163, 0.023971518501639366, -0.03374136611819267, -0.04317903891205788, 0.0003798520192503929, 0.0024736779741942883, 0.030404623597860336, 0.02679981105029583, -0.002196667017415166, 0.017131656408309937, -0.03038063831627369, 0.009621814824640751, -0.04314512014389038, -0.03907618299126625, -0.007248841691762209, 0.0006534142303280532, -0.008571350947022438, 0.035859715193510056, -0.023351486772298813, -0.034661464393138885, 0.021048616617918015, -0.03530552238225937, -0.01968294009566307, 0.019757486879825592, 0.09503298997879028, -0.041875436902046204, -0.031715381890535355, 0.006446897983551025, 0.024611840024590492, 0.02118886634707451, 0.03205332159996033, 0.02938448265194893, -0.04312983155250549, 0.0711488202214241, -0.04440681263804436, -0.009907404892146587, -0.02305147610604763, -0.039047032594680786, -0.05135132372379303, -0.01816803589463234, -0.026886746287345886, 0.0018314891494810581, 2.7103328648081515e-07, 0.020431887358427048, -0.032742489129304886, -0.023399775847792625, 0.0551924966275692, 0.05987340584397316, -0.043717123568058014, -0.012506251223385334, 0.04369271546602249, 0.006903378758579493, -0.05073220655322075, 0.009541998617351055, -0.0023403011728078127, -0.005901881493628025, 0.004420130979269743, -0.011107555590569973, 0.01911911927163601, 0.03708479180932045, 0.09130176901817322, 0.06423956155776978, 0.04574141651391983, 0.012786599807441235, 0.02559479884803295, 0.07524793595075607, 0.026745520532131195, 0.07272841036319733, -0.005474052857607603, 0.020285962149500847, 0.010444867424666882, -0.004427527543157339, -0.0057457988150417805, 0.021782847121357918, -0.0496053621172905, 0.04613688960671425, 0.02176521345973015, 0.024180443957448006, 0.005395028740167618, 0.013387197628617287, -0.0030435281805694103, -0.0037249906454235315, 0.04445195943117142, -0.023153705522418022, -0.05560353770852089, 0.06323091685771942, -0.03250269219279289, 0.03444201499223709, 0.031219281256198883, -0.011781224049627781, 0.01185651496052742, -0.09405319392681122, -0.02328645810484886, -0.012150119990110397, 0.04281838610768318, -0.0028452537953853607, 0.0009018342825584114, -0.01811067946255207, -0.012169580906629562, 0.03363511338829994, 0.04850446432828903, 0.028291869908571243, 0.010874572210013866, -0.020851802080869675, -0.07494322210550308, 0.05912093445658684, 0.04094333201646805, 0.03527439013123512, 0.014989444054663181, 0.016824617981910706, 2.456357076516408e-34, 0.039916183799505234, 0.020477918907999992, 0.015186777338385582, -0.04119909182190895, -0.01845700293779373, -0.01721862517297268, 0.03799353167414665, -0.03879900276660919, 0.03864534571766853, -0.056016553193330765, -0.04282192885875702]

['Daiki Koizumi', 'Toshiyasu Matsushima', 'Shigeichi Hirasawa']

0906.3923v4

Traffic forecasting from past observed traffic data with small calculation complexity is one of important problems for planning of servers and networks. Focusing on World Wide Web (WWW) traffic as fundamental investigation, this paper would deal with Bayesian forecasting of network traffic on the time varying Poisson model from a viewpoint from statistical decision theory. Under this model, we would show that the estimated forecasting value is obtained by simple arithmetic calculation and expresses real WWW traffic well from both theoretical and empirical points of view.

Bayesian Forecasting of WWW Traffic on the Time Varying Poisson Model

http://arxiv.org/pdf/0906.3923v4

Title Bayesian Forecasting WWW Traffic Time Varying Poisson Model Summary Traffic forecasting past observed traffic data small calculation complexity one important problem planning server network Focusing World Wide Web WWW traffic fundamental investigation paper would deal Bayesian forecasting network traffic time varying Poisson model viewpoint statistical decision theory model would show estimated forecasting value obtained simple arithmetic calculation express real WWW traffic well theoretical empirical point view Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.015096246264874935, -0.011536497622728348, -0.046419329941272736, -0.04279458895325661, -0.07753831148147583, -0.020055068656802177, 0.02243761718273163, -0.021788857877254486, -0.023257344961166382, -0.05591873824596405, 0.02656463533639908, -0.06583771854639053, -0.0016926690004765987, 0.08179090172052383, -0.009204898960888386, -0.036894503980875015, -0.014983350411057472, 0.0053804838098585606, -0.06271213293075562, 0.03186247497797012, 0.050316449254751205, -0.014828243292868137, 0.027371292933821678, 0.028748376294970512, 0.028393011540174484, -0.0026831477880477905, -0.03109837882220745, 0.007699110079556704, -0.019738376140594482, -0.04550692439079285, 0.029024530202150345, -0.027663610875606537, 0.011654666624963284, 0.017770351842045784, 1.9954427443735767e-06, -0.004264849703758955, -0.02902897074818611, 0.00447822455316782, 0.0030130217783153057, 0.014917397871613503, 0.033611103892326355, 0.007074891123920679, 0.0190008282661438, 0.07901595532894135, 0.026275036856532097, 0.04847506433725357, -0.007076170761138201, 0.05239001289010048, -0.03047589398920536, -0.0095143411308527, -0.015028601512312889, -0.015235206112265587, -0.008154727518558502, 0.042665380984544754, 0.024677008390426636, -0.02857876569032669, -0.013223113492131233, 0.0006830801139585674, 0.016190802678465843, -0.07207062840461731, -0.01708071492612362, -0.03055107221007347, -0.01321577001363039, -0.014708342961966991, 0.03624718636274338, 0.02419428713619709, 0.06654705107212067, 0.023143764585256577, -0.029257403686642647, -0.02975156530737877, 0.04872577637434006, 0.024200238287448883, 0.0656069815158844, 0.032441649585962296, -0.07142562419176102, 0.028027556836605072, -0.0578833632171154, -0.0062935845926404, 0.026333926245570183, 0.007802072912454605, 0.0028939037583768368, 0.02305091917514801, -0.015110304579138756, 0.034456122666597366, -0.004832668695598841, 0.0235359538346529, 0.0003357876848895103, 0.004371363669633865, -0.04085874930024147, 0.008669118396937847, 0.05624185502529144, 0.019877545535564423, 0.035513680428266525, -0.002607029862701893, -0.01435624249279499, 0.02455131523311138, 0.04254291579127312, 0.021330803632736206, 0.045059025287628174, -0.05625952035188675, -0.027528652921319008, -0.020363643765449524, 0.015757303684949875, 0.016373589634895325, 0.014315315522253513, -0.046744924038648605, -0.017008904367685318, -0.06675581634044647, 0.03827711194753647, 0.04539750888943672, -0.04348886385560036, -0.00886637531220913, 0.07713283598423004, 0.031457867473363876, 0.03577403724193573, -0.03511616960167885, -0.01021458301693201, 0.055577315390110016, 0.025882352143526077, -0.03670327365398407, 0.05590997263789177, -0.026769375428557396, 0.0005371724837459624, 0.032096344977617264, -0.038331132382154465, -0.01785462535917759, -0.04615363851189613, 0.04416528344154358, -0.014357290230691433, -0.03408702462911606, 0.02979391999542713, -0.02395567297935486, 0.019889704883098602, -0.0012658212799578905, -0.04302617162466049, 0.05169371888041496, 0.03356733173131943, 0.09196005016565323, -0.06196701154112816, -0.05365002900362015, 0.013888764195144176, 0.040108710527420044, -0.036355774849653244, 0.008726879954338074, -0.03952992707490921, -0.012890410609543324, -0.014358513988554478, 0.07183805853128433, -0.012530853971838951, -0.0372779555618763, -0.030461562797427177, -0.030572572723031044, 0.021705301478505135, 0.0022367725614458323, 0.035966113209724426, -0.05579044297337532, 0.03928698971867561, -0.008764785714447498, -0.027423465624451637, 0.030209746211767197, 0.0004933378659188747, 0.0034615485928952694, 0.012607919983565807, -0.026466289535164833, -0.0028876301366835833, 0.042262330651283264, -0.02272655814886093, 0.00361253903247416, -0.0014911432517692447, -0.052873190492391586, -0.0044638714753091335, 0.0032529698219150305, 0.011794489808380604, -0.030839597806334496, 0.005705195479094982, -0.048597317188978195, 0.017941294237971306, 0.015864649787545204, 0.04936498776078224, 0.0091303251683712, -0.03436567634344101, -0.06953810155391693, 0.0037747803144156933, 0.04536812752485275, -0.06921476125717163, -0.012596813030540943, -0.016346536576747894, 0.009069093503057957, -0.011912820860743523, 0.034119412302970886, 0.0433204211294651, -0.01393231563270092, -0.071492038667202, -0.021659301593899727, 0.10100666433572769, -0.053523287177085876, -0.01397497858852148, -0.0014469710877165198, 0.04525381699204445, 0.03509274125099182, 0.03925832360982895, -0.05161699652671814, 0.005480922758579254, 0.0032213127706199884, 0.004287657793611288, 0.03843051567673683, -0.038398828357458115, -0.014510507695376873, -0.045303087681531906, -0.036310866475105286, 0.027442486956715584, 0.04931899160146713, -0.05890382081270218, -0.026372555643320084, 0.007204167079180479, 0.04930536076426506, 0.01623045653104782, -0.023547833785414696, -0.052982933819293976, 0.04847303405404091, 0.03583262115716934, 0.0070061106234788895, -0.005986517295241356, 0.00015272494056262076, 0.016890861093997955, 0.04795035719871521, 0.003902895376086235, 0.0019293201621621847, 0.05634359270334244, -0.015093621797859669, -0.01499095931649208, 0.029158122837543488, 0.03687188774347305, 0.053591348230838776, -0.02490362897515297, 0.06349452584981918, 0.06594781577587128, 0.01657984033226967, -0.007196671329438686, -0.009869776666164398, 0.09019620716571808, -0.0012098326114937663, 0.03030536323785782, -0.04273805767297745, 0.08638700097799301, -0.009322531521320343, -0.010329569689929485, 0.012029995210468769, 0.011957921087741852, 0.01475247647613287, 0.005162573419511318, 0.026626020669937134, -0.024573441594839096, 0.04782135412096977, 0.0008060926338657737, -0.03920140489935875, 0.018947822973132133, -0.030241243541240692, 0.0077596078626811504, -0.0004943618550896645, -0.05512519180774689, -0.006048472132533789, 0.02086608111858368, 0.026003751903772354, -0.032771192491054535, -0.04287993907928467, -0.008748271502554417, -0.049212872982025146, 0.022349851205945015, -0.015970997512340546, -0.0043982286006212234, 0.021165115758776665, -0.04055817052721977, -0.011078319512307644, -0.030089298263192177, 0.025643736124038696, 0.035246722400188446, -0.03218395635485649, -0.02053779922425747, 0.009466259740293026, 0.02990884706377983, -0.039838116616010666, -0.01033239159733057, -0.05190146341919899, -0.029912391677498817, 0.0005192697863094509, 0.07431335747241974, -0.08379167318344116, 0.07014604657888412, 0.028874753043055534, -0.0646420493721962, -0.04689954221248627, -0.025626376271247864, -0.018251566216349602, -0.09150092303752899, -0.035133372992277145, 0.0032264874316751957, -0.04860302805900574, 0.048269521445035934, -0.04460019990801811, -0.040862079709768295, -0.036127977073192596, -0.04490327462553978, -0.0004804304626304656, -0.04313969239592552, -0.0058671822771430016, 0.01777159608900547, -0.03763597086071968, 0.02309749647974968, 0.0058644236996769905, 0.0019967607222497463, 0.01152943354099989, 0.011577780358493328, 0.002915664343163371, -0.04211888462305069, 0.012681709602475166, -0.07056733220815659, 0.07284443080425262, -0.03917929157614708, 0.03401147574186325, 0.034219253808259964, -0.03523879125714302, 1.301418524235487e-05, 0.07529707252979279, 0.051491644233465195, -0.012301051989197731, -0.05091744661331177, 0.001386628719046712, -0.07654426991939545, 0.038262903690338135, 0.029192283749580383, -0.052276816219091415, -0.007034006528556347, 0.0027430737391114235, 0.040236614644527435, 0.00913466326892376, -0.015714650973677635, -0.06197236478328705, 0.10534323006868362, -0.023320632055401802, 0.02711114101111889, 0.020349448546767235, -0.03113684058189392, -0.030897872522473335, -0.036831267178058624, -0.04629119858145714, -0.0057635074481368065, -0.010783283971250057, 0.007883705198764801, 0.016661524772644043, -0.03484063223004341, 0.0017924531130120158, -0.040239375084638596, -0.02461601234972477, 0.037748441100120544, -0.00053709268104285, 0.015242595225572586, -0.026974894106388092, -0.00903204083442688, 0.001973190577700734, -0.014595801942050457, -0.023442277684807777, 0.03605937212705612, 0.016417792066931725, -0.00640272069722414, 0.04972667992115021, 0.03626183420419693, -0.013798505067825317, -0.04726242274045944, 0.10780176520347595, -0.057573117315769196, 0.004044462461024523, 0.029909100383520126, 0.02794860489666462, -0.004310584161430597, -0.03979858383536339, -0.027355926111340523, -0.03261755779385567, -0.029205946251749992, -0.019404606893658638, 0.044927529990673065, 0.009619896300137043, 0.006839729379862547, 0.004746525548398495, 0.026924604550004005, -0.026100484654307365, -0.04427702724933624, -0.007053377106785774, -0.03909687325358391, 0.02833167463541031, -0.024612227454781532, 0.06368862837553024, 0.06901483982801437, -0.1010885238647461, 0.02741042710840702, -0.009983477182686329, -0.030872058123350143, 0.024099526926875114, 0.05855468660593033, -0.012068974785506725, 0.08903031796216965, -0.09146953374147415, -0.0740942656993866, -0.011131023056805134, -0.040268488228321075, 0.05431383475661278, 0.011685731820762157, 0.014971180818974972, -0.07863126695156097, -0.015112927183508873, -0.0017582655418664217, 0.03978829085826874, -0.011449628509581089, -0.015525019727647305, 0.05226554349064827, 0.04161401093006134, 0.011439881287515163, -0.04842161759734154, 0.06256011128425598, -0.0008518266840837896, 0.02728419378399849, 0.09680011868476868, 0.06440352648496628, -0.04247160255908966, -0.025101615116000175, -0.04323626309633255, 0.05683261156082153, -0.0013929769629612565, -0.012166347354650497, -0.00894357543438673, -0.0282867643982172, -0.029986362904310226, -0.00689681526273489, -0.030577171593904495, -0.012867778539657593, 0.03969358652830124, -0.009963011369109154, -0.004448830150067806, -0.0409926101565361, -0.03711507096886635, -0.0022587967105209827, -0.05130108818411827, 0.038811322301626205, 0.05072636529803276, 0.004645790439099073, 0.028520364314317703, -0.0018028841586783528, 0.004816531203687191, -0.06259504705667496, 0.016021130606532097, 0.039338164031505585, -0.10165534168481827, 0.05307457223534584, 0.03631138801574707, -0.046510543674230576, -0.05679496005177498, -0.09784290939569473, -0.029008222743868828, -0.026377694681286812, 0.01577138714492321, 0.04794684797525406, 0.018930252641439438, -0.051691412925720215, -0.00945843756198883, 0.03211258724331856, -0.05095237120985985, -0.009182019159197807, -0.017084307968616486, -0.026706749573349953, 0.01761392317712307, -0.0051807439886033535, -0.02163712866604328, -0.030950428918004036, 0.015769006684422493, 0.045277878642082214, -0.021697821095585823, -0.09225049614906311, -0.006256327498704195, -0.003343314630910754, -0.014623125083744526, 0.022219721227884293, 0.030999286100268364, 0.023795804008841515, -0.012474539689719677, 0.017679907381534576, -0.04176247492432594, -0.004394095856696367, 0.02035735920071602, 0.01186053454875946, -0.04894144833087921, 0.04340227320790291, 0.046249888837337494, -0.03130488097667694, 0.03254859894514084, 0.025932177901268005, -0.14173848927021027, 0.03550182282924652, -0.029818052425980568, 0.01779998280107975, -0.0012407373869791627, -0.04120669886469841, 0.005738147534430027, 0.02515384741127491, -0.09617592394351959, 0.03925781324505806, 0.05151304230093956, 0.012399323284626007, 0.022239889949560165, -0.018659166991710663, -0.019943302497267723, -0.02233368158340454, -0.05426707863807678, -0.0006192962173372507, -0.02467743493616581, -0.0032199148554354906, -0.018487736582756042, -0.03450262174010277, 0.004097457509487867, 0.0007465878152288496, -0.0519111305475235, 0.049389444291591644, -0.028622128069400787, 0.04267584905028343, -0.006030151154845953, 0.062196530401706696, 0.01944679580628872, -0.01264958456158638, -0.04804519936442375, 0.03060094639658928, 0.019365401938557625, 0.00826422031968832, -0.016049137338995934, -0.006573094055056572, -0.0545104444026947, -0.021592410281300545, 0.08053375035524368, 0.009487430565059185, -0.002194745000451803, 0.011555438861250877, -0.008674165233969688, -0.012112942524254322, 0.013528948649764061, -0.012209456413984299, -0.032763171941041946, 0.06550395488739014, -0.004363976418972015, 0.011240404099225998, 0.03147450089454651, -0.03131338581442833, 0.0703686997294426, -0.06824173778295517, -0.010909751057624817, -0.017208870500326157, 0.07845114916563034, -0.034114401787519455, -6.0572496560742904e-33, 0.03774694725871086, 0.025379352271556854, -0.01732526533305645, -0.022536279633641243, -0.01544377114623785, 0.03497609123587608, 0.02410251274704933, -0.0056466832756996155, 0.02412668615579605, -0.04758818820118904, -0.00790427066385746, 0.008858918212354183, 0.00904792919754982, -0.024208491668105125, 0.051703374832868576, 0.016358980908989906, 0.02512865886092186, 0.032020580023527145, 0.015183236449956894, -0.003245752304792404, 0.02656576596200466, 0.013004426844418049, -0.005113315302878618, 0.04516441747546196, -0.010132333263754845, -0.01528975646942854, 0.0007453694706782699, -0.0016389894299209118, 0.058185648173093796, 0.016872383654117584, 0.025823485106229782, -0.013953693211078644, -0.02754366584122181, -0.020790109410881996, -0.04063967987895012, -0.00741193862631917, 0.015119166113436222, -0.02382650598883629, 0.019750896841287613, 0.039957866072654724, 0.02703162655234337, 0.02054143138229847, -0.00819637905806303, 0.053279243409633636, -0.023596158251166344, -0.003124753013253212, 0.0376310721039772, 0.03540593758225441, -0.007420588284730911, -0.011089948005974293, 0.030068667605519295, 0.007546558976173401, -0.06393641978502274, 0.0446261502802372, 0.021269746124744415, 0.01848403364419937, -0.05322140082716942, -0.027538731694221497, -0.03174734488129616, 0.03611774742603302, 0.025441547855734825, -0.01588963344693184, 0.005393295083194971, 0.041043300181627274, 0.011403779499232769, 0.02236982248723507, -0.01918274722993374, -0.03794832527637482, -0.012249903753399849, 0.0045643397606909275, 0.022345460951328278, 0.007585436571389437, -0.017814261838793755, -0.0027829583268612623, 0.06746356189250946, -0.062193457037210464, -0.03493550792336464, 0.0013842449989169836, 0.0974326804280281, 0.013250202871859074, 0.030965620651841164, -0.05278708413243294, -0.02144729532301426, -0.01632850058376789, 0.034211236983537674, 0.018429070711135864, 0.01768275909125805, -0.04667477309703827, 0.023462757468223572, 0.01839345507323742, -0.023511255159974098, 0.016860315576195717, 0.03997860103845596, -0.012614909559488297, -0.04630535840988159, 0.0010506968246772885, 0.023424219340085983, 0.03497690334916115, -0.009012788534164429, -0.02404981292784214, -0.03396054357290268, -0.05718819424510002, -0.058443646878004074, -0.007505594287067652, -0.017024097964167595, 0.009487350471317768, 0.020194387063384056, 0.016213612630963326, 0.004533244296908379, -0.024320309981703758, -0.006198493298143148, -0.014155794866383076, 0.05217397212982178, 0.03202272206544876, 0.02317981794476509, -0.023793982341885567, 0.0003923692274838686, -0.002784989308565855, 0.036322128027677536, -0.028808843344449997, 0.021697845309972763, -0.011145980097353458, -0.0001325353077845648, -0.0303341094404459, -0.0513308048248291, -0.059213124215602875, -0.00871876161545515, 0.01071525365114212, 0.014786005020141602, -0.0491286925971508, -0.006738284602761269, 0.0025113928131759167, 2.64524146587064e-07, 0.003761074272915721, 0.02767419070005417, -0.08460347354412079, 0.024565603584051132, 0.022512437775731087, 6.74280381645076e-05, -0.0036486100871115923, -0.004141050856560469, 0.06339967250823975, 0.04650314152240753, 0.03036152571439743, -0.05534650385379791, -0.0007455515442416072, 0.01147090271115303, 0.001698275445960462, -0.06751996278762817, -0.08019642531871796, 0.0495724193751812, -0.041877906769514084, 0.029951725155115128, 0.04064217209815979, 0.08076584339141846, 0.05248749628663063, 0.02839159034192562, 0.04957878962159157, -0.00015541580796707422, -0.020877256989479065, -0.0571240596473217, -0.02497360296547413, 0.0216056015342474, 0.05892583355307579, 0.056242361664772034, 0.01081260945647955, 0.00747869024053216, -0.03526036813855171, -0.012221015989780426, 0.007320909295231104, 0.02456067129969597, 0.021620843559503555, 0.07019288092851639, 0.04557982459664345, -0.027017366141080856, 0.0170173030346632, -0.03706064075231552, 0.013600185513496399, 0.029933499172329903, -0.06244625523686409, -0.01277890894562006, -0.013767194002866745, -0.0013341186568140984, 0.007445646449923515, -0.009906494058668613, -0.0515875443816185, -0.004501137416809797, 0.003702635644003749, -0.040690645575523376, 0.00944526121020317, -0.0009577794698998332, 0.016087034717202187, 0.014149606227874756, 0.005286738276481628, -0.007311680354177952, -0.015478470362722874, -0.010538890026509762, 0.06769894063472748, -0.0007345573394559324, 0.03513343259692192, 2.2658004882872396e-34, 0.014307656325399876, 0.02695101872086525, 0.008158612996339798, 0.010704869404435158, -0.009311889298260212, -0.00021804493735544384, 0.010545944795012474, 0.0005398185458034277, 0.01806148700416088, -0.012770092114806175, -0.039584528654813766]

['Anjana Pandey', 'K. R. Pardasani']

0906.4172v1

In this paper, the mining of hybrid association rules with rough set approach is investigated as the algorithm RSHAR.The RSHAR algorithm is constituted of two steps mainly. At first, to join the participant tables into a general table to generate the rules which is expressing the relationship between two or more domains that belong to several different tables in a database. Then we apply the mapping code on selected dimension, which can be added directly into the information system as one certain attribute. To find the association rules, frequent itemsets are generated in second step where candidate itemsets are generated through equivalence classes and also transforming the mapping code in to real dimensions. The searching method for candidate itemset is similar to apriori algorithm. The analysis of the performance of algorithm has been carried out.

Rough Set Model for Discovering Hybrid Association Rules

http://arxiv.org/pdf/0906.4172v1

Title Rough Set Model Discovering Hybrid Association Rules Summary paper mining hybrid association rule rough set approach investigated algorithm RSHARThe RSHAR algorithm constituted two step mainly first join participant table general table generate rule expressing relationship two domain belong several different table database apply mapping code selected dimension added directly information system one certain attribute find association rule frequent itemsets generated second step candidate itemsets generated equivalence class also transforming mapping code real dimension searching method candidate itemset similar apriori algorithm analysis performance algorithm carried Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.017824845388531685, -0.03582732751965523, -0.06261902302503586, 0.01001622062176466, -0.014077071100473404, -0.016911715269088745, -0.033608876168727875, 0.04516800493001938, 0.013008534908294678, 0.0033757470082491636, 0.020963769406080246, -0.0077780550345778465, 0.005536691285669804, 0.051231108605861664, -0.04752981662750244, 0.04067561775445938, 0.035723187029361725, 0.058454886078834534, -0.025372352451086044, 0.03719489648938179, 0.0609549954533577, -0.00905976165086031, -0.04025919362902641, 0.03498173505067825, 0.029516929760575294, 0.026288725435733795, 0.03471765294671059, -0.07594604045152664, 0.023856597021222115, -0.0007395570864900947, 0.04000335559248924, 0.01514195092022419, -0.05324293673038483, -0.0013156112981960177, 1.932918166858144e-06, -0.03229412063956261, -0.05435105413198471, -0.007771259639412165, 0.0708794891834259, 0.012754696421325207, -0.011776505038142204, 0.048630550503730774, 0.04229885712265968, 0.028230981901288033, -0.07896112650632858, -0.06689785420894623, 0.005414184648543596, 0.02753113955259323, 0.012267346493899822, 0.022182852029800415, -0.002804921707138419, -0.018424686044454575, -0.014448064379394054, 0.015853241086006165, 0.009219265542924404, -0.018089303746819496, 0.041296277195215225, -0.008556997403502464, -0.008767441846430302, -0.0797588899731636, 0.013399647548794746, -0.06991472095251083, -0.029988214373588562, 0.017233029007911682, 0.013366482220590115, -0.01327590923756361, -0.02512020617723465, 0.02880069985985756, 0.021718617528676987, 0.027227111160755157, -0.0014932879712432623, 0.0014188530622050166, 0.0645502582192421, 0.020738832652568817, -0.024469727650284767, 0.049419332295656204, -0.011248292401432991, 0.011332509107887745, -0.06566675752401352, 0.010934718884527683, -0.007299428340047598, 0.0406423881649971, -0.02498912252485752, -0.0052359518595039845, -0.01284524705260992, -0.002883841749280691, -0.016825783997774124, 0.03527751937508583, -0.04062661528587341, -0.03820393234491348, -0.012163698673248291, -0.0276204664260149, 0.03184298053383827, 0.0065474193543195724, -0.02408428117632866, 0.0006827766774222255, 0.05740635097026825, 0.03280286863446236, 0.07934343069791794, -0.03572894260287285, 0.037273891270160675, 0.021777166053652763, 0.03758217766880989, -0.01717464253306389, 0.003958121873438358, -0.07855269312858582, 0.03863191232085228, 0.021158140152692795, -0.0015251963632181287, 0.0312831737101078, -0.06819186359643936, 0.030187789350748062, 0.008692823350429535, 0.03628091141581535, 0.021670609712600708, 0.02141696587204933, -0.06718710064888, -0.001793375937268138, -0.026045409962534904, 0.019686361774802208, 0.03168851137161255, 0.0016355037223547697, 0.07461293041706085, 0.04104050621390343, -0.07073598355054855, -0.05138382315635681, -0.05766593664884567, 0.05236896872520447, -0.043272715061903, 0.04266750440001488, 0.0619584359228611, -0.03195873647928238, 0.05523992329835892, 0.016968989744782448, -0.040610648691654205, 0.006717194337397814, 0.008433770388364792, -0.014648372307419777, -0.06804083287715912, -0.03936552256345749, 0.051660068333148956, 0.0010927324183285236, -0.018155574798583984, -0.03437415137887001, 0.021580589935183525, -0.02886326052248478, 0.0032001836225390434, 0.027201605960726738, -0.016183817759156227, 0.01376533042639494, -0.03187837451696396, 0.0028399808797985315, -0.032972656190395355, 0.056658342480659485, -0.010025919415056705, 0.004115581978112459, 0.017426656559109688, -0.007458135951310396, 1.0008558092522435e-05, -0.02498103678226471, -0.002761716255918145, -0.025986557826399803, -0.004814983811229467, -0.002002354245632887, -0.0227785836905241, -0.016214968636631966, 0.034740883857011795, 0.024085380136966705, 0.003369673155248165, -0.045402418822050095, -0.07387778908014297, -0.030156835913658142, -0.04532985761761665, -0.027487942948937416, -0.0003518768644426018, -0.053417500108480453, 0.06319911032915115, 0.06416479498147964, -0.05719039589166641, 0.02169402502477169, 0.0386071503162384, -0.017794858664274216, 0.09087523818016052, -0.0036726573016494513, -0.03816211223602295, -0.05538559332489967, -0.04587651416659355, 0.0268207099288702, -0.007179484236985445, -0.013075649738311768, 0.026619235053658485, -0.025211762636899948, 0.0344332717359066, -0.01697589084506035, 0.016864649951457977, 0.01684982143342495, 0.049756236374378204, -0.05789221450686455, 0.06220445781946182, 0.030636683106422424, -0.06596336513757706, -0.04556864872574806, 0.04354771226644516, 0.016925938427448273, 0.010402626357972622, -0.052948515862226486, 0.010653000324964523, -0.012869680300354958, 0.014572092331945896, -0.0711468905210495, 0.012812593020498753, -0.010266929864883423, -0.06121796742081642, -0.026529960334300995, -0.04694844037294388, 0.0956507995724678, 0.014204718172550201, -0.0024372441694140434, -0.03053957223892212, 0.023296156898140907, -0.04094410315155983, 0.019444825127720833, 0.023498592898249626, -0.010576564818620682, 0.02943134494125843, 0.09896507114171982, 0.08373772352933884, 0.01941516064107418, 0.04080887511372566, 0.040364570915699005, 0.028580527752637863, 0.004342337138950825, 0.07646530121564865, -0.04175277426838875, -0.03491955250501633, 0.05531954765319824, 0.06874789297580719, 0.045052897185087204, -0.006246911361813545, -0.011742332018911839, -0.00541340745985508, -0.023152288049459457, 0.02533743903040886, -0.0040166075341403484, 0.0037421626038849354, -0.007818836718797684, 0.03409150615334511, -0.03417501971125603, 0.014325126074254513, -0.017541145905852318, 0.000811850477475673, 6.077093712519854e-05, 0.06668224185705185, 0.02363480068743229, 0.007331003434956074, -0.015430787578225136, -0.11515170335769653, 0.06929372251033783, 0.005626570899039507, 0.0671922117471695, -0.02890348620712757, -0.02980894222855568, -0.0002914338547270745, 0.01202409528195858, 0.003873762208968401, -0.01905631273984909, -0.0043777842074632645, 0.046285782009363174, 0.023065773770213127, 0.04970517009496689, 0.00454733008518815, -0.024294136092066765, -0.009982624091207981, -0.008929825387895107, 0.018872637301683426, -0.014423753134906292, 0.06940067559480667, -0.04926588013768196, -0.0004705758474301547, 0.0261631328612566, 0.05752656236290932, -0.04301026836037636, 0.015844518318772316, 0.0117515092715621, -0.04911108687520027, -0.0010400203755125403, 0.037950579077005386, 0.020815221592783928, -0.006847170647233725, 0.01483259815722704, -0.004808647558093071, -0.056471697986125946, -0.0009857126278802752, -0.00442750658839941, -0.04626438766717911, 0.03362848237156868, -0.034772951155900955, -0.0763581395149231, 0.022557832300662994, -0.015899047255516052, 0.02284093387424946, -0.02085423842072487, -0.010794546455144882, 0.0013626363361254334, -0.0006268361466936767, 0.059172969311475754, 0.07606618851423264, -0.06232621520757675, -0.0073095266707241535, -0.05156401917338371, 0.05253599211573601, -0.018853669986128807, -0.01721015013754368, 0.020839955657720566, 0.041800547391176224, 0.04353867471218109, -0.019264552742242813, 0.005208061542361975, 0.04410819709300995, 0.058245301246643066, 0.017338162288069725, 0.004923366941511631, -0.004761368967592716, 0.042681436985731125, 0.06024517863988876, -0.048107702285051346, -0.032108940184116364, -0.032371778041124344, -0.036670275032520294, 0.011082135140895844, 0.04524249583482742, -0.019959043711423874, 0.025927767157554626, 0.018547672778367996, -0.0239546075463295, 0.03873579949140549, -0.02373218722641468, 0.03874923288822174, 0.02181996777653694, -0.027352280914783478, -0.0016380851157009602, -0.010787487961351871, -0.01111750490963459, -0.003862087382003665, 0.04448884725570679, -0.008877555839717388, 0.0034189620055258274, -0.012874536216259003, 0.011896822601556778, 0.040535423904657364, -0.04465266317129135, -0.012162214145064354, 0.005089405924081802, -0.02288210391998291, 0.040838517248630524, 0.016091180965304375, 0.046814318746328354, -0.08589286357164383, -0.04460674896836281, 0.048291996121406555, -0.0014194973045960069, 0.030300026759505272, -0.04368247464299202, -3.048107828362845e-05, -0.03302508220076561, 0.00045482703717425466, -0.028755811974406242, -0.01355815026909113, 0.0388212613761425, 0.0543297715485096, -0.07095704227685928, -0.024961723014712334, 0.05557743459939957, -0.012608037330210209, 0.07347385585308075, -0.0452505461871624, 0.010732621885836124, 0.0004072717565577477, -0.0348222479224205, -0.0011872132308781147, 0.003835159819573164, -0.10161053389310837, 0.02914639748632908, -0.056288812309503555, -0.03740552067756653, -0.05658059939742088, -0.08376188576221466, 0.026592692360281944, -0.03155578300356865, 0.014985772781074047, -0.008444956503808498, -0.11010048538446426, -0.004695615265518427, -0.043594397604465485, 0.017450882121920586, -0.049464982002973557, -0.06222796067595482, -0.022835146635770798, 0.006656372454017401, -0.02309739589691162, 0.01673917844891548, -0.08216910809278488, -1.2035337931592949e-05, 0.04401557892560959, -0.036191217601299286, 0.04954219609498978, -0.01098718587309122, 0.06213593855500221, -0.04864918440580368, -0.022193588316440582, -0.037274319678545, -0.006545267067849636, -0.0023537143133580685, -0.04911096766591072, 0.042159028351306915, 0.03785412386059761, -0.004176476038992405, 0.011563063599169254, -0.007757932413369417, -0.008759361691772938, -0.0034480434842407703, 0.09152799099683762, 0.09857044368982315, -0.0030948256608098745, 0.006139160133898258, -0.02699754387140274, -0.021511904895305634, -0.011962574906647205, -0.004872436635196209, -0.014049360528588295, 0.020668895915150642, 0.04033234342932701, -0.030095020309090614, 0.006302922964096069, 0.019444119185209274, -0.02885223738849163, -0.001802333164960146, -0.017397943884134293, -0.04926265403628349, -0.04676095396280289, 0.02272874303162098, 0.04136396199464798, 0.019016144797205925, 0.008961851708590984, 0.054999951273202896, 0.008584681898355484, 0.0010709629859775305, -0.0636298805475235, -0.061096079647541046, 0.03005140647292137, 0.021290255710482597, 0.012819734402000904, -0.04410863295197487, -0.01032956037670374, -0.02391241490840912, -0.025121446698904037, -0.0692785456776619, 0.042308975011110306, -0.0007129228906705976, -0.004575131926685572, 0.009996344335377216, 0.00454696174710989, -0.04690196365118027, -0.013885453343391418, 0.007665561977773905, -0.06768179684877396, 0.01617087796330452, 0.008697506040334702, -0.07955239713191986, -0.02050001360476017, -0.037868231534957886, -0.013611694797873497, 0.001019436283968389, 0.02532382868230343, -0.00758559163659811, 0.00046569807454943657, 0.0011144515592604876, -0.03915855661034584, 0.0075838202610611916, 0.06379391252994537, -0.001623723073862493, -0.0010693100048229098, 0.051167625933885574, -0.07645467668771744, -0.00859067402780056, 0.02820579893887043, -0.012340035289525986, -0.005962961819022894, -0.013123354874551296, -0.01035384926944971, 0.002450666157528758, 0.023681433871388435, -0.01981256902217865, -0.06628306955099106, -0.00462908623740077, 0.007678036577999592, 0.0163277480751276, 0.0522993803024292, -0.01651480793952942, 0.02546676993370056, -0.018541166558861732, -0.014788905158638954, 0.036835677921772, -0.058065660297870636, 0.028714260086417198, 0.041309479624032974, -0.018531301990151405, 0.028502577915787697, 0.013527315109968185, -0.010855033062398434, -0.017894115298986435, 0.0006037162384018302, 0.04843032360076904, 0.047733113169670105, 0.020496707409620285, 0.016772998496890068, 0.0010998465586453676, -0.036573626101017, -0.030237561091780663, 0.00028276239754632115, 0.027775444090366364, 0.010722002014517784, 0.042964912950992584, -0.049359507858753204, -0.0002913472126238048, 0.008173411712050438, 0.015601740218698978, -0.02555839717388153, -0.020616043359041214, 0.059175726026296616, -0.020863110199570656, 0.02171744592487812, -0.027807345613837242, -0.037793658673763275, -0.018672356382012367, 0.012185302563011646, 0.07330742478370667, 0.030455203726887703, -0.027295714244246483, -0.028074605390429497, -0.055022068321704865, 0.02550676465034485, -0.02403172105550766, -0.03087516874074936, 0.02770235389471054, 0.014357319101691246, -0.014240523800253868, 0.022877104580402374, 0.016657432541251183, 0.011389157734811306, -0.0025307275354862213, -0.07634495943784714, -0.0013400394236668944, 0.01386970467865467, 0.021530548110604286, -5.2032070924538195e-33, 0.004439548589289188, -0.03662629798054695, 0.011740574613213539, 0.024724671617150307, 0.026051774621009827, -0.04271179065108299, 0.01556228194385767, -0.01766834780573845, 0.016200369223952293, -0.027522603049874306, -0.005917910020798445, -0.003373973537236452, 0.019527124240994453, -0.051745280623435974, 0.026766452938318253, -0.008497423492372036, -0.02182857133448124, 0.027373408898711205, 0.02686804160475731, -0.0301903635263443, -0.01388942077755928, -0.005108120385557413, -0.005230535753071308, -0.09119249135255814, -0.043473728001117706, 0.04077005013823509, -0.028310174122452736, 0.02183353342115879, -0.03095146454870701, 0.055886559188365936, -0.018563415855169296, -0.011037573218345642, 0.016250545158982277, -0.0061416360549628735, 0.01117075327783823, -0.05244017764925957, -0.06313588470220566, -0.0162688996642828, 0.0055175963789224625, -0.007170723285526037, 0.09479527175426483, 0.017074966803193092, -0.006450315471738577, 0.024484992027282715, -0.005951314233243465, 0.019636915996670723, 0.05093194171786308, -0.08383846282958984, -0.027031950652599335, -0.027302302420139313, 0.020863253623247147, 0.023110423237085342, -0.02273447997868061, 0.019185151904821396, -0.0022942430805414915, -0.04321862384676933, -0.027054212987422943, -0.01604856736958027, -0.022313475608825684, 0.04956702142953873, -0.03030400350689888, -0.012794416397809982, -0.0673232153058052, -0.04053129255771637, 0.041333116590976715, 0.0051673781126737595, 0.026698319241404533, 0.028954925015568733, 0.04980485513806343, 0.020325295627117157, -0.02157685160636902, 0.022963255643844604, -0.023582706227898598, 0.04911740869283676, 0.046203963458538055, -0.033199235796928406, -0.04402511194348335, 0.080809585750103, 0.05870093032717705, -0.0277278833091259, -0.003922418225556612, 0.006164548918604851, -0.050911832600831985, -0.0303594209253788, 0.04380834475159645, 0.07532532513141632, -0.03481249511241913, -0.0637759417295456, 0.022957108914852142, -0.0015114424750208855, 0.018361395224928856, 0.05908197909593582, -0.05945870652794838, -0.016996508464217186, -0.010274210944771767, -0.03922194987535477, 0.020887091755867004, -0.005316757597029209, -0.022681914269924164, -0.039342403411865234, -0.026063740253448486, -0.04641876369714737, -0.005389968864619732, -0.03689694404602051, 0.031225569546222687, 0.020271090790629387, 0.022403324022889137, -0.016361601650714874, -0.037304967641830444, -0.006396681070327759, 0.03909023106098175, -0.0612277090549469, 0.006807592231780291, -0.038622479885816574, -0.04723533242940903, 0.031404800713062286, 0.007913749665021896, 0.03278345614671707, 0.0366620197892189, 0.004563355818390846, -0.04056903347373009, -0.0192125141620636, -0.03826310485601425, -0.017701899632811546, 0.03124064765870571, -0.02331322617828846, -0.02127748727798462, -0.037619784474372864, 0.04723958298563957, -0.017906436696648598, 0.002880761167034507, -0.06295524537563324, 2.5047577878467564e-07, 0.0030033907387405634, -0.004049590788781643, -0.05994720384478569, -0.01248479075729847, -0.030052149668335915, -0.011519819498062134, -0.031024135649204254, 0.01806984469294548, 0.036534667015075684, 0.07979459315538406, 0.09044426679611206, -0.017940785735845566, 0.010329676792025566, 0.07658074796199799, -0.018283670768141747, -0.04500551149249077, 0.013204073533415794, -0.09036224335432053, -0.042696427553892136, 0.02079610712826252, -0.0025706328451633453, 0.038268037140369415, 0.05448177084326744, 0.030510304495692253, 0.007829776033759117, -0.01621743105351925, -0.008685566484928131, -0.03689523786306381, -0.030206348747015, 0.027430785819888115, 0.009300284087657928, -0.0635785162448883, -0.003267081920057535, 0.06307852268218994, -0.016126206144690514, 0.0173493605107069, 0.013274217955768108, -0.004000053741037846, -0.01875421777367592, 0.07030068337917328, 0.035794276744127274, -0.06009246036410332, 0.007413703482598066, 0.018482930958271027, 0.04471071437001228, -0.026512792333960533, -0.03034789115190506, 0.0646500289440155, 0.0395854227244854, -0.021196210756897926, -0.0005444078706204891, 0.03828900307416916, -0.018204623833298683, 0.031559258699417114, -0.0013957854826003313, 0.013652998954057693, 0.019825533032417297, 0.005043214187026024, 0.006348576862365007, 0.017457999289035797, 0.0019789698999375105, -0.004556373227387667, 0.0206772368401289, 0.03563978150486946, -0.00044604422873817384, -0.025653263553977013, 0.006211601663380861, 2.5586482735007267e-34, 0.010851127095520496, 0.045432187616825104, 0.013147521764039993, 0.022057557478547096, 0.03740527853369713, -0.025563504546880722, 0.05783599242568016, 0.013455535285174847, -0.016064751893281937, -0.02416611835360527, -0.008542938157916069]

['Michael W. Mahoney', 'Hariharan Narayanan']

0906.4539v2

Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly, popular distribution-independent methods such as those based on the VC dimension fail to provide nontrivial results for even simple learning problems such as binary classification in these two settings. In this paper, we develop distribution-dependent learning methods that can be used to provide dimension-independent sample complexity bounds for the binary classification problem in these two popular settings. In particular, we provide bounds on the sample complexity of maximum margin classifiers when the magnitude of the entries in the feature vector decays according to a power law and also when learning is performed with the so-called Diffusion Maps kernel. Both of these results rely on bounding the annealed entropy of gap-tolerant classifiers in a Hilbert space. We provide such a bound, and we demonstrate that our proof technique generalizes to the case when the margin is measured with respect to more general Banach space norms. The latter result is of potential interest in cases where modeling the relationship between data elements as a dot product in a Hilbert space is too restrictive.

Learning with Spectral Kernels and Heavy-Tailed Data

http://arxiv.org/pdf/0906.4539v2

Title Learning Spectral Kernels HeavyTailed Data Summary Two ubiquitous aspect largescale data analysis data often heavytailed property diffusionbased spectralbased method often used identify extract structure interest Perhaps surprisingly popular distributionindependent method based VC dimension fail provide nontrivial result even simple learning problem binary classification two setting paper develop distributiondependent learning method used provide dimensionindependent sample complexity bound binary classification problem two popular setting particular provide bound sample complexity maximum margin classifier magnitude entry feature vector decay according power law also learning performed socalled Diffusion Maps kernel result rely bounding annealed entropy gaptolerant classifier Hilbert space provide bound demonstrate proof technique generalizes case margin measured respect general Banach space norm latter result potential interest case modeling relationship data element dot product Hilbert space restrictive Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.01529476698487997, -0.020869920030236244, -0.026234326884150505, 0.0217269416898489, -0.01323604118078947, -0.01262324582785368, -0.003040436888113618, 0.01090823020786047, 0.016808170825242996, 0.01965317316353321, 0.024234110489487648, 0.005948793608695269, 0.011132503859698772, 0.0354897640645504, 0.000489734869915992, -0.04540729895234108, 0.0025278113316744566, 0.013370763510465622, -0.05609596148133278, -0.021058008074760437, 0.013807500712573528, -0.03438938781619072, 0.016253836452960968, -0.0035623074509203434, -0.05419056490063667, 0.00953360553830862, -0.018812688067555428, -0.05676279962062836, 0.02555856667459011, -0.042671073228120804, 0.0469328872859478, -0.0010230792686343193, 0.022564826533198357, 0.01883123815059662, 2.129081394741661e-06, -0.0514024943113327, -0.01357861328870058, -0.00722294207662344, 0.06248137354850769, 0.03283555060625076, 0.022579697892069817, -0.01237881276756525, -0.005473595578223467, -0.02980760857462883, 0.016837211325764656, 0.0014722072519361973, 0.05561774969100952, 0.08298278599977493, 0.0006524648051708937, 0.0035815369337797165, -0.015880372375249863, -0.0820196345448494, 0.008331858552992344, 0.005644691176712513, 0.05815887078642845, 0.07882186025381088, 0.04537157341837883, 0.04415099695324898, 0.0136452317237854, -0.01921931654214859, -0.05890274420380592, 0.048388395458459854, 0.03612569719552994, 0.0009226544643752277, 0.08833739161491394, 0.06647216528654099, -0.012506981380283833, 0.013029990717768669, 0.019842933863401413, 0.0959412232041359, -0.02733844891190529, 0.004329684190452099, 0.062229372560977936, 0.02379712089896202, -0.044983427971601486, 0.018811192363500595, -0.00820995680987835, -0.029357166960835457, -0.009060816839337349, 0.01034313254058361, -0.04079270362854004, 0.03296373039484024, 0.0033370580058544874, -0.015013477765023708, -0.022664790973067284, 0.05311571806669235, 0.0060324901714921, -0.03150748088955879, 0.07351646572351456, -0.039399635046720505, -0.06180613860487938, 0.054145049303770065, -0.0024252175353467464, -0.012825933285057545, 0.01226038858294487, -0.012595532462000847, 0.02729961834847927, -0.022383200004696846, 0.06493563950061798, -0.08230762928724289, 0.04395107179880142, -0.04827209934592247, -0.012458421289920807, 0.030812615528702736, -0.02831210568547249, -0.0611385740339756, -0.05152058228850365, 0.008624647743999958, -0.005185937043279409, 0.02746080979704857, -0.07616867125034332, 0.0339716337621212, 0.014922007918357849, 0.06883178651332855, 0.0648464486002922, -0.002168654464185238, -0.08355500549077988, 0.03919563069939613, -0.010704098269343376, -0.007073941174894571, -0.010384216904640198, 0.020244671031832695, 0.034241847693920135, 0.03622506186366081, -0.022282371297478676, -0.016992179676890373, 0.0006646729307249188, 0.01810978725552559, -0.030884960666298866, 0.04905759170651436, 0.026586711406707764, 0.03394673019647598, 0.046464208513498306, -0.029550351202487946, 0.013728050515055656, 0.024172721430659294, 0.010907946154475212, -0.006195510271936655, -0.04122503101825714, -0.019207702949643135, -0.032741643488407135, -0.03278540447354317, -0.020625824108719826, -0.05831819027662277, -0.020872533321380615, -0.012688948772847652, -0.035827212035655975, 0.04419446364045143, -0.0018418080871924758, -0.052021801471710205, -0.025268523022532463, 0.06713617593050003, 0.01983281597495079, 0.0030397057998925447, 0.13763563334941864, -0.008241375908255577, -0.0143068116158247, 0.021042941138148308, -0.01700475625693798, 0.0253377053886652, 0.008582139387726784, -0.05953070893883705, 0.007118611130863428, -0.009311657398939133, 0.0019602824468165636, -0.04446426033973694, -0.013905066065490246, -0.006110422313213348, -0.013395607471466064, -0.03060910850763321, 0.01187844853848219, 0.05742167681455612, -0.005485382862389088, -0.03635164350271225, 0.0025706072337925434, 0.07256970554590225, -0.0029694056138396263, -0.012619729153811932, -0.012115084566175938, 0.05143856257200241, -0.010427136905491352, 0.013945632614195347, 0.042414434254169464, 0.030994068831205368, -0.015783848240971565, -0.01698043756186962, -0.007037663832306862, -0.008489728905260563, -0.030315084382891655, -0.05969022214412689, 0.027130041271448135, -0.03720948100090027, -0.0025946872774511576, -0.028612419962882996, 0.08985971659421921, -0.03036358393728733, 0.010995101183652878, 0.011674349196255207, 0.034506723284721375, 0.009418916888535023, -0.005860368255525827, -0.010326662100851536, 0.012043912895023823, -0.051219381392002106, -0.026880335062742233, -0.07326916605234146, 0.0859568789601326, -0.014167657122015953, 0.029252834618091583, -0.08458895981311798, 0.0051335785537958145, -0.0054868971928954124, 0.018962401896715164, -0.016766510903835297, 0.007091094274073839, 0.01889984682202339, 0.007131112273782492, -0.02058892324566841, -0.06485117226839066, 0.03626248240470886, 0.033031877130270004, -0.008196145296096802, -0.020224789157509804, -0.0013382969191297889, 0.019039887934923172, -0.01645617000758648, 0.045267459005117416, 0.043215829879045486, 0.018356338143348694, -0.03376318886876106, -0.0174893569201231, -0.03211648017168045, 0.03845373913645744, -0.060648635029792786, -0.07296749204397202, -0.0027465384919196367, 0.010037798434495926, 0.04043082892894745, 0.031404539942741394, -0.02749873511493206, 0.015436613000929356, 0.017310449853539467, -0.016701221466064453, -0.018769877031445503, 0.0653051882982254, -0.024871569126844406, -0.005612269043922424, -0.058970771729946136, 0.010528228245675564, -0.01654885895550251, 0.04871487617492676, -0.012232719920575619, 0.06162029504776001, 0.031753942370414734, 0.057438936084508896, -0.06202663108706474, -0.03135884553194046, 0.03016766533255577, 0.0015395607333630323, -0.017321515828371048, 0.006435651332139969, -0.05738481506705284, 0.011131951585412025, 0.01687433198094368, -0.035784296691417694, 0.03121054731309414, 0.03662039712071419, -0.024300293996930122, -0.022125937044620514, -0.010192942805588245, -0.009484726004302502, -0.028883211314678192, -0.007072738837450743, 0.04266439750790596, -0.0014886988792568445, -0.0001624933211132884, 0.05839012190699577, -0.040943097323179245, -0.03691667318344116, 0.05723029002547264, 0.0007212003110907972, -0.05617727339267731, -0.027011901140213013, -0.05016922205686569, -0.0056908754631876945, 0.04415452852845192, 0.004849941469728947, -0.03697013854980469, 0.009488221257925034, 0.05102647468447685, -0.014568452723324299, 0.034468263387680054, -0.004583846777677536, -0.02483212575316429, -0.04779364913702011, -0.038126688450574875, 0.04279223829507828, 0.06197472661733627, 0.051669877022504807, 0.01948121190071106, 0.04778790846467018, 0.027159836143255234, -0.003880492178723216, 0.008834263309836388, -0.08790180087089539, 0.012538905255496502, 0.0031358585692942142, 0.004670940805226564, 0.05055796355009079, -0.0007935455651022494, 0.03724658489227295, -0.006445884704589844, 0.013920019380748272, -0.051304370164871216, -0.0224215779453516, 0.005633621942251921, -0.048586927354335785, 0.019842172041535378, -0.011711019091308117, 0.013339565135538578, 0.006836004089564085, -0.017619185149669647, 0.06635957956314087, 0.031777508556842804, 0.020567860454320908, 0.019357286393642426, -0.09270617365837097, -0.024207845330238342, -0.00254674069583416, 0.022266551852226257, 0.03351827710866928, -0.005996381863951683, 0.008048477582633495, 0.020194953307509422, -0.033525142818689346, 0.0348801389336586, -0.035394828766584396, -0.017712103202939034, -0.012082137167453766, 0.007159052882343531, -0.020605558529496193, -0.026416726410388947, -0.02191431261599064, -0.017717542126774788, 0.08170635253190994, -0.03734278306365013, -0.04246380180120468, -0.035710275173187256, 0.015067264437675476, -0.003087027231231332, 0.0022895631846040487, 0.005752228200435638, 0.005063646472990513, -0.03321266546845436, 0.024367548525333405, 0.05432838946580887, 0.05334857106208801, -0.017172668129205704, -0.034934915602207184, -0.017162656411528587, 0.031153479591012, 0.023124536499381065, -0.0015901437727734447, -0.01205757912248373, -0.048941999673843384, -0.010138039477169514, -0.018267406150698662, 0.006586868781596422, -0.03791871666908264, -0.015312626957893372, 0.050755515694618225, 0.008229739032685757, 0.03362816572189331, 0.04454489424824715, -0.013292544521391392, -0.03795820474624634, 0.008442004211246967, 0.015347929671406746, 0.02218490093946457, 0.008912308141589165, 0.021881604567170143, -0.014989166520535946, 0.028090493753552437, -0.052284158766269684, 0.014481148682534695, 0.002591261174529791, -0.060443177819252014, 0.013769377022981644, -0.04463309794664383, 0.04496709257364273, 0.01887897215783596, -0.0057936543598771095, -0.03364633396267891, -0.0561806783080101, -0.005152959376573563, -0.03966716304421425, -0.0615907646715641, -0.057715386152267456, -0.006622415967285633, -0.0382230170071125, 0.05725463107228279, -0.049905166029930115, 0.0018417368410155177, 0.023388437926769257, -0.07297331839799881, -0.05182250589132309, -0.015272723510861397, 0.02393101342022419, -0.051438815891742706, -0.08587542921304703, 0.011506685987114906, -0.09529441595077515, -0.029488230124115944, -0.031204557046294212, 0.043993666768074036, 0.04542677104473114, -0.013321549631655216, 0.002817518310621381, 0.10482017695903778, -0.010529677383601665, 0.04706180468201637, 0.019738202914595604, 0.09089207649230957, -0.02247857116162777, -0.02900959737598896, -0.03481381759047508, -0.036419082432985306, 0.032031480222940445, 0.004799503367394209, -0.003856808179989457, -0.048627231270074844, -0.05079168453812599, 0.009346898645162582, 0.018093924969434738, 0.06574192643165588, -0.023682842031121254, 0.005575389601290226, -0.012472153641283512, -0.08187779039144516, -0.06610613316297531, 0.05033888295292854, -0.017054099589586258, 0.05819983035326004, -0.008754951879382133, 0.01830894872546196, 0.013446510769426823, -0.03052620030939579, -0.0654604434967041, 0.0023775743320584297, 0.07700173556804657, 0.0518360398709774, -0.015180160291492939, 0.027284350246191025, 0.040383122861385345, 0.01993393339216709, -0.015726033598184586, -0.07518941909074783, -0.0252641923725605, -0.08939996361732483, -0.004176365211606026, 0.0002629999944474548, 0.010386849753558636, -0.021858947351574898, -0.01949102245271206, -0.04072762280702591, 0.048405345529317856, 0.03645780682563782, -0.00042462715646252036, 0.01090571004897356, 0.04424901306629181, -0.049075253307819366, 0.008925980888307095, 0.004580473992973566, 0.013070234097540379, 0.06803224980831146, -0.017265556380152702, -0.05605309084057808, -0.023515326902270317, 0.01265508122742176, -0.005920011550188065, 0.013969521969556808, 0.06842357665300369, 0.058855801820755005, -0.018507059663534164, 0.0005445568240247667, 0.024474315345287323, 0.04696003720164299, 0.007751854602247477, 0.016056369990110397, -0.018428964540362358, 0.055168066173791885, 0.06137867271900177, -0.053139787167310715, 0.013171108439564705, 0.0633942186832428, 0.023646745830774307, -0.00015827640891075134, 0.0017511890036985278, -0.03393111750483513, -0.011054485104978085, 0.01110667735338211, 0.02878490835428238, -0.016965003684163094, -0.026168454438447952, 0.0502748042345047, 0.043806929141283035, 0.053180012851953506, 0.010162142105400562, -0.010189132764935493, 0.039377473294734955, -0.030110182240605354, -0.014569674618542194, -0.03717641532421112, -0.0010652387281879783, 0.014092998579144478, -0.016403725370764732, 0.009927164763212204, -0.020130829885601997, 0.0034398760180920362, -0.035466767847537994, -0.00149369181599468, -0.045754339545965195, 0.06808795034885406, -0.03667579963803291, 0.019099397584795952, 0.06036990508437157, 0.006245048251003027, -0.035912539809942245, 0.0399206206202507, 0.032812073826789856, 0.042329829186201096, -0.010845889337360859, -0.04936223477125168, -0.021626733243465424, -0.02254745550453663, 0.03958095237612724, 0.0032840773928910494, -0.002704018261283636, -0.0031050536781549454, -0.00348190451040864, -0.023982767015695572, -0.04772036150097847, 0.015703821554780006, -0.024550054222345352, 0.007039152085781097, 0.020283391699194908, -0.0044601489789783955, 0.011905273422598839, 0.014353087171912193, -0.024341240525245667, -0.032350748777389526, -0.033855605870485306, -0.010105665773153305, -0.025108085945248604, -0.0013808257644996047, -5.860479248586332e-33, 0.03596450015902519, -0.02278219535946846, -0.0743027999997139, 0.0719342902302742, -0.009570104070007801, 0.012589231133460999, 0.02483520098030567, -0.007552464958280325, 0.007817843928933144, -0.024187032133340836, -0.007613929454237223, -0.027561157941818237, 0.0007009587716311216, 0.01416134275496006, 0.030540706589818, 0.00836609210819006, 0.012074180878698826, 0.006343021523207426, 0.04531576856970787, 0.014866655692458153, 0.045424409210681915, 0.01351168006658554, -0.017479222267866135, -0.07744625955820084, -0.043551623821258545, 0.052813004702329636, 0.004683573730289936, 0.004651346243917942, 0.011070138774812222, 0.014490523375570774, -0.045212823897600174, 0.061066050082445145, -0.016950733959674835, 0.020036643370985985, -0.007526037283241749, -0.010550608858466148, -0.07488805055618286, 0.013358336873352528, -0.05171069875359535, 0.016345851123332977, -0.05303250253200531, 0.010224245488643646, 0.05288116633892059, -0.02719309739768505, -0.0319039523601532, -0.010014334693551064, 0.0856233462691307, -0.017036013305187225, -0.02375727705657482, -0.038675665855407715, -0.0034815077669918537, 0.025749797001481056, -0.035410184413194656, 0.054648689925670624, 0.03972423076629639, 0.018126223236322403, -0.00585207948461175, 0.014075088314712048, -0.026288557797670364, -0.005797676742076874, -0.028345048427581787, 0.020310724154114723, 0.02300926484167576, 0.03368203341960907, 0.07235906273126602, 0.05862817168235779, 0.0396646112203598, 0.0264145378023386, 0.03344129025936127, -0.06078486517071724, -0.010573988780379295, 0.06947703659534454, -0.035731442272663116, -0.008186443708837032, 0.06575056165456772, -0.07820457220077515, -0.07077758014202118, 0.044174280017614365, -0.02579049952328205, -0.013133962638676167, -0.027723757550120354, -0.002722482429817319, -0.026425600051879883, -0.02901580184698105, 0.027695659548044205, 0.05360613763332367, 0.01375867985188961, -0.01963958889245987, -0.02184325084090233, -0.011769120581448078, -0.021433720365166664, 0.03321383148431778, -0.03192857280373573, -0.022312982007861137, -0.03538540005683899, -0.03699792921543121, 0.02759786695241928, 0.04811284691095352, 0.03476779907941818, -0.04224110394716263, -0.041667740792036057, -0.05757522210478783, -0.023493291810154915, -0.0046588038094341755, 0.021727783605456352, -0.011504302732646465, 0.026762356981635094, 0.04122038185596466, -0.025198761373758316, -0.01871882565319538, -0.003703307593241334, -0.05612519755959511, 0.014872630126774311, 0.051004260778427124, 0.015325220301747322, -0.027737680822610855, -0.010970382019877434, 0.07746569812297821, 0.027296820655465126, 0.02436322346329689, -0.022130001336336136, -0.02282319776713848, 0.009286794811487198, 0.013193883933126926, -0.04099222645163536, -0.021015850827097893, -0.04335063695907593, -0.010135314427316189, 0.041179101914167404, -0.0430222786962986, 0.01646866463124752, -0.040873683989048004, 2.919903749898367e-07, -0.012752150185406208, 0.01155146025121212, -0.03388454020023346, -0.041771821677684784, 0.017067380249500275, 0.023981450125575066, -0.00927919615060091, 0.039733223617076874, -0.08206874877214432, -0.05940021947026253, 0.04215237498283386, -0.03482557460665703, 0.05947362259030342, -0.014910763129591942, -0.05365891009569168, -0.07866533100605011, -0.012863799929618835, -0.014327473007142544, -0.06715961545705795, 0.001271954970434308, 0.06444063782691956, 0.0741117000579834, 0.013049612753093243, -0.024847712367773056, 0.060992151498794556, -0.022644659504294395, 0.04529491439461708, -0.035660117864608765, 0.027010027319192886, -0.015418732538819313, 0.014282305724918842, -0.03172813728451729, 0.016694799065589905, 0.003942711278796196, -0.024072932079434395, 0.0221234280616045, -0.018217694014310837, -0.011326471343636513, 0.034140150994062424, -0.0044202543795108795, 0.035463377833366394, 0.046963341534137726, 0.01696058176457882, -0.017938118427991867, 0.03936414048075676, -0.007954927161335945, -0.05973467975854874, -0.029359446838498116, 0.011640381999313831, 0.000480588962091133, 0.055573709309101105, -0.009423467330634594, -0.0007192034972831607, -0.01141632441431284, -0.03984709084033966, -0.05838266387581825, 0.02659343183040619, -0.03088124841451645, 0.03110409900546074, 0.05340539291501045, -0.004330013412982225, -0.03265073522925377, 0.01641239784657955, 0.02892153523862362, 0.07058119028806686, 0.04206352308392525, 0.020506737753748894, 3.066739176254352e-34, 0.006377972662448883, 0.01093306764960289, 0.005055055022239685, -0.006430554669350386, -0.03602918982505798, -0.009759982116520405, -0.012586795724928379, -0.0166994109749794, -0.00694086542353034, -0.06857317686080933, -0.023937398567795753]

['Susmit Jha']

0906.5110v1

Security protocols often use randomization to achieve probabilistic non-determinism. This non-determinism, in turn, is used in obfuscating the dependence of observable values on secret data. Since the correctness of security protocols is very important, formal analysis of security protocols has been widely studied in literature. Randomized security protocols have also been analyzed using formal techniques such as process-calculi and probabilistic model checking. In this paper, we consider the problem of validating implementations of randomized protocols. Unlike previous approaches which treat the protocol as a white-box, our approach tries to verify an implementation provided as a black box. Our goal is to infer the secrecy guarantees provided by a security protocol through statistical techniques. We learn the probabilistic dependency of the observable outputs on secret inputs using Bayesian network. This is then used to approximate the leakage of secret. In order to evaluate the accuracy of our statistical approach, we compare our technique with the probabilistic model checking technique on two examples: crowds protocol and dining crypotgrapher's protocol.

Statistical Analysis of Privacy and Anonymity Guarantees in Randomized Security Protocol Implementations

http://arxiv.org/pdf/0906.5110v1

Title Statistical Analysis Privacy Anonymity Guarantees Randomized Security Protocol Implementations Summary Security protocol often use randomization achieve probabilistic nondeterminism nondeterminism turn used obfuscating dependence observable value secret data Since correctness security protocol important formal analysis security protocol widely studied literature Randomized security protocol also analyzed using formal technique processcalculi probabilistic model checking paper consider problem validating implementation randomized protocol Unlike previous approach treat protocol whitebox approach try verify implementation provided black box goal infer secrecy guarantee provided security protocol statistical technique learn probabilistic dependency observable output secret input using Bayesian network used approximate leakage secret order evaluate accuracy statistical approach compare technique probabilistic model checking technique two example crowd protocol dining crypotgraphers protocol Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03760193660855293, 0.05400317534804344, 0.01567978784441948, 0.02113720029592514, -0.0974990725517273, -0.07174403220415115, 0.07942143827676773, -0.009884009137749672, -0.0013513421872630715, -0.006680652499198914, 0.04271978139877319, 0.04769531637430191, 0.05991615727543831, 0.058318931609392166, 0.00472458777949214, -0.013737681321799755, 0.04912370443344116, -0.01791336014866829, 0.009570644237101078, 0.0009735663188621402, 0.006738743279129267, -0.022717803716659546, -0.014812199398875237, 0.00930978823453188, 0.058792419731616974, -0.014770390465855598, -0.02207408845424652, -0.01888349838554859, 0.002372613176703453, -0.042392630130052567, 0.006458131596446037, 0.0472111701965332, -0.04327467083930969, 0.01663067936897278, 2.49354752668296e-06, -0.015316898934543133, -0.03275416046380997, 0.07370106130838394, 0.009381284937262535, 0.03029417246580124, -0.018101079389452934, 0.03901033103466034, 0.02306290902197361, 0.015091030858457088, 0.01937338151037693, -0.003354415064677596, 0.037427790462970734, 0.06463246792554855, 0.003957789856940508, -0.01056584157049656, 0.005328651051968336, -0.023589881137013435, -0.0037010833621025085, -0.00016498210607096553, -0.01298370398581028, -0.04443593695759773, 0.021108534187078476, -0.04668298363685608, -0.0032757704611867666, 0.0451352559030056, 0.015354804694652557, -0.0395548976957798, 0.017910348251461983, -0.012636213563382626, 0.023470507934689522, 0.034796565771102905, -0.015441743656992912, -0.02626936137676239, -0.037591200321912766, 0.0019429444801062346, 0.06177500635385513, -0.004186232108622789, 0.017544278874993324, 0.03818020969629288, -0.02485225535929203, 0.03852434828877449, 0.014148976653814316, 0.022445037961006165, -0.029395142570137978, -0.02732577919960022, -0.0557081438601017, 0.08782774209976196, 0.021320797502994537, -0.017472457140684128, 0.062604621052742, 0.07211296260356903, 0.028530677780508995, 0.0046044704504311085, -0.05748239904642105, -0.03483220189809799, 0.002902337582781911, -0.04399256780743599, 0.04195498675107956, -0.03732292726635933, 0.03673179820179939, -0.011522660031914711, 0.007281063590198755, -0.0074347835034132, 0.05182240903377533, -0.019573889672756195, -0.033633485436439514, -0.04431188479065895, 0.016944581642746925, 0.014747066423296928, 0.038248103111982346, -0.037453316152095795, 0.0011624546023085713, 0.012057467363774776, 0.03581954166293144, 0.04825239256024361, -0.014864103868603706, 0.009039632976055145, 0.017676610499620438, 0.058163125067949295, -0.005213399883359671, 0.042394887655973434, -0.056444160640239716, 0.0229856725782156, -0.038970161229372025, 0.04485480859875679, -0.0018933464307338, 0.008014297112822533, 0.0036797011271119118, 0.016851171851158142, -0.0006393041112460196, -0.07558918744325638, -0.027453232556581497, 0.015449599362909794, -0.02098855748772621, 0.036561477929353714, 0.011080835945904255, -0.015393936075270176, 0.0071702515706419945, 0.01707625761628151, -0.03952741622924805, 0.07634354382753372, 0.035497989505529404, 0.017288969829678535, -0.027476079761981964, -0.05964600667357445, 0.04532289132475853, -0.007034461013972759, -0.033618368208408356, -0.06642197072505951, -0.02714884653687477, -0.05248478800058365, -0.004654581658542156, 0.02044583298265934, -0.03445671871304512, -0.02555827982723713, -0.050548117607831955, 0.0640643760561943, 0.040244098752737045, -0.002984273247420788, 0.042368266731500626, 0.04816693440079689, 0.050837211310863495, -0.02552337758243084, -0.007389316335320473, 0.02281235158443451, 0.030417906120419502, -0.036375969648361206, 0.0875997319817543, -0.07008344680070877, -0.008342311717569828, -0.0317075252532959, 0.01758289895951748, 0.01918129436671734, 0.04260428622364998, -0.08150776475667953, -0.07777529209852219, 0.03445902094244957, -0.009942411445081234, -0.03829285129904747, 0.03891991451382637, 0.029371041804552078, -0.04012535139918327, -0.0035944259725511074, -0.0632399469614029, 0.049056097865104675, 0.03159497678279877, 0.00198118994012475, -0.0323028601706028, 0.044353507459163666, -0.055432211607694626, -0.04370805248618126, 0.009076348505914211, -0.03749346360564232, -0.030482152476906776, -0.004653424024581909, -0.014919165521860123, -0.05939778313040733, -0.01086235698312521, -0.03829434886574745, 0.009947361424565315, 0.006042910274118185, 0.009741365909576416, -0.040115006268024445, 0.021025585010647774, -0.0024556107819080353, -0.06714507192373276, -0.04642009735107422, 0.05066025257110596, 0.037514828145504, 0.0012205601669847965, 0.031364310532808304, 0.04199773445725441, -0.011417346075177193, -0.0329873152077198, -0.025417035445570946, -0.017268652096390724, 0.008878781460225582, 0.04839643836021423, 0.005967687349766493, -0.009026453830301762, 0.05657731369137764, 0.030558452010154724, 0.03231379762291908, -0.017200466245412827, -0.0020392057485878468, 0.015374633483588696, 0.031049031764268875, 0.029178403317928314, -0.010457164607942104, -0.014052611775696278, 0.01660463958978653, 0.04711960628628731, 0.005131707526743412, 0.02218601107597351, 0.02647806890308857, -0.004439110867679119, 0.03574758023023605, -0.011366750113666058, 0.05646718293428421, 0.02950236387550831, 0.02006150595843792, 0.06949657946825027, 0.0520813874900341, -0.044582609087228775, -0.03584499657154083, 0.03432152792811394, 0.03295409679412842, -0.008711126632988453, 0.012743418104946613, 0.05509566888213158, 0.020254844799637794, 0.011367889121174812, -0.014336870983242989, -0.030887559056282043, -0.019558580592274666, 0.024994567036628723, -0.028612734749913216, -0.05140027403831482, 0.010134480893611908, 0.006605092901736498, -0.09768494963645935, -0.014761668629944324, 0.06456423550844193, -0.007552953902631998, -0.017753049731254578, -0.016704637557268143, -0.025100499391555786, 0.006826575379818678, 0.01642243005335331, 0.01711202599108219, 0.0035173993092030287, 0.02363279089331627, -0.017712075263261795, 0.03348851203918457, 0.0014290583785623312, 0.029069943353533745, 0.026081472635269165, 0.030785100534558296, 0.009294088929891586, -0.03696545213460922, 0.002124410355463624, -0.03222677484154701, -0.07356864213943481, -0.026259373873472214, 0.029944537207484245, 0.01648624986410141, -0.042179886251688004, 0.006263814400881529, -0.03387998044490814, -0.005856857169419527, 0.036463331431150436, 0.021607056260108948, 0.00019903600332327187, -0.008118069730699062, 0.033978421241045, -0.034439243376255035, -0.025325214490294456, -0.003166758920997381, -0.0571245402097702, 0.026311751455068588, 0.040124308317899704, -0.03637155517935753, -0.020661741495132446, 0.04089684039354324, -0.010575550608336926, 0.02494765818119049, 0.023641547188162804, 0.00019574757607188076, -0.02498846873641014, -0.020770829170942307, 0.005922222509980202, 0.039605703204870224, -0.04993002116680145, 0.015880245715379715, -0.007997281849384308, 0.017756201326847076, -0.026731329038739204, -0.01197254378348589, 0.01783539168536663, 0.01571437530219555, 0.007267005741596222, -0.06601016223430634, -0.04382787272334099, 0.005532761570066214, 0.040001410990953445, -0.013228358700871468, -0.004541720729321241, 0.04476683586835861, -0.02320973388850689, 0.03101535700261593, -0.03207812458276749, -0.029694637283682823, 0.05066508427262306, 0.05470413342118263, -0.0008513466455042362, 0.021010704338550568, 0.03717315196990967, -0.020129257813096046, 0.01129104383289814, -0.07926717400550842, 0.05370638146996498, -0.026559792459011078, -0.10536883771419525, 0.0008940464467741549, -0.04525407776236534, 0.020377689972519875, -0.0009072400280274451, -0.008957920596003532, -0.07975934445858002, 0.019874142482876778, -0.020376048982143402, -0.06817041337490082, -0.03486582264304161, 0.03306557610630989, 0.015958860516548157, 0.026621157303452492, -0.004044491332024336, 0.0038536235224455595, 0.0013745584292337298, -0.01919987052679062, -0.05394664779305458, -0.021340524777770042, -0.11074421554803848, -0.00986841507256031, 0.03987918049097061, -0.023990634828805923, 0.03669073432683945, -0.019424457103013992, 0.04453965276479721, -0.05566585063934326, -0.06542222946882248, -0.0069879754446446896, -0.021136660128831863, 0.012225640937685966, 0.04301256313920021, 0.0060497974045574665, 0.013467509299516678, 0.027441127225756645, 0.02135876752436161, 0.0016380025772377849, -0.024041566997766495, -0.014184514060616493, 0.015581103973090649, -0.03920648992061615, -0.008904935792088509, 0.03950794041156769, -0.06986162811517715, 0.06737834960222244, -0.02242782898247242, 0.05834311991930008, -0.09713447839021683, -0.04442378506064415, -0.033833615481853485, -0.019284212961792946, 0.06490689516067505, -0.018518904224038124, -0.054986875504255295, 0.011822143569588661, -0.10633126646280289, 0.014783013612031937, -0.0070674302987754345, 0.0006904813344590366, -0.0032767215743660927, 0.047301847487688065, -0.0036698023322969675, 0.007166301365941763, -0.12670332193374634, -0.0460151806473732, 0.021960828453302383, -0.034858815371990204, 0.03826865926384926, 0.038242533802986145, 0.02014550380408764, -0.05786433443427086, -0.02212698571383953, 0.0031938422471284866, 0.05640527233481407, -0.06431541591882706, 0.018112491816282272, 0.018424365669488907, 0.04442176967859268, 0.0031324115116149187, -0.02019236609339714, 0.0005930971237830818, 0.02400556392967701, -0.0071486192755401134, 0.010216360911726952, -0.019368812441825867, -0.02456035651266575, -0.027069101110100746, -0.0226464681327343, 0.035892535001039505, 0.05985867977142334, 0.012207466177642345, -0.03213191032409668, 0.04999973997473717, -0.0289420485496521, -0.015636060386896133, 0.019896013662219048, -0.03292298689484596, 0.04701336845755577, 0.0034659665543586016, -0.029289372265338898, -0.12152819335460663, -0.05089057236909866, 0.04115787148475647, -0.04418650642037392, 0.04999352619051933, 0.021416932344436646, 0.031210562214255333, 0.048700135201215744, 0.014488388784229755, -0.010498840361833572, -0.0755121037364006, 0.01364724151790142, 0.011737444438040257, -0.0038053866010159254, 0.02489805966615677, -0.022558487951755524, 0.03036048635840416, -0.03372553363442421, -0.018434729427099228, -0.021828915923833847, -0.038911450654268265, 0.03952400013804436, 0.04832521453499794, 0.028496772050857544, -0.02576536126434803, -0.053524505347013474, -0.026334501802921295, -0.02891155704855919, -0.008116873912513256, 0.034783147275447845, -0.031860630959272385, -0.005304678808897734, -0.049057576805353165, 0.011813954450190067, -0.06318505108356476, 0.011399674229323864, 0.01175018958747387, 0.022043049335479736, -0.07652871310710907, -0.03270570561289787, -0.006726424675434828, -0.026215091347694397, 0.04873417690396309, 0.035820815712213516, 0.04255828261375427, 0.014237537048757076, -0.004285542760044336, 0.01710544526576996, -0.07451590895652771, -0.012186847627162933, 0.014485642313957214, -0.01280394196510315, 0.003069178434088826, 0.01773662492632866, 0.028120243921875954, -0.036932431161403656, 0.011267054826021194, 0.0024337314534932375, 0.08417590707540512, 0.0320340171456337, 0.06070894002914429, 0.02932796999812126, 0.028775040060281754, 0.007311446592211723, -0.01589103788137436, 0.006597721949219704, 0.052687324583530426, 0.05391756072640419, 0.0038233106024563313, -0.044933512806892395, -0.025037648156285286, -0.02896365523338318, -0.017326584085822105, 0.008936372585594654, -0.04583410918712616, -0.03521108627319336, 0.06152211129665375, 0.06404732167720795, -0.023108601570129395, 0.052440185099840164, -0.07034401595592499, -0.02204228565096855, 0.06083973869681358, -0.03574998676776886, 0.05046983063220978, -0.04101700708270073, 0.030194075778126717, 0.003839903511106968, 0.003398304572328925, -0.004938120488077402, 0.05488186329603195, 0.003796246135607362, 0.037545304745435715, -0.046461861580610275, -0.04974529147148132, -0.051428455859422684, -0.01886921189725399, 0.04055391252040863, -0.0038854170124977827, 0.05435362830758095, -0.05451001599431038, -0.020105116069316864, 0.0218595489859581, -0.010592250153422356, -0.03109334595501423, 0.004772545769810677, 0.07653860747814178, 0.05054417997598648, -0.008294399827718735, 0.02823016233742237, 0.0015220878412947059, -0.038874223828315735, -0.07911074161529541, -0.035175882279872894, 0.02731996402144432, -0.0714976042509079, -0.0030019923578947783, -6.314253863466321e-33, 0.022672263905405998, -0.06126456707715988, -0.02875933051109314, -0.005730826407670975, 0.04145190119743347, -0.03534570708870888, -0.03638780862092972, 0.0158787053078413, 0.038425203412771225, -0.007847381755709648, 0.006515450309962034, 0.005283087491989136, 0.03741860389709473, -0.009950362145900726, -0.01544953417032957, -0.017476389184594154, -0.012384440749883652, -0.0015509037766605616, 0.01898733526468277, -0.02013516053557396, 0.04844613000750542, 0.008901678957045078, -0.012656464241445065, -0.017451761290431023, 0.09959840029478073, -0.013827459886670113, -0.04815641790628433, -0.007495544850826263, -0.008423582650721073, 0.00018343186820857227, 0.014209244400262833, -0.07890956103801727, -0.015995441004633904, 0.012284995056688786, 5.898118615732528e-05, 0.04061388224363327, -0.012982799671590328, -0.04453763738274574, 0.014026075601577759, 0.004882066510617733, -0.03469568490982056, -0.03594697639346123, 0.0005109990597702563, -0.022596094757318497, -0.022797537967562675, 0.04973564296960831, 0.01066894456744194, 0.015755200758576393, -0.007928174920380116, 0.0026652468368411064, 0.05918075144290924, -0.0018782933475449681, -0.01279484760016203, 0.07167885452508926, 0.01233263872563839, -0.02978850156068802, -0.015728697180747986, -0.07648879289627075, 0.0038936971686780453, 0.024087000638246536, 0.016799315810203552, -0.020305978134274483, -0.009755848906934261, 0.009931671433150768, 0.0343199297785759, -0.03817891329526901, -0.030214449390769005, 0.022747058421373367, -0.008583287708461285, -0.023063935339450836, -0.02686794474720955, 0.039468877017498016, 0.022962607443332672, 0.01740528643131256, 0.01587785966694355, -0.07014404237270355, -0.05676883086562157, 0.043928422033786774, 0.00582299567759037, -0.03594619408249855, 0.02836799807846546, -0.024573052302002907, -0.06633676588535309, -0.023299871012568474, 0.0237882062792778, 0.003729419317096472, -0.009347772225737572, -0.01980249211192131, -0.04802481457591057, -0.014308531768620014, -0.004900116007775068, -0.007219539023935795, 0.0228671133518219, -0.05012236908078194, -0.02096215821802616, -0.024668443948030472, 0.08084828406572342, 0.005938273388892412, -0.033852603286504745, -0.016794756054878235, -0.041276268661022186, 0.010010740719735622, -0.023348337039351463, -0.014762954786419868, 0.007858898490667343, 0.01794576831161976, 0.014908427372574806, 0.003954993095248938, -0.04621570184826851, 0.013714547269046307, 0.014777330681681633, 0.011210838332772255, 0.021083373576402664, -0.022984376177191734, -0.010110851377248764, -0.011844168417155743, 0.009645724669098854, 0.013707899488508701, 0.017355965450406075, -0.004651273600757122, -0.01716248318552971, 0.09986867755651474, -0.05012453347444534, 0.017327550798654556, 0.03106297366321087, -0.021503282710909843, -0.023534825071692467, -0.037128984928131104, 0.05364033207297325, 0.060541070997714996, 0.010241352021694183, -0.05002935603260994, 3.1412727707902377e-07, -0.015699513256549835, -0.030770327895879745, -0.003748237621039152, -0.01015123538672924, 0.027752842754125595, 0.019015230238437653, -0.015984710305929184, 0.06499852985143661, -0.010511529631912708, -0.01919182762503624, -0.029752159491181374, -0.04684155061841011, 0.062037382274866104, 0.016173196956515312, -0.05468032881617546, -0.08007727563381195, -0.01263322401791811, 0.010651845484972, 0.004568844567984343, -0.007958524860441685, 0.01985854096710682, -0.001544416998513043, 0.08819012343883514, 0.030444301664829254, -0.027992499992251396, -0.01572679914534092, -0.0048373243771493435, -0.020967112854123116, -0.012867037206888199, 0.0033602281473577023, 0.035650916397571564, 0.052507463842630386, 0.05604751780629158, 0.03710408881306648, -0.03423929959535599, -0.08154278248548508, -0.03103933297097683, 0.06091790273785591, 0.035422928631305695, 0.046777185052633286, -0.02144935354590416, -0.05659213289618492, -0.014728154055774212, -0.021453943103551865, 0.027690891176462173, 0.02841845527291298, -0.08208203315734863, 0.02529471181333065, -0.023712005466222763, -0.017149057239294052, 0.04923965036869049, 0.036639146506786346, 0.011311098001897335, -0.010516596026718616, -0.023334354162216187, 0.010180181823670864, 0.03715198487043381, 0.010649657808244228, -0.03581018000841141, -0.02631743811070919, 0.016940373927354813, -0.05300192907452583, 0.07217525690793991, -0.004354757722467184, 0.041852183640003204, 0.04267352819442749, 0.030643535777926445, 3.117710172509441e-34, -0.025975778698921204, 0.0034221564419567585, -0.01810719631612301, -0.00844001304358244, -0.004577234853059053, 0.003910369705408812, 0.04229035973548889, -0.0032439413480460644, 0.026285307481884956, 0.03988261893391609, -0.007677966263145208]

['Nicholas Mastronarde', 'Mihaela van der Schaar']

0906.5325v1

In our previous work, we proposed a systematic cross-layer framework for dynamic multimedia systems, which allows each layer to make autonomous and foresighted decisions that maximize the system's long-term performance, while meeting the application's real-time delay constraints. The proposed solution solved the cross-layer optimization offline, under the assumption that the multimedia system's probabilistic dynamics were known a priori. In practice, however, these dynamics are unknown a priori and therefore must be learned online. In this paper, we address this problem by allowing the multimedia system layers to learn, through repeated interactions with each other, to autonomously optimize the system's long-term performance at run-time. We propose two reinforcement learning algorithms for optimizing the system under different design constraints: the first algorithm solves the cross-layer optimization in a centralized manner, and the second solves it in a decentralized manner. We analyze both algorithms in terms of their required computation, memory, and inter-layer communication overheads. After noting that the proposed reinforcement learning algorithms learn too slowly, we introduce a complementary accelerated learning algorithm that exploits partial knowledge about the system's dynamics in order to dramatically improve the system's performance. In our experiments, we demonstrate that decentralized learning can perform as well as centralized learning, while enabling the layers to act autonomously. Additionally, we show that existing application-independent reinforcement learning algorithms, and existing myopic learning algorithms deployed in multimedia systems, perform significantly worse than our proposed application-aware and foresighted learning methods.

Online Reinforcement Learning for Dynamic Multimedia Systems

http://arxiv.org/pdf/0906.5325v1

Title Online Reinforcement Learning Dynamic Multimedia Systems Summary previous work proposed systematic crosslayer framework dynamic multimedia system allows layer make autonomous foresighted decision maximize system longterm performance meeting application realtime delay constraint proposed solution solved crosslayer optimization offline assumption multimedia system probabilistic dynamic known priori practice however dynamic unknown priori therefore must learned online paper address problem allowing multimedia system layer learn repeated interaction autonomously optimize system longterm performance runtime propose two reinforcement learning algorithm optimizing system different design constraint first algorithm solves crosslayer optimization centralized manner second solves decentralized manner analyze algorithm term required computation memory interlayer communication overhead noting proposed reinforcement learning algorithm learn slowly introduce complementary accelerated learning algorithm exploit partial knowledge system dynamic order dramatically improve system performance experiment demonstrate decentralized learning perform well centralized learning enabling layer act autonomously Additionally show existing applicationindependent reinforcement learning algorithm existing myopic learning algorithm deployed multimedia system perform significantly worse proposed applicationaware foresighted learning method Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.019158542156219482, -0.031203465536236763, -0.023693520575761795, -0.029850810766220093, -0.010953031480312347, -0.017850598320364952, 0.044847168028354645, 0.012045525945723057, -0.06280073523521423, -0.03129338473081589, -0.016614306718111038, 0.01629253290593624, -0.010995802469551563, 0.06079670041799545, 0.010450230911374092, -0.07558141648769379, 0.01318901777267456, -0.0038370941765606403, 0.0239624734967947, -0.004104272928088903, 0.05371885001659393, -0.05086846277117729, 0.0023657511919736862, -0.026555465534329414, -0.04868081957101822, -0.013197171501815319, -0.05666417255997658, 0.003266235813498497, 0.051728155463933945, -0.0307894516736269, -0.002292484510689974, -0.014057086780667305, 0.024441229179501534, 0.04564553126692772, 2.215639824498794e-06, -0.005342867691069841, -0.00484914006665349, -0.026179837062954903, 0.053500961512327194, -0.0069557297974824905, 0.036121416836977005, -0.0031258580274879932, -0.04465172439813614, 0.014565597288310528, -0.016927937045693398, -0.007399588357657194, 0.030560435727238655, 0.05780878663063049, 0.053256575018167496, 0.020346686244010925, -0.02189737930893898, 0.0010664649307727814, 0.003452640026807785, 0.013879790902137756, -0.008443072438240051, -0.0023811401333659887, 0.0026455787010490894, 0.019802825525403023, 0.03556930646300316, -0.07638423889875412, -0.036746345460414886, 0.021044516935944557, 0.01892567239701748, -0.008768108673393726, 0.026960430666804314, 0.005223674234002829, -0.012166979722678661, -0.030263684689998627, -0.03206239640712738, 0.013988230377435684, -0.03829013556241989, 0.04079795628786087, 0.030052853748202324, -0.012538558803498745, -0.011459973640739918, 0.018815889954566956, -0.018084323033690453, 0.04541575163602829, -0.053573425859212875, -0.0017650959780439734, -0.06279218941926956, 0.039323460310697556, -0.00557176535949111, 0.020610053092241287, 0.018462693318724632, 0.057212069630622864, -0.0140449870377779, -0.015194566920399666, -0.03868358954787254, -0.0014517955714836717, 0.06223488226532936, -0.04050154238939285, 0.028947122395038605, 0.008745254017412663, -0.030419550836086273, -0.007921282202005386, -0.005555277690291405, 0.005390816368162632, -0.020180214196443558, -0.07372211664915085, 0.07185880094766617, -0.02838955447077751, 0.0022052295971661806, 0.005924941971898079, 0.014514067210257053, 0.029498258605599403, -0.0593402124941349, -0.016026418656110764, 0.03496544435620308, 0.046571943908929825, -0.0346553809940815, -0.0036103648599237204, 0.005518503487110138, 0.08814176172018051, -0.022362787276506424, -0.059444401413202286, -0.08262075483798981, 0.0456896647810936, -0.06236589327454567, 0.03815525397658348, -0.021903686225414276, 0.05053479224443436, -0.003953739535063505, 0.008327492512762547, -0.05113987252116203, 0.012557657435536385, -0.010489552281796932, 0.04247394576668739, -0.011991293169558048, -0.02099393866956234, 0.0724022164940834, -0.0061664883978664875, -0.01199636422097683, 0.019465157762169838, 0.001001834636554122, 0.10963533818721771, 0.0005177254206500947, 0.050258569419384, -0.00951263029128313, -0.017321934923529625, 0.03341434523463249, -0.0063255345448851585, -0.011799875646829605, -0.040674805641174316, -0.03091883845627308, -0.04428791254758835, -0.0185906533151865, 0.08904977142810822, -0.0038590484764426947, -9.970289102056995e-05, 0.010730622336268425, 0.05700348690152168, 0.029859712347388268, 0.013454101048409939, 0.09672681242227554, 0.026782073080539703, -0.020433714613318443, 0.03243003785610199, 0.03353305906057358, 0.007693217135965824, 0.04924185574054718, -0.01413505245000124, 0.014884572476148605, 0.0010451454436406493, -0.01769942231476307, -0.005312255118042231, -0.048189178109169006, -0.028347095474600792, -0.0006593376165255904, 0.04136060178279877, -0.02137361466884613, 0.011369919404387474, -0.057315703481435776, -0.002013685181736946, 0.035260532051324844, -0.02912094071507454, 0.024116136133670807, -0.030018728226423264, 0.019449507817626, 0.07048673182725906, -0.03545483946800232, 0.017823249101638794, 0.01207828614860773, 0.13411292433738708, 0.03047829680144787, -0.0014274836285039783, -0.0421387143433094, 0.04269598796963692, -0.05229821056127548, -0.010992788709700108, 0.028662942349910736, -0.03745514154434204, 0.00012738803343381733, 0.04161616042256355, 0.025906076654791832, 0.012191487476229668, -0.03227291256189346, -0.022490907460451126, -0.0030814707279205322, 0.015556148253381252, 0.0003094251442234963, -0.047726258635520935, 0.029116947203874588, 0.012746049091219902, -0.011832158081233501, -0.007973057217895985, -0.03054887242615223, -0.04406341537833214, 0.007345212623476982, 0.000493137224111706, -0.022799694910645485, -0.044299717992544174, 0.01060631312429905, -0.025456959381699562, -0.03228158503770828, 0.0004472140863072127, 0.001329624094069004, 0.047571536153554916, -0.031210025772452354, 0.04654597491025925, -0.04714334383606911, 0.07778183370828629, 0.03145815432071686, -0.007808584254235029, -0.007699323818087578, -0.028887266293168068, 0.02227625623345375, 0.04369845613837242, 0.03583016246557236, -0.025345059111714363, -0.004050263669341803, -0.023331305012106895, -0.0026598565746098757, 0.021499712020158768, -0.044461145997047424, -0.009980502538383007, -0.032839443534612656, 0.0005135680548846722, 0.020521130412817, -0.0632811188697815, 0.0590982623398304, 0.01564774103462696, -0.04058864340186119, -0.0424736887216568, 0.030493082478642464, 0.010297507047653198, 0.0010550046572461724, 0.011043506674468517, 0.012508602812886238, 0.026258831843733788, 0.021983999758958817, -0.0075020259246230125, 0.00840740092098713, 0.03984849154949188, -0.014869144186377525, 0.009235799312591553, 0.02166691981256008, 0.0634906068444252, -0.0550822913646698, 0.028047341853380203, 0.008052031509578228, -0.029342250898480415, -0.01728459820151329, 0.004716738127171993, 0.02391842193901539, 0.0008179315482266247, 0.006365537643432617, 0.034862518310546875, -0.017977355048060417, 0.001751478179357946, -0.04041054844856262, 0.0018506725318729877, 0.033223047852516174, -0.017607124522328377, -0.06435562670230865, 0.016131918877363205, 0.06323318928480148, -0.004711939021945, -0.003397774649783969, 0.002987892832607031, 0.04873639717698097, 0.017574699595570564, 0.0021371496841311455, -0.037247221916913986, 0.005153246223926544, -0.00714331679046154, 0.015727512538433075, -0.021400418132543564, -0.008045376278460026, -0.09148462116718292, -0.05356406420469284, 0.03463347628712654, 0.012705237604677677, -0.03716466575860977, -0.0032558662351220846, 0.03577769920229912, -0.022990625351667404, 0.03726687282323837, 0.0291167963296175, 0.02512136846780777, -0.005118336528539658, -0.007995488122105598, -0.05348385497927666, 0.036143265664577484, -0.023338474333286285, 0.009535521268844604, -0.02618061564862728, 0.05743345990777016, 0.0012542405165731907, 0.034779347479343414, 0.0067565287463366985, 0.04167843610048294, -0.04762699082493782, -0.006132376845926046, -0.004159184172749519, -0.014020689763128757, -0.03349924832582474, -0.018285857513546944, -0.027562011033296585, -0.016472063958644867, 0.009945663623511791, -0.02474799193441868, 0.059752415865659714, 0.06184255704283714, -0.01667831465601921, 0.02122662216424942, -0.05933411791920662, -0.0062887961976230145, -0.008151189424097538, -0.023196376860141754, 0.019987624138593674, -0.023124150931835175, -0.04284181073307991, -0.055773112922906876, -0.0021250369027256966, 0.0743880644440651, -0.03504228591918945, -0.08299610763788223, 0.01671784743666649, -0.04303693398833275, -0.022553350776433945, -0.04127311334013939, -0.02667361870408058, 0.07618605345487595, -0.017252078279852867, -0.030245980247855186, -0.0831688642501831, 0.02163025550544262, -0.00807095691561699, 0.030804254114627838, 0.02873222343623638, 0.01874234341084957, -0.03235163167119026, -0.020155979320406914, 0.001511814771220088, 0.016071347519755363, 0.037362344563007355, -0.04619834944605827, -0.06879553198814392, 0.007753120735287666, 0.10840906947851181, 0.0050154924392700195, 0.022244978696107864, -0.05459163337945938, -0.06436430662870407, 0.05475115031003952, 0.036841608583927155, -0.021871061995625496, -0.035463809967041016, 0.06341646611690521, -0.02682715654373169, -0.04991839826107025, 0.03679102286696434, 0.02330826409161091, 0.0002353908639634028, -0.07735931128263474, -0.040066909044981, -0.007370044942945242, -0.06674525886774063, 0.022964229807257652, 0.017390377819538116, -0.02812703512609005, 0.009407412260770798, -0.03227341175079346, 0.0018992047989740968, 0.009513488970696926, 0.0055677881464362144, 0.027088019996881485, -0.07374818623065948, 0.0631285235285759, -0.039594829082489014, 0.00318765826523304, 0.02887176163494587, -0.002213024068623781, -0.005791781470179558, -0.026047412306070328, 0.01472187414765358, 0.009110435843467712, 0.0035305931232869625, -0.013348568230867386, 0.029851069673895836, -0.019095564261078835, -0.014572303742170334, -0.013582002371549606, -0.08670525252819061, 0.014804540202021599, 0.05687379464507103, 0.026558808982372284, -0.018654517829418182, -0.0886668935418129, -0.023857668042182922, 0.008600774221122265, 0.019900014623999596, -0.01293178554624319, 0.03768850490450859, 0.007009843830019236, 0.0028558538760989904, -0.009264298714697361, -0.00023316936858464032, 0.08716059476137161, 0.027299664914608, 0.013964107260107994, 0.04761850833892822, -0.012668321840465069, 0.013674418441951275, -0.05913473293185234, 0.02674298919737339, 0.03850778564810753, -0.04211806878447533, -0.072859026491642, -0.040431153029203415, -0.08016171306371689, 0.03300853446125984, -0.01841260865330696, -0.03556197136640549, 0.019708935171365738, -0.003530992427840829, 0.01398987602442503, 0.0004000373010057956, -0.024184241890907288, 0.040038373321294785, -0.05631284788250923, 0.050536975264549255, -0.0035550750326365232, 0.015889564529061317, 0.051281899213790894, 0.0666591003537178, -0.058408621698617935, -0.06879335641860962, 0.10476513206958771, -0.011088059283792973, -0.005616382230073214, 0.026886286213994026, 0.03351396322250366, -0.0630466639995575, -0.004598962143063545, -0.08700685948133469, 0.020399924367666245, -0.021914159879088402, -0.02314823307096958, 0.04331217706203461, 0.007229464594274759, 0.033976975828409195, -0.005822291132062674, -0.02218841016292572, 0.04813068360090256, -0.02625402994453907, -0.043854035437107086, -0.0338529534637928, 0.042964525520801544, 0.010223204270005226, -0.01988445408642292, 0.022200152277946472, -0.0530347116291523, 0.02176687866449356, 0.030899830162525177, -0.03477461263537407, -0.0019005542853847146, 0.06161407753825188, -0.026301326230168343, -0.05063042417168617, 0.041994526982307434, -0.003335769986733794, -0.044308457523584366, 0.013233848847448826, 0.0288680512458086, 0.009578047320246696, 0.0175738837569952, -0.032215870916843414, 0.01880820281803608, -0.0007551355520263314, 0.017355352640151978, 0.027302974835038185, -0.0017692471155896783, 0.07741417735815048, -0.11654901504516602, -0.01146005466580391, 0.018730048090219498, 0.005208722781389952, -0.019508399069309235, -0.019980154931545258, 0.03366905450820923, 0.06376408785581589, 0.002482537878677249, 0.05594676360487938, 0.01297817099839449, -0.012259669601917267, 0.033611658960580826, 0.007661949377506971, 0.02757374756038189, 0.012004759162664413, 0.004440187476575375, 0.04536061733961105, -0.02704884670674801, 0.0037790080532431602, 0.0520348995923996, 0.04678376391530037, 0.024861587211489677, -0.0408584326505661, 0.01190793327987194, 0.04009382054209709, 0.0005728502874262631, 0.013524731621146202, -0.06350042670965195, -0.045461256057024, 0.03301724046468735, 0.017239751294255257, -0.0004410550754982978, 0.04896046221256256, 0.03001168929040432, 0.004940901417285204, -0.02605169638991356, -0.07169082015752792, -0.029370011761784554, -0.021333418786525726, 0.04146517068147659, 0.02984859049320221, 0.027929633855819702, -0.03628787770867348, 0.039336785674095154, 0.0179605595767498, -0.049171820282936096, -0.012128681875765324, 0.028754616156220436, 0.04358445852994919, -0.024714389815926552, 0.043381158262491226, -0.019606970250606537, 0.05437715724110603, 0.04035809636116028, -0.02926034666597843, -0.052210234105587006, -0.03097836673259735, 0.007569687440991402, -0.023297196254134178, -6.0806155450327604e-33, 0.013386692851781845, 0.027454758062958717, -0.0022551764268428087, -0.02267698012292385, -0.03414074331521988, -0.012978321872651577, 0.025244133546948433, -0.02289784513413906, 0.04994242638349533, -0.029626837000250816, 0.009766233153641224, 0.04419754445552826, 0.017578275874257088, 0.03832172229886055, 0.027851270511746407, -0.012129275128245354, 0.003487645648419857, -0.03497093915939331, -0.007546029053628445, -0.003995815292000771, -0.0013371027307584882, 0.04817914217710495, -0.011826357804238796, -0.019537126645445824, -0.09358000010251999, 0.052029091864824295, -0.01102695893496275, -0.036061566323041916, -0.04890039190649986, 0.06645350903272629, -0.03669090196490288, -0.02768678218126297, -0.029242299497127533, -0.07115835696458817, 0.01483000349253416, 0.055900394916534424, -0.06495241075754166, -0.002071707509458065, -0.03818732500076294, 0.05109994113445282, -0.05365622043609619, 0.029750211164355278, 0.011170323938131332, 0.024367736652493477, -0.0606018491089344, 0.026308221742510796, 0.05907059460878372, -0.002969135995954275, -0.012036552652716637, -0.044704582542181015, -0.04680028185248375, 0.008578897453844547, 0.004903849214315414, 0.035779133439064026, 0.045010797679424286, 0.0019093749579042196, -0.02429276332259178, -0.008962987922132015, -0.035204704850912094, 0.0381261445581913, -0.06710716336965561, -0.010085982270538807, 0.00355741148814559, 0.025442153215408325, 0.03283311054110527, 0.02494940720498562, -0.017311295494437218, -0.053597353398799896, -0.0037288866005837917, 0.015823163092136383, -0.0040048956871032715, 0.05651741847395897, 0.0200932789593935, 0.016784217208623886, 0.04426401108503342, -0.0527925081551075, -0.015148477628827095, 0.006955211516469717, 0.01929270476102829, 0.010780036449432373, 0.009300640784204006, 0.0013674964429810643, -0.01897595450282097, 0.03137848898768425, 0.030204588547348976, 0.04806619882583618, -0.010319868102669716, -0.06810344010591507, 0.04224604740738869, 0.050164178013801575, 0.02620350569486618, -0.03569271042943001, 0.03534659370779991, -0.05693448707461357, 0.021092072129249573, -0.03996171057224274, 0.00608996395021677, 0.04912794381380081, 0.03503117710351944, -0.03695718199014664, -0.04807617515325546, -0.02978498302400112, -0.034216754138469696, 1.655598134675529e-05, -0.015918103978037834, 0.007286372594535351, 0.016310611739754677, 0.08271516114473343, -0.014146801084280014, 0.02874053828418255, 0.021816540509462357, 0.00408521294593811, 0.05424017831683159, 0.033848732709884644, 0.005861165467649698, -0.034518856555223465, -0.04383346438407898, 0.02522236481308937, -0.028933323919773102, -0.03372633084654808, -0.014405928552150726, -0.05964658409357071, -0.04464991018176079, -0.017358921468257904, -0.07524820417165756, 0.022256607189774513, -0.09276755154132843, 0.01942473277449608, -0.052592404186725616, -0.06392017751932144, -0.021439822390675545, 0.029905037954449654, 2.9034103476988093e-07, -0.08612588793039322, 0.018193557858467102, 0.004940976854413748, -0.017959048971533775, 0.0268211979418993, 0.00014783938240725547, -0.022662177681922913, -0.003148699412122369, -0.00380976521410048, 0.026508798822760582, 0.010611794888973236, -0.04290800914168358, 0.036684177815914154, -0.010026700794696808, -0.05886014550924301, -0.03616664558649063, -0.022970404475927353, 0.05701290816068649, -0.0014293332351371646, 0.0318179652094841, -0.038542136549949646, 0.045987971127033234, 0.05105651542544365, 0.018053235486149788, 0.0812700167298317, 0.027399659156799316, 0.00037700170651078224, 0.04895015433430672, 0.045387379825115204, -0.05718943849205971, -9.69654502114281e-05, 0.05230672284960747, -0.05405472218990326, -0.013626529835164547, -0.06550433486700058, 0.039176106452941895, -0.022257264703512192, 0.0021456049289554358, 0.01146668754518032, -0.011530974879860878, 0.010011616162955761, -0.004683586768805981, 0.052032530307769775, -0.018489282578229904, 0.02799900434911251, -0.015328798443078995, -0.03505133464932442, -0.014174236916005611, -0.00539533793926239, -0.016327043995261192, 0.016984708607196808, 0.014212390407919884, 0.005586463492363691, -0.055240631103515625, -0.0014511507470160723, -0.013183857314288616, -0.010001656599342823, -0.07022880762815475, 0.05361777916550636, 0.04947242513298988, 0.028517816215753555, 0.027409086003899574, -0.029738113284111023, 0.03672780841588974, 0.04837393760681152, 0.004880966618657112, -0.02175411395728588, 2.371977704291484e-34, -0.024814611300826073, -0.007390934508293867, -0.03684777393937111, -0.02016514725983143, -0.03409253805875778, 0.036305222660303116, -0.02646467089653015, 0.019888801500201225, 0.014114162884652615, 0.02617739513516426, -0.03751411288976669]

['Mikhail Belkin', 'Kaushik Sinha']

0907.1054v2

In this paper we present a method for learning the parameters of a mixture of $k$ identical spherical Gaussians in $n$-dimensional space with an arbitrarily small separation between the components. Our algorithm is polynomial in all parameters other than $k$. The algorithm is based on an appropriate grid search over the space of parameters. The theoretical analysis of the algorithm hinges on a reduction of the problem to 1 dimension and showing that two 1-dimensional mixtures whose densities are close in the $L^2$ norm must have similar means and mixing coefficients. To produce such a lower bound for the $L^2$ norm in terms of the distances between the corresponding means, we analyze the behavior of the Fourier transform of a mixture of Gaussians in 1 dimension around the origin, which turns out to be closely related to the properties of the Vandermonde matrix obtained from the component means. Analysis of this matrix together with basic function approximation results allows us to provide a lower bound for the norm of the mixture in the Fourier domain. In recent years much research has been aimed at understanding the computational aspects of learning parameters of Gaussians mixture distributions in high dimension. To the best of our knowledge all existing work on learning parameters of Gaussian mixtures assumes minimum separation between components of the mixture which is an increasing function of either the dimension of the space $n$ or the number of components $k$. In our paper we prove the first result showing that parameters of a $n$-dimensional Gaussian mixture model with arbitrarily small component separation can be learned in time polynomial in $n$.

Learning Gaussian Mixtures with Arbitrary Separation

http://arxiv.org/pdf/0907.1054v2

Title Learning Gaussian Mixtures Arbitrary Separation Summary paper present method learning parameter mixture k identical spherical Gaussians ndimensional space arbitrarily small separation component algorithm polynomial parameter k algorithm based appropriate grid search space parameter theoretical analysis algorithm hinge reduction problem 1 dimension showing two 1dimensional mixture whose density close L2 norm must similar mean mixing coefficient produce lower bound L2 norm term distance corresponding mean analyze behavior Fourier transform mixture Gaussians 1 dimension around origin turn closely related property Vandermonde matrix obtained component mean Analysis matrix together basic function approximation result allows u provide lower bound norm mixture Fourier domain recent year much research aimed understanding computational aspect learning parameter Gaussians mixture distribution high dimension best knowledge existing work learning parameter Gaussian mixture assumes minimum separation component mixture increasing function either dimension space n number component k paper prove first result showing parameter ndimensional Gaussian mixture model arbitrarily small component separation learned time polynomial n Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.009492437355220318, 0.002892538206651807, -0.013830075040459633, 0.05537648871541023, 0.007328925654292107, -0.004724267870187759, 0.030971813946962357, 0.014210057444870472, -0.026026485487818718, 0.028949648141860962, 0.013553285971283913, -0.0219118595123291, 0.017657479271292686, 0.015026496723294258, -0.005476448684930801, -0.07949398458003998, -0.052053336054086685, -0.011659682728350163, -0.056851256638765335, -0.026618190109729767, 0.009381021372973919, -0.025932637974619865, -0.0198485367000103, -0.02251683548092842, -0.04180173575878143, 0.018653692677617073, 0.0025469500105828047, -0.0640837773680687, 0.010893026366829872, 0.022909339517354965, 0.04393720254302025, -0.005658573005348444, 0.013286448083817959, 0.001209654496051371, 1.9577989860408707e-06, -0.015854530036449432, 0.015157991088926792, -0.01168209407478571, 0.04586265981197357, -0.02246754989027977, 0.025974556803703308, 0.03615446016192436, -0.023792529478669167, -0.03026629239320755, -0.028967399150133133, -0.03451238200068474, -0.006572276819497347, 0.08450658619403839, 0.031216448172926903, -0.007781888358294964, -0.03705960139632225, -0.028795316815376282, -0.0006514866836369038, -0.0018698087660595775, 0.08365867286920547, -0.0088882427662611, 0.012442483566701412, 0.006686710752546787, -0.0076545425690710545, 0.014065745286643505, -0.028752893209457397, 0.05765306577086449, 0.02289402484893799, 0.035491228103637695, 0.04870076850056648, 0.08208948373794556, 0.01605667546391487, 0.0043515837751328945, -0.05387166142463684, 0.036668337881565094, -0.05186385661363602, -0.00019614350458141416, 0.048531193286180496, -0.0036581445019692183, -0.01887582615017891, 0.03284143656492233, -0.01132826879620552, 0.009854506701231003, -0.06515095382928848, 0.006088361609727144, -0.06445063650608063, 0.03304646536707878, -0.02650734782218933, -0.01561038102954626, -0.03043939359486103, 0.0633886381983757, 0.033462006598711014, 0.007252307143062353, -0.0181308314204216, -0.04100340977311134, 0.011603765189647675, 0.026018792763352394, -0.01720341667532921, -0.018816107884049416, -0.019313054159283638, -0.042995523661375046, 0.010139566846191883, -0.019363999366760254, -0.007294710725545883, -0.0024544564075767994, -0.04153261333703995, 0.017558977007865906, 0.012026166543364525, 0.02407245710492134, 0.018625782802700996, -0.014291016384959221, -0.05735108256340027, -0.03382701426744461, 0.0005548849585466087, -0.03092876821756363, 0.003179984400048852, 0.017190607264637947, 0.02749691717326641, 0.0525159016251564, -0.041100114583969116, -0.027157597243785858, -0.042016785591840744, 0.030694102868437767, 0.013763157650828362, 0.020916683599352837, 0.007935678586363792, 0.035811278969049454, 0.027544451877474785, -0.0049095735885202885, 0.007953573949635029, -0.04503058269619942, -0.044561125338077545, 0.03171507269144058, -0.01080033928155899, 0.01621825248003006, 0.03071119263768196, 0.04098515212535858, 0.016066523268818855, 0.012868889607489109, 0.007191232405602932, 0.05942758172750473, -0.01708870567381382, -0.004171586595475674, -0.00624129781499505, 0.06613562256097794, -0.0056526027619838715, -0.012076451443135738, -0.002672705100849271, -0.09120597690343857, 0.05525142699480057, -0.006861972622573376, -0.02781571075320244, 0.0010806677164509892, 0.0018205230589956045, -0.04606076329946518, 0.00025156044284813106, 0.06375640630722046, -0.007743434980511665, -0.02357865869998932, 0.1683124154806137, -0.0009165625087916851, -0.04645702987909317, 0.04140736907720566, -0.040940962731838226, 0.00037118871114216745, -0.010893155820667744, -0.03497150167822838, 0.06406202167272568, -0.026837114244699478, -0.045739542692899704, -0.03462892770767212, -0.027468577027320862, -0.03721864894032478, -0.014224172569811344, -0.002374150324612856, -0.0075616417452692986, 0.02906394563615322, -0.042474064975976944, -0.036543820053339005, 0.018107054755091667, 0.041496675461530685, -0.007165614981204271, -0.024420203641057014, -0.009642798453569412, 0.020795969292521477, -0.023223239928483963, 0.03220352530479431, 0.056299254298210144, 0.01845673844218254, -0.08092465996742249, -0.04190264642238617, 0.045617830008268356, 0.05055167153477669, -0.035442598164081573, -0.04108012095093727, 0.04376600682735443, -0.055160537362098694, -0.025402475148439407, -0.050388436764478683, 0.05919310450553894, -0.0465860553085804, 0.025406548753380775, -0.03403608128428459, 0.021992385387420654, -0.0403580367565155, -0.005427144467830658, 0.008288025856018066, 0.06298566609621048, -0.05319301038980484, -0.03251802921295166, -0.07401899993419647, -0.036236610263586044, -0.038719937205314636, -0.040346659719944, -0.030354801565408707, -0.052969176322221756, 0.02130734547972679, 0.06759016960859299, -0.029112286865711212, -0.00991648156195879, 0.0355217382311821, 0.0390436165034771, -0.03986465930938721, -0.0014841139782220125, -0.012217342853546143, 0.04204914718866348, -0.028002265840768814, 0.06960888206958771, 0.00900840014219284, 0.004741152748465538, 0.008954777382314205, 0.02185172587633133, 0.04179250821471214, 0.04126641899347305, -0.020936420187354088, 0.028482379391789436, -0.03927456587553024, 0.01772778108716011, -0.035717498511075974, -0.06326542794704437, 0.0031549863051623106, 0.006118775345385075, -0.026111382991075516, -0.003191645722836256, -0.010109429247677326, 0.04194287955760956, -0.08573320508003235, -0.02205631509423256, -0.05019182711839676, 0.03994012624025345, 0.03264794871211052, -0.01740742288529873, -0.04180579632520676, 0.027932405471801758, -0.002819850342348218, 0.02801954559981823, -0.004391810391098261, 0.0461772158741951, -0.005708085838705301, 0.03152507543563843, -0.017361102625727654, -0.02947916090488434, 0.03609146922826767, 0.0131227420642972, 0.0332060270011425, -0.017967958003282547, -0.05408027023077011, 0.06227446720004082, -0.010482621379196644, -0.005128069780766964, -0.00020367024990264326, -0.05656054988503456, 0.04064009338617325, 0.027089953422546387, -0.014578421600162983, -0.020029280334711075, 0.006057417951524258, -0.004047709982842207, -0.0011104460572823882, 0.03737326338887215, -0.0023868621792644262, 0.06825493276119232, 0.015141867101192474, -0.11629427969455719, 0.018686799332499504, 0.0024566510692238808, -0.020443951711058617, -0.02183355577290058, -0.005088789388537407, 0.02028571628034115, 0.007189166732132435, -0.023456603288650513, -0.006656075362116098, 0.008694471791386604, -0.014330564998090267, -0.04705379903316498, 0.03904777020215988, -0.005107310600578785, -0.022656699642539024, -0.0027223527431488037, -0.05092921108007431, 0.0850239098072052, 0.07038106769323349, 0.06480573862791061, -0.010451111942529678, -0.009998015128076077, 0.03315066546201706, -0.007856410928070545, 0.028347674757242203, -0.03234737366437912, 0.0422479622066021, 0.024634964764118195, 0.011229157447814941, 0.03362264111638069, 0.014501187019050121, 0.029399115592241287, -0.023053236305713654, -0.038139376789331436, 0.028592534363269806, -0.008331289514899254, 0.018470974639058113, -0.046699415892362595, 0.013975085690617561, -0.0027903306763619184, -0.02526659332215786, -0.0015136332949623466, -0.030727095901966095, 0.016412150114774704, -0.002693676156923175, 0.022792980074882507, -0.07694773375988007, -0.07986032217741013, 0.014840572141110897, -0.08245091885328293, -0.042360711842775345, 0.01045595295727253, -0.09425153583288193, 0.003987610340118408, -0.005316033493727446, 0.04258227348327637, 0.022752251476049423, -0.02298586815595627, -0.004922731779515743, -0.006444943603128195, -0.033838901668787, 0.02764982357621193, 0.023245662450790405, -0.026307011023163795, 0.015466674230992794, 0.03818054124712944, -0.012851173058152199, 0.0019936785101890564, -0.04021240025758743, -0.02280423603951931, -0.015074520371854305, 0.01063300110399723, 0.05636118724942207, -0.0017905515851452947, -0.008210262283682823, 0.001770878559909761, 0.03515882045030594, -0.006324176210910082, 0.00015029957285150886, -0.061157338321208954, -0.01360774040222168, 0.02314731478691101, -0.012965836562216282, 0.04075051099061966, -0.03302546218037605, -0.030611321330070496, -0.012835009023547173, -0.0007448290125466883, 0.03247375041246414, -0.04800407215952873, 0.021922994405031204, 0.06543631106615067, 0.04660303518176079, 0.042703818529844284, 0.04054563492536545, -0.0037647562567144632, -0.0756133571267128, -0.03381709009408951, 0.00853934045881033, -0.03515633940696716, 0.019687432795763016, -0.01985001750290394, 0.057516034692525864, 0.041474662721157074, -0.011679229326546192, -0.011111604981124401, 0.047686971724033356, 0.005662024952471256, 0.02123178541660309, -0.03407036513090134, -0.0025556329637765884, 0.011373008601367474, -0.08446438610553741, -0.09461508691310883, -0.05715266242623329, -0.002801849041134119, 0.004366799723356962, -0.018389204517006874, -0.015444564633071423, 0.025324854999780655, -0.03838310018181801, 0.036708999425172806, -0.022237680852413177, -0.0442957878112793, -0.028100186958909035, -0.10046011209487915, 0.0077001918107271194, -0.028672002255916595, 0.01088122557848692, -0.01585782691836357, -0.03828822076320648, -0.051270902156829834, -0.08225131779909134, -0.019149387255311012, -0.00877554714679718, 0.05277475714683533, 0.03556247055530548, 0.02448386140167713, 0.001522117294371128, 0.07820653915405273, -0.0062776231206953526, -0.007732648402452469, 0.04977569729089737, 0.075320303440094, -0.025599028915166855, -0.014738102443516254, -0.020365562289953232, -0.00601599644869566, 0.056123267859220505, 0.003231261856853962, 0.007808089721947908, -0.04074781760573387, 0.028968920931220055, -0.022784247994422913, 0.04460421949625015, 0.09048880636692047, 0.0996554046869278, 0.002846084302291274, 0.053656917065382004, -0.042087238281965256, -0.07695131748914719, 0.05233036354184151, -0.0059148273430764675, 0.059770017862319946, 0.02790047973394394, 0.032912030816078186, -0.042980339378118515, -0.03121241182088852, -0.0076936776749789715, -0.03168512508273125, 0.07184938341379166, -0.03352634981274605, -0.01166048925369978, 0.03299989551305771, -0.004600188694894314, -0.019397694617509842, -0.012124069035053253, -0.056936316192150116, -0.050806526094675064, -0.06354450434446335, -0.013238156214356422, 0.0493059903383255, -0.0027657346799969673, 0.0032451592851430178, -0.03023279272019863, -0.04214300960302353, 0.0267880130559206, -0.02306586690247059, 0.03861422836780548, 0.05290194973349571, 0.03714437037706375, -0.007093769032508135, 0.003692125203087926, -0.005689140874892473, 0.01653536781668663, 0.06617709249258041, -0.011583086103200912, -0.07042019814252853, -0.044874098151922226, -0.005608379375189543, -0.005508805625140667, -0.012637126259505749, 0.0543636828660965, 0.02680067904293537, 0.029831331223249435, -0.06660957634449005, 0.04049564152956009, -0.01798604242503643, 0.022182688117027283, 0.015499521046876907, -0.017791571095585823, 0.04575642943382263, 0.04025837406516075, -0.043383605778217316, 0.0007114062318578362, 0.06299569457769394, 0.01645667478442192, 0.01614905521273613, 0.007391818333417177, 0.06893683969974518, -0.06207755208015442, -0.017030740156769753, 0.007324713282287121, 0.011602031998336315, -0.04172428697347641, 0.0569579042494297, -0.00122151430696249, 0.015635622665286064, 0.03990018740296364, 0.012434093281626701, -0.0041065216064453125, -0.048858195543289185, -0.017990419641137123, -0.01659686118364334, -0.02871064282953739, -0.008652637712657452, 0.06256081163883209, 0.007999860681593418, -0.03036220744252205, 0.009653981775045395, -0.018417401239275932, 0.003926408942788839, -0.035061854869127274, 0.03378267586231232, -0.006108507979661226, 0.029574472457170486, 0.023995259776711464, 0.008345849812030792, -0.04833342134952545, 0.02798873744904995, 0.06345734745264053, -0.0016190516762435436, -0.03503277897834778, -0.030331119894981384, 0.047928377985954285, -0.06734182685613632, 0.10625138133764267, 0.007434219121932983, -0.011359366588294506, 0.007106769364327192, 0.0658542662858963, 0.021129528060555458, 0.02075175568461418, 0.03232353925704956, -0.051977597177028656, 0.012375070713460445, 0.021119581535458565, 0.008891536854207516, 0.06262195855379105, -0.03568146750330925, 0.009647919796407223, -0.005185326561331749, -0.03132881596684456, 0.027255801483988762, 0.015783041715621948, -0.00898758228868246, -5.5815112965911715e-33, 0.00900835171341896, 0.004609156399965286, -0.058425214141607285, -0.03886929899454117, 0.015844406560063362, 0.02989795058965683, 0.005789598450064659, 0.003895876696333289, 0.050120774656534195, -0.021523267030715942, -0.0049951146356761456, 0.027696676552295685, 0.004301480017602444, -0.00142369803506881, 0.035629753023386, 0.03721446916460991, 0.01246182806789875, 0.027259599417448044, 0.017638180404901505, 0.020189857110381126, 0.03544357791543007, 0.03198074921965599, 0.004701615311205387, -0.03282247111201286, -0.0943170115351677, 0.023845892399549484, -0.0261995792388916, -0.009833524003624916, -0.043684616684913635, 0.011020176112651825, -0.0218744408339262, 0.02221161127090454, -0.016905827447772026, 0.019998177886009216, -0.009796706959605217, -0.018667755648493767, 0.022267866879701614, -0.03884816914796829, -0.03686388581991196, -0.041377149522304535, -0.035143859684467316, -0.009039847180247307, 0.06974807381629944, -0.02667817659676075, -0.006533817853778601, -0.007265467196702957, 0.06296414881944656, -0.00275778747163713, -0.03133401647210121, -0.032241784036159515, 0.020519481971859932, 0.037283096462488174, -0.024551738053560257, 0.012401272542774677, 0.045608073472976685, -0.04626624286174774, -0.015140185132622719, 0.0066527025774121284, 0.0004190737381577492, 0.03611787408590317, 0.013647610321640968, 0.07906874269247055, -0.019023574888706207, 0.03736849129199982, 0.060921624302864075, 0.04985640570521355, 0.0503171905875206, -0.020452605560421944, -0.054249852895736694, -0.07820751518011093, 0.015601090155541897, 0.020746709778904915, -0.024282163009047508, 0.008415444754064083, 0.041443899273872375, -0.08743978291749954, -0.013860698789358139, 0.016641026362776756, -0.046333931386470795, -0.01700224168598652, -0.009295130148530006, -0.006050960626453161, -0.01943039707839489, -0.02055523544549942, 0.008783983998000622, -0.0042021069675683975, 0.006363896653056145, 0.009213698096573353, -0.009515862911939621, 0.0009063732577487826, -0.03445100784301758, -0.07209412753582001, -0.02117205411195755, -0.006751082371920347, 0.04811827093362808, -0.019142478704452515, -0.0021965326741337776, -0.010654019191861153, 0.06035216152667999, -0.011950679123401642, -0.038870345801115036, -0.05909166857600212, 0.0105740400031209, -0.03452468290925026, 0.006395643576979637, 0.037220463156700134, 0.0034875564742833376, 0.03290568292140961, 0.0037505871150642633, -0.013913125731050968, 0.02531570754945278, -0.04176470264792442, 0.004300398752093315, 0.08265526592731476, 0.028410909697413445, -0.02394554577767849, -0.013017733581364155, 0.04150877147912979, 0.048346154391765594, -0.004238999914377928, -0.024863898754119873, 0.025206493213772774, -0.004214589484035969, 0.018846428021788597, -0.026806654408574104, 0.025574302300810814, -0.04297378659248352, -0.08022770285606384, 0.024262316524982452, -0.0330558717250824, -0.019489388912916183, -0.010874543339014053, 2.586672280813218e-07, -0.020236821845173836, 0.05844876170158386, -0.054090749472379684, -0.06981714069843292, 0.01356576569378376, -0.023066531866788864, 0.004519438836723566, -0.018787963315844536, -0.05500762164592743, -0.030837852507829666, 0.0473615862429142, 0.00882371049374342, 0.037593334913253784, 0.011092145927250385, -0.036209940910339355, -0.007864574901759624, -0.01623903401196003, 0.02611713483929634, -0.036542851477861404, 0.03771209716796875, 0.025519097223877907, 0.07636332511901855, 0.03574403375387192, -0.0037410191725939512, 0.04675675556063652, 0.04675218090415001, 0.010700304061174393, -0.01487627811729908, 0.05001409351825714, 0.009427673183381557, 0.033880315721035004, -0.032114069908857346, 0.03301694989204407, 0.039115991443395615, -0.0059445081278681755, 0.011944063939154148, 0.029083196073770523, 0.017137710005044937, -0.04188629239797592, -0.0061335437931120396, 0.043279170989990234, 0.045397814363241196, 0.002241038251668215, -0.036001164466142654, 0.022296341136097908, 0.02560674026608467, -0.010581948794424534, -0.03603748604655266, 0.011082732118666172, 0.04728394374251366, 0.04682376608252525, 0.01348758302628994, -0.0203643087297678, -0.05312144011259079, -0.03686906769871712, -0.0032569526229053736, 0.05949545279145241, 0.008205050602555275, 0.016307277604937553, 0.03747227042913437, -0.023890456184744835, -0.003957647364586592, 0.03320961818099022, -0.05611724779009819, 0.05362825468182564, 0.08152548968791962, 0.001423523062840104, 1.9763049282722596e-34, -0.0003562223573680967, 0.004731362219899893, 0.0014824530808255076, 0.010720528662204742, -0.04895809665322304, -0.021712852641940117, -0.09529079496860504, 0.007208310998976231, -0.03170967102050781, 0.0104365861043334, 0.0011453432962298393]

['Olivier Bournez', 'Johanne Cohen']

0907.1916v1

We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak convergence for probabilistic processes) towards their mean-field limit, i.e an ordinary differential equation (ODE) in the general case. We focus then on a class of stochastic dynamics where this ODE turns out to be related to multipopulation replicator dynamics. Using facts known about convergence of this ODE, we discuss the convergence of the initial stochastic dynamics: For general games, there might be non-convergence, but when convergence of the ODE holds, considered stochastic algorithms converge towards Nash equilibria. For games admitting Lyapunov functions, that we call Lyapunov games, the stochastic dynamics converge. We prove that any ordinal potential game, and hence any potential game is a Lyapunov game, with a multiaffine Lyapunov function. For Lyapunov games with a multiaffine Lyapunov function, we prove that this Lyapunov function is a super-martingale over the stochastic dynamics. This leads a way to provide bounds on their time of convergence by martingale arguments. This applies in particular for many classes of games that have been considered in literature, including several load balancing game scenarios and congestion games.

Learning Equilibria in Games by Stochastic Distributed Algorithms

http://arxiv.org/pdf/0907.1916v1

Title Learning Equilibria Games Stochastic Distributed Algorithms Summary consider class fully stochastic fully distributed algorithm prove learn equilibrium game Indeed consider family stochastic distributed dynamic prove converge weakly sense weak convergence probabilistic process towards meanfield limit ie ordinary differential equation ODE general case focus class stochastic dynamic ODE turn related multipopulation replicator dynamic Using fact known convergence ODE discus convergence initial stochastic dynamic general game might nonconvergence convergence ODE hold considered stochastic algorithm converge towards Nash equilibrium game admitting Lyapunov function call Lyapunov game stochastic dynamic converge prove ordinal potential game hence potential game Lyapunov game multiaffine Lyapunov function Lyapunov game multiaffine Lyapunov function prove Lyapunov function supermartingale stochastic dynamic lead way provide bound time convergence martingale argument applies particular many class game considered literature including several load balancing game scenario congestion game Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0017748619429767132, 0.033690471202135086, -0.04115977883338928, -0.015719696879386902, -0.04115026071667671, -0.035663992166519165, -0.009805106557905674, -0.008123403415083885, -0.03405008465051651, 0.046093255281448364, 0.013781813904643059, -0.019432177767157555, -0.020313270390033722, 0.05026637390255928, 0.007319759111851454, -0.02151102013885975, 0.01734817586839199, 0.011742228642106056, -0.04916930943727493, -0.029778340831398964, 0.01395300030708313, -0.07787210494279861, -0.021000536158680916, -0.0019763410091400146, 0.0468374565243721, -0.04208512604236603, -0.016775693744421005, -0.005595495458692312, 0.02276751771569252, -0.0349409244954586, 0.003450819756835699, -0.028874089941382408, 0.01963391900062561, 0.021132251247763634, 1.695990818006976e-06, 0.004700229968875647, -0.0261207427829504, -0.042608607560396194, 0.04058258980512619, -0.06106185540556908, -0.005914770998060703, -0.028598403558135033, 0.00155931047629565, 0.019530370831489563, 0.011141961440443993, 0.015205077826976776, 0.01855696178972721, -0.004067030269652605, 0.037255797535181046, 0.014874067157506943, 0.009729497134685516, -0.02591252326965332, 0.013923360034823418, -0.02445305325090885, -0.01382693275809288, -0.031353093683719635, 0.023794302716851234, 0.07285431772470474, 0.01959163136780262, -0.09409107267856598, -0.01757242903113365, -0.0010856406297534704, -0.015275373123586178, -0.022759918123483658, -0.002761687384918332, 0.033397603780031204, 0.026140417903661728, 0.025586506351828575, -0.03680306673049927, 0.03531765937805176, -0.013615583069622517, -0.016027305275201797, 0.029971783980727196, 0.005180268548429012, -0.0041472758166491985, 0.04698861390352249, -0.03372907266020775, -0.012788007967174053, -0.007418565917760134, 0.025448264554142952, 0.01421708706766367, 0.047284260392189026, 0.03817707300186157, -0.014820669777691364, 0.05724724382162094, 0.05052643641829491, -0.018462305888533592, -0.014118405990302563, -0.01081804372370243, 0.03106054849922657, 0.006748112849891186, -0.014945568516850471, 0.027828700840473175, 0.04598187282681465, -0.015909619629383087, -0.015385142527520657, -0.001415841979905963, -0.05452814698219299, -0.017946496605873108, -0.03451516851782799, 0.031270015984773636, -0.07025214284658432, 0.09010954201221466, 0.05182443931698799, 0.01850033365190029, -0.02813355065882206, -0.04484998807311058, 0.0001683510490693152, 0.034679535776376724, 0.06753924489021301, -0.0482797734439373, 0.010586459189653397, -0.015895666554570198, 0.04802431911230087, 0.06120406091213226, 0.03969190642237663, -0.038708608597517014, 0.07869590818881989, -0.06859926879405975, 0.03683452308177948, -0.017650587484240532, -0.00116136041469872, 0.029769521206617355, 0.02082860842347145, -0.015443411655724049, 0.008009322918951511, -0.052404966205358505, 0.03742543235421181, -0.014233565889298916, -0.010556870140135288, 0.008841535076498985, -0.023727387189865112, -0.010284106247127056, 0.012631882913410664, -0.026453865692019463, 0.10740122199058533, -0.004381455946713686, 0.07263914495706558, -0.07141193002462387, 0.010505572892725468, 0.0397508405148983, -0.01881338655948639, -0.06345290690660477, -0.04347364604473114, -0.017822010442614555, -0.041331905871629715, -0.02015938237309456, 0.01034561824053526, -0.04010554403066635, -0.02831382118165493, -0.06675638258457184, 0.04742749035358429, -0.009740357287228107, 0.019861280918121338, 0.04695189371705055, -0.04598873481154442, -0.00699698505923152, 0.07540389150381088, 0.0331270731985569, -0.01685684360563755, 0.05235908553004265, -0.008085904642939568, 0.044591303914785385, 0.006536287255585194, 0.033034633845090866, 0.016641762107610703, 0.07326013594865799, -0.048251498490571976, -0.013582751154899597, 0.054945703595876694, 0.014879124239087105, -0.01672520488500595, -0.044066786766052246, -0.04638209566473961, 0.04180213436484337, -0.0032350034452974796, 0.01315194834023714, -0.0074596405029296875, -0.023448755964636803, 0.021249523386359215, -0.05321561172604561, 0.0753469467163086, -0.013810543343424797, 0.03728323429822922, 0.025259602814912796, -0.01600932888686657, -0.018606312572956085, 0.04193408787250519, -0.06814111024141312, -0.00988894235342741, 0.02338423579931259, -0.034952688962221146, -0.01629122532904148, 0.04126996919512749, 0.023421645164489746, -0.016672911122441292, -0.052994634956121445, -0.028119642287492752, -0.01877797208726406, 0.07802843302488327, 0.030311981216073036, -0.08364886790513992, 0.021002618595957756, -0.03548441082239151, 0.03887562453746796, -0.05466828495264053, -0.025027409195899963, -0.04814920946955681, -0.03352717310190201, -0.013209830038249493, 0.027862027287483215, 0.028606366366147995, -0.012732449918985367, 0.0123570766299963, -0.021567782387137413, 0.04045868292450905, -0.024623945355415344, 0.016000304371118546, -0.06808614730834961, 0.013631351292133331, -0.020825132727622986, 0.04253640025854111, -0.031712159514427185, -0.01846904680132866, -0.010122006759047508, -0.03888772428035736, 0.02049829252064228, 0.02770276926457882, 0.08932192623615265, -0.05599932000041008, -0.050229452550411224, -0.008518153801560402, -0.0028928134124726057, 0.036781370639801025, -0.009395207278430462, 0.05138860270380974, 0.022071747109293938, -0.009170196950435638, 0.004245624877512455, 0.01120593398809433, 0.010357119143009186, -0.007301246747374535, -0.008166752755641937, -0.010291445069015026, 0.061380334198474884, -0.008684632368385792, 0.006452674046158791, 0.023521818220615387, -0.009908136911690235, -0.00586726376786828, 0.08272232860326767, 0.014914294704794884, 0.01115310750901699, 0.02212640456855297, -0.019483286887407303, -0.05989180505275726, -0.01248940359801054, 0.013695323839783669, -0.026832623407244682, -0.000587849470321089, 0.008756697177886963, -0.04271410033106804, -0.03944607451558113, 0.01457333192229271, -0.005878306459635496, 0.01435281801968813, 0.021105658262968063, 0.0157688707113266, -0.0018899365095421672, -0.027444012463092804, 0.048340823501348495, -0.008949064649641514, -0.03736687824130058, -0.005653019528836012, -0.00013168907025828958, 0.009457017295062542, 0.06771576404571533, 0.02666977234184742, 0.009441227652132511, 0.01420604344457388, 0.032590530812740326, -0.029096011072397232, 0.021901674568653107, -0.05867724493145943, -0.008742916397750378, 0.05525839328765869, 0.033212874084711075, 0.031827956438064575, -0.014897983521223068, 0.014110582880675793, -0.021614110097289085, 0.03870083764195442, 0.001862035132944584, -0.025615932419896126, 0.004351659677922726, 0.0085356580093503, -0.010172111913561821, 0.05165093392133713, 0.007037888281047344, 0.029691601172089577, -0.0009163865470327437, -0.004806401673704386, -0.011983894743025303, 0.037774212658405304, -0.024252543225884438, -0.04820314794778824, -0.04671706631779671, 0.011439569294452667, 0.062301404774188995, 0.09691514074802399, -0.019016083329916, -0.05362948775291443, 0.024528279900550842, -0.05398905277252197, 0.018725231289863586, -0.044528599828481674, -0.06694192439317703, 0.017554515972733498, -0.0058300369419157505, -0.06845703721046448, 0.007138995919376612, 0.018351364880800247, 0.12394575774669647, 0.03578947111964226, 0.021057207137346268, 0.012755170464515686, -0.08462215214967728, -0.01731797493994236, -0.04472767189145088, 0.022325068712234497, 0.027107203379273415, -0.07733514159917831, -0.0015244928654283285, 0.008708902634680271, -0.048058222979307175, 0.07247813791036606, -0.017737802118062973, -0.033576421439647675, 0.026669245213270187, 0.007852759212255478, -0.012274065986275673, -0.05120592936873436, 0.01661490648984909, 0.0407685749232769, -0.01512889564037323, -0.006156388204544783, -0.009857195429503918, -0.009817153215408325, -0.0009773420169949532, 0.00687392707914114, 0.009431722573935986, -0.01293989084661007, -0.01806238852441311, -0.03074360452592373, 0.02880934253334999, 0.03545127436518669, 0.014585159718990326, -0.001830090070143342, -0.016802866011857986, -0.0631767138838768, 0.02254168689250946, -0.005627126432955265, 0.03691298887133598, -0.02632167376577854, 0.014925206080079079, 0.024819761514663696, 0.01776053197681904, -0.0612793043255806, -0.0028596611227840185, 0.01966516114771366, -0.025957562029361725, -0.008365078829228878, -0.013506907969713211, 0.010851483792066574, -0.04819942265748978, -0.02810538001358509, -0.004643513821065426, -0.03356208652257919, 0.0647730678319931, -0.01990417018532753, 0.018252365291118622, -0.05619058012962341, -0.029936686158180237, -0.054755646735429764, -0.003010960528627038, -0.03484145551919937, -0.05169897526502609, 0.009801952168345451, -0.024939319118857384, -0.02796490676701069, -0.014362954534590244, -0.07958990335464478, 0.00837024673819542, -0.04730865731835365, -0.016016824170947075, -0.07855711877346039, -0.05047910660505295, -0.008655263110995293, 0.02321661449968815, 0.0071456581354141235, 0.012343648821115494, 0.009094670414924622, 0.0408753976225853, -0.0606207400560379, -0.05174703896045685, 0.0407223105430603, 0.009148516692221165, 0.015565977431833744, -0.06129049137234688, -0.00448413984850049, 0.03622008487582207, -0.003949443809688091, -0.04903764650225639, 0.03250033035874367, 0.00572964595630765, -0.003689761972054839, -0.0033085227478295565, 0.0014023935655131936, -0.01853974349796772, 0.05522195249795914, 0.03967322036623955, 0.05111899599432945, 0.01159962359815836, 0.01614646427333355, -0.061499275267124176, -0.02715669758617878, 0.02762916311621666, 0.09647832065820694, -0.00783535186201334, -0.03887292742729187, -0.01713123731315136, -0.03830115497112274, -0.002424728125333786, 0.02350061759352684, -0.034818753600120544, 0.004097932018339634, -0.009465361945331097, 0.006178474985063076, 0.023672841489315033, -0.030257858335971832, -0.002315426478162408, -0.057488467544317245, 0.028386332094669342, -0.0011664973571896553, 0.04371827095746994, 0.07110801339149475, 0.0455060675740242, -0.008578888140618801, -0.07704082131385803, 0.03698556125164032, 0.03161541372537613, -0.024607723578810692, 0.005058668088167906, 0.00556093780323863, -0.006743564736098051, -0.04783492162823677, -0.023200061172246933, -0.0433930940926075, -0.06639862060546875, 0.02323133870959282, 0.024524817243218422, 0.007609757594764233, -0.003870543325319886, 0.022006774321198463, -0.001070103608071804, -0.0007403111085295677, 0.015620765276253223, 0.04639590159058571, -0.003770074574276805, 0.03206081688404083, -0.03350832313299179, 0.01677027717232704, 0.04386300966143608, -0.0028701014816761017, 0.028357114642858505, 0.03415755182504654, -0.04903564602136612, -0.007753310259431601, 0.032615963369607925, -0.06995487213134766, 0.012703276239335537, 0.024342138320207596, 0.0037903091870248318, -0.051357902586460114, 0.023911595344543457, 0.043875209987163544, 0.0450916588306427, 0.012796739116311073, -0.02702482044696808, -0.010528103448450565, -0.007323999423533678, 0.019699489697813988, 0.03200541436672211, 0.030750127509236336, 0.11611127108335495, -0.049834243953228, 0.06775127351284027, -0.0008636900456622243, 0.024822667241096497, -0.011873643845319748, -6.316839426290244e-05, 0.01214111689478159, 0.03979117423295975, 0.010155098512768745, 0.050796717405319214, 0.08120333403348923, 0.04607085883617401, -0.002081278245896101, 0.03895983844995499, 0.002160488860681653, 0.011251217685639858, -0.018436545506119728, -0.054873380810022354, -0.015469297766685486, -0.008808334358036518, 0.05380336940288544, 0.10779131203889847, 0.0048601701855659485, -0.03164193406701088, -0.03109634481370449, 0.018037710338830948, 0.03164646402001381, 0.012930421158671379, -0.13385659456253052, 0.011356018483638763, 0.008629145100712776, 0.03199354559183121, 0.002298063365742564, 0.04395300894975662, 0.029859699308872223, 0.023804951459169388, 0.031559720635414124, -0.02481894940137863, 0.0038772441912442446, 0.0006740621174685657, 0.029020529240369797, -0.01168601494282484, 0.012582140974700451, -0.0039046602323651314, 0.008812782354652882, -0.0025318057741969824, 0.017917444929480553, -0.033975109457969666, 0.08327616751194, 0.03896297886967659, 0.02136148512363434, 0.027306698262691498, -0.05446942150592804, -0.0222361758351326, 0.03227948024868965, -0.07048230618238449, 0.04306284338235855, -0.0010560430819168687, -0.02810448594391346, 0.03368755429983139, -5.3236838758115804e-33, 0.05853324010968208, -0.033512622117996216, 0.009236618876457214, -0.002027672715485096, -0.038184843957424164, -0.05312873050570488, -0.023328805342316628, -0.0059698657132685184, -0.059876229614019394, 0.01340669859200716, -0.02504907362163067, 0.013907737098634243, 0.04052896052598953, 0.04421951249241829, -0.0016020734328776598, -0.027597805485129356, -0.020464397966861725, -0.032327983528375626, -0.02937403880059719, 0.02644813060760498, 0.00395149877294898, -0.009344897232949734, 0.02376217022538185, 0.039257120341062546, -0.008851127699017525, 0.000644427549559623, -0.000181596667971462, 0.014706854708492756, -0.04628945142030716, -0.0021813863422721624, 0.012265951372683048, 0.031963009387254715, -0.019735774025321007, -0.031043516471982002, 0.044776733964681625, 0.005206745583564043, -0.007126539014279842, 0.01609044149518013, -0.06218523532152176, 0.0250950176268816, -0.04553631693124771, 0.01086894329637289, 0.039151400327682495, 0.020367590710520744, -0.023829448968172073, -0.011116263456642628, 0.049172211438417435, 0.04021121934056282, 0.0030393479391932487, -0.04286858066916466, 0.05612066015601158, 0.0033732240553945303, -0.03789323940873146, 0.06243962049484253, -0.009559760801494122, -0.023035533726215363, -0.0037375350948423147, -0.023169631138443947, -0.005251683294773102, 0.05008408799767494, -0.020438767969608307, 0.018422583118081093, 0.005454263184219599, 0.02326471358537674, 0.07173193246126175, 0.00909392163157463, -0.060793958604335785, 0.017310503870248795, -0.04672250896692276, -0.01884857751429081, -0.02969062514603138, -0.016917213797569275, -0.0027690157294273376, -0.01302176620811224, -9.589667752152309e-05, -0.05417425185441971, -0.04891512542963028, -0.00817709881812334, 0.04572571441531181, -0.001416096813045442, -0.0446881465613842, -0.026175646111369133, -0.044800251722335815, 0.010667860507965088, 0.01335104275494814, -0.012637656182050705, 0.05311984196305275, -0.007212131284177303, -0.03362201154232025, -0.0007843523053452373, 0.04372174292802811, -0.006932219490408897, -0.004335423465818167, -0.03647203743457794, -0.08053573220968246, 0.004837807267904282, 0.06994827836751938, 0.019673842936754227, 0.02234269119799137, -0.009518664330244064, -0.03014679253101349, -0.06933122128248215, -0.10584919899702072, -0.012553180567920208, -0.04553860425949097, 0.03587569296360016, -0.007802851963788271, -0.032514866441488266, 0.0003700331144500524, 0.035609662532806396, 0.030154334381222725, 0.04326773062348366, 0.04490882530808449, -0.018017729744315147, 0.0382530502974987, -0.058108627796173096, -0.01762930490076542, 0.004041142296046019, 0.02782106027007103, -0.039325784891843796, 0.046801693737506866, 0.05335410684347153, -0.05050089210271835, 0.030035603791475296, -0.021298039704561234, 0.02082872949540615, -0.08542082458734512, 0.039399612694978714, -0.0647517517209053, -0.02834627963602543, 0.004778954200446606, -0.048519328236579895, 2.4191990632971283e-07, -0.03423573449254036, 0.017379898577928543, 0.008372918702661991, 0.006889129523187876, -0.020772811025381088, 0.035082556307315826, -0.10241026431322098, 0.03338797762989998, -0.024719834327697754, 0.010499682277441025, 0.03252217918634415, 0.014450563117861748, 0.05252350494265556, -0.03396430239081383, -0.07686833292245865, -0.038156118243932724, -0.04559385031461716, 0.08904853463172913, 0.012104193679988384, -0.08062861114740372, -0.021059663966298103, 0.001903651631437242, 0.024540815502405167, 0.0029389155097305775, 0.0490805022418499, -0.04232170060276985, 0.0167158804833889, 0.011654827743768692, 0.044864244759082794, 0.0609515942633152, 0.03213803470134735, -0.011644315905869007, -0.020736439153552055, -0.02726045250892639, -0.03429176285862923, 0.009375576861202717, -0.04848413169384003, -0.006206450518220663, 0.03874783217906952, 0.012782929465174675, -0.03259187564253807, -0.011700965464115143, 0.015211284160614014, -0.009681226685643196, 0.043872009962797165, -0.013885208405554295, -0.018293991684913635, -0.00558620085939765, 0.008123929612338543, -0.03434617817401886, 0.09130610525608063, 0.017201881855726242, -0.050545431673526764, -0.017381535843014717, -0.0005318516050465405, -0.00039951398503035307, 0.02673984505236149, 0.004664386622607708, -0.005078027490526438, 0.05525282397866249, -0.0031277446541935205, -0.02470982074737549, 0.016562137752771378, 0.030405256897211075, 0.06470493227243423, 0.01269452553242445, -0.044581782072782516, 1.7432687981458807e-34, 0.06744208186864853, -0.038799211382865906, 0.035137660801410675, -0.016455305740237236, -0.02365664206445217, -0.04441612586379051, -0.0006509602535516024, -0.04497199133038521, 0.04244529455900192, 0.02363160066306591, -0.013609642162919044]

['Dilip Krishnaswamy', 'Shanyu Zhao']

0907.2222v1

This paper suggests the use of intelligent network-aware processing agents in wireless local area network drivers to generate metrics for bandwidth estimation based on real-time channel statistics to enable wireless multimedia application adaptation. Various configurations in the wireless digital home are studied and the experimental results with performance variations are presented.

Network-aware Adaptation with Real-Time Channel Statistics for Wireless LAN Multimedia Transmissions in the Digital Home

http://arxiv.org/pdf/0907.2222v1

Title Networkaware Adaptation RealTime Channel Statistics Wireless LAN Multimedia Transmissions Digital Home Summary paper suggests use intelligent networkaware processing agent wireless local area network driver generate metric bandwidth estimation based realtime channel statistic enable wireless multimedia application adaptation Various configuration wireless digital home studied experimental result performance variation presented Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.014558868482708931, -0.022290294989943504, -0.021463194862008095, -0.029481446370482445, -0.04680358245968819, 0.0014375123428180814, 0.009441381320357323, 0.016647551208734512, -0.11258663982152939, -0.06664770096540451, -0.018090946599841118, 0.014460238628089428, 0.014184718951582909, 0.011695180088281631, -0.011182496324181557, 0.0007789100054651499, -0.008118933066725731, -0.018671860918402672, 0.026910198852419853, 0.049895964562892914, 0.021706080064177513, -0.0035599300172179937, 0.03330019861459732, 0.031065698713064194, -0.03490672633051872, -0.018319718539714813, 0.001656996668316424, 0.02024349570274353, -0.005477378144860268, -0.008732895366847515, 0.0481567457318306, 0.017405621707439423, 0.013825375586748123, 0.002344978740438819, 2.0924951513734413e-06, 0.005783005151897669, 0.036592066287994385, -0.0003540520847309381, 0.021383633837103844, 0.019138343632221222, 0.003428190713748336, 0.03253718838095665, -0.0382109209895134, 0.020491765812039375, 0.06104354187846184, 0.035278838127851486, 0.028989054262638092, 0.038301728665828705, -0.005413338541984558, 0.04165302589535713, -0.013530904427170753, -0.039489682763814926, -0.031449947506189346, 0.01076368149369955, 0.035317204892635345, 0.007076041307300329, 0.01519830897450447, 0.04864591732621193, -0.004336636047810316, -0.05746148154139519, -0.03916805982589722, -0.019982241094112396, 0.03078940138220787, -0.03596437722444534, 0.037626493722200394, -0.01623089611530304, -0.04575548693537712, 0.013481095433235168, -0.034263987094163895, -0.0017839380307123065, -0.014394747093319893, -0.029947003349661827, 0.01641572080552578, -0.010782758705317974, 0.005240093916654587, -0.007448930758982897, -0.04441051557660103, -0.06260513514280319, -0.057944104075431824, 0.0004908812115900218, -0.009953050874173641, 0.06782303005456924, -0.020883075892925262, -0.0025438093580305576, -0.03081427328288555, 0.026962807402014732, 0.017516039311885834, -0.00264477776363492, 0.014694789424538612, 0.0006173212896101177, 0.046246238052845, 0.0004906064714305103, 0.020693013444542885, -0.026951726526021957, -0.03485586494207382, -0.004030730575323105, -0.04919544607400894, 0.025828206911683083, -0.017906567081809044, -0.05440429970622063, 0.0028010178357362747, -0.0009536854340694845, 0.022096414119005203, -0.014667869545519352, 0.02488446608185768, -0.007598795462399721, -0.021572772413492203, -0.00045089013292454183, -0.04964364320039749, 0.019554780796170235, -0.028143025934696198, -0.05361488088965416, 0.009434728883206844, 0.042950548231601715, 0.021819019690155983, -0.08212370425462723, -0.03717999905347824, 0.047343213111162186, 0.018221238628029823, -0.055647075176239014, 0.04110952839255333, -0.006467083934694529, -0.04364994913339615, -0.029862824827432632, -0.0025075331795960665, -0.001217598794028163, -0.025456201285123825, 0.05663897842168808, -0.008195937611162663, -0.029859062284231186, 0.02979670651257038, 0.042495567351579666, -0.01442726794630289, -0.005676774308085442, 0.0010871950071305037, 0.024513021111488342, 0.008190655149519444, 0.006155053619295359, 0.026507200673222542, -0.014390063472092152, 0.08556938171386719, 0.03686532378196716, -0.034471139311790466, -0.016431644558906555, -0.022319404408335686, 0.00535299489274621, -0.020023401826620102, 0.049449969083070755, -0.0703822672367096, -0.059529297053813934, 0.038299355655908585, 0.010577674023807049, 0.0066433316096663475, 0.03697732836008072, 0.08485787361860275, -0.008907829411327839, 0.004735376685857773, 0.017510557547211647, 0.008884910494089127, 0.007072771899402142, -0.0026129421312361956, -0.03313145041465759, -0.059939175844192505, 0.007128134369850159, -0.023002387955784798, 0.005299193784594536, 0.006144615821540356, -0.009456349536776543, 0.014937485568225384, -0.02359667979180813, 0.007016179617494345, 0.003956543281674385, 0.036180540919303894, 0.014075400307774544, 0.010675372555851936, 0.017404215410351753, 0.1357012838125229, -0.010210296139121056, -0.05965287983417511, 0.05152680352330208, 0.01513159740716219, 0.02180599234998226, 0.04547056928277016, 0.10248147696256638, -0.00816098041832447, 0.0003104939532931894, 0.01708149164915085, 0.04267448931932449, -0.0038649386260658503, -0.020843055099248886, 0.026454579085111618, -0.02752489410340786, -0.0025702225975692272, 0.023436347022652626, 0.014128880575299263, -0.03728964924812317, 0.0029518702067434788, -0.004219105001538992, 0.05911809578537941, 0.008645165711641312, 0.023200003430247307, -0.05442388728260994, -0.006336705759167671, -0.019402388483285904, 0.004633720498532057, -0.012789352796971798, -0.002944158622995019, 0.0010503499070182443, 0.00788975041359663, -0.06720582395792007, 0.00549056613817811, -0.014727208763360977, -0.0465732216835022, 0.019523372873663902, -0.05507918447256088, 0.020427295938134193, 0.027903655543923378, 0.029191968962550163, -0.036801692098379135, 0.03650970757007599, 0.03657088801264763, 0.013439690694212914, -0.02789171040058136, 0.05253024771809578, 0.054900236427783966, 0.02016923949122429, 0.006957308389246464, 0.003961652982980013, 0.01145643275231123, -0.014840907417237759, -0.0035920259542763233, 1.7856065426258283e-07, -0.06339095532894135, -0.045440737158060074, -0.0037946412339806557, 0.04954076185822487, -0.015332636423408985, 0.05336432904005051, 0.01231227908283472, -0.06065783277153969, 0.08877354115247726, 0.023127669468522072, 0.020354993641376495, -0.009686151519417763, 0.0068259770050644875, -0.034203022718429565, 0.007016405463218689, 0.010154932737350464, 0.022518614307045937, -0.058910854160785675, 0.004793097730726004, -0.01045608427375555, -0.009604295715689659, 0.09322763234376907, -0.016153298318386078, -0.01619444042444229, 0.031056618317961693, -0.0036048153415322304, 0.03271746635437012, 0.036972008645534515, -0.04956108331680298, -0.005457164719700813, 0.001358545501716435, 0.01814197190105915, 0.012366360984742641, 0.015205061994493008, -0.0018041105940937996, 0.034853849560022354, 0.020315242931246758, -0.07425970584154129, 0.02495521493256092, 0.05755821615457535, 0.02429846301674843, -0.0008264824282377958, -0.05365883558988571, -0.01847676932811737, 0.01619870401918888, -0.007754546124488115, -0.014361520297825336, -0.022316329181194305, -0.020129790529608727, -0.0124464500695467, -0.017744984477758408, -0.0038626850582659245, 0.028377549722790718, -0.004220605827867985, 0.059261541813611984, -0.08194109797477722, 0.003024113131687045, -0.024135762825608253, 0.027445800602436066, -0.023295287042856216, 0.018619908019900322, -0.029270580038428307, 0.015815727412700653, 0.036923784762620926, -0.03431788459420204, -0.02314889244735241, 0.03378336876630783, -0.007715336512774229, -0.006207209546118975, 0.0015432070940732956, -0.02730209194123745, 0.004343705717474222, 0.035307396203279495, 0.02098163031041622, -0.0195967648178339, 0.011039186269044876, 0.03830937296152115, -0.03373240306973457, 0.01665753871202469, 0.03199295699596405, -0.001927385339513421, -0.026394590735435486, -0.029216617345809937, 0.0001791508839232847, -0.04726843163371086, 0.011216346174478531, -0.0027262538205832243, -0.020738374441862106, 0.05987975746393204, -0.024647485464811325, -0.015389513224363327, 0.04662187024950981, -0.029082870110869408, -0.014099803753197193, -0.04212890937924385, 0.00812236312776804, -0.04312992841005325, -0.004351770039647818, 0.03419571369886398, -0.054046910256147385, -0.04632174223661423, 0.026805218309164047, -0.018938811495900154, 0.016555318608880043, -0.05668831616640091, -0.03249967098236084, -0.02375706471502781, -0.022211866453289986, -0.005407379940152168, 0.02503347024321556, -0.027398185804486275, 0.05710595101118088, 0.03858200088143349, -0.05399076268076897, -0.05322973057627678, 0.013991877436637878, 0.05586469918489456, 0.0013723705196753144, 0.01581999659538269, 0.031679678708314896, -0.04680653661489487, 0.0008796420297585428, 0.006217415444552898, -0.015346327796578407, 0.07312715798616409, 0.018842581659555435, -0.0446024127304554, 0.059046197682619095, 0.01887483522295952, -0.025826074182987213, -0.00021616574667859823, 0.05107037350535393, -0.06661009043455124, 0.07678419351577759, -0.022836845368146896, -0.02907993644475937, 0.009600342251360416, 0.06583274900913239, 0.019804343581199646, -0.006198476068675518, 0.07610062509775162, 0.061262451112270355, 0.011614822782576084, -0.049407683312892914, -0.04885435476899147, -0.019531773403286934, -0.07508692145347595, 0.033964719623327255, 0.04089898243546486, -0.044505104422569275, -0.0023582065477967262, -0.028825020417571068, -0.0025860669557005167, -0.017867911607027054, -0.008369074203073978, -0.0008192430250346661, 0.0006421611178666353, -0.004838900174945593, 0.00023688290093559772, 0.0182101558893919, 0.03468956798315048, 0.011733699589967728, -0.03032752498984337, 0.006316785700619221, 0.044290199875831604, -0.015987779945135117, 0.05592850595712662, -0.00466496404260397, 0.025916142389178276, -0.10118523240089417, -0.07146871089935303, -0.013564076274633408, -0.025443891063332558, 0.07598715275526047, -0.014074521139264107, -0.0053093330934643745, -0.005049385130405426, -0.060602132230997086, -0.040613576769828796, -0.023756077513098717, -0.03279499709606171, 0.0198344849050045, -0.034203577786684036, 0.025544622913002968, -0.0104693453758955, -0.023875117301940918, 0.08422920107841492, 0.020882530137896538, 0.0413161963224411, 2.6202855224255472e-05, -0.06338819861412048, -0.007436343468725681, -0.007702697534114122, -0.06229078024625778, -0.004896640777587891, 0.04271823540329933, -0.01596490852534771, -0.006977843586355448, 0.0072022187523543835, -0.0043787527829408646, -0.0010924221714958549, -0.01970517821609974, 0.011414172127842903, -0.048274844884872437, 0.044076450169086456, -0.015139131806790829, -0.050461072474718094, -0.029622651636600494, 0.034041959792375565, -0.006482068914920092, 0.04351871460676193, 0.019424112513661385, 0.046660102903842926, 0.006334960460662842, -0.0020904485136270523, -0.02407609112560749, -0.09072502702474594, 0.05158736929297447, -0.018929777666926384, 0.04009237885475159, 0.039244551211595535, 0.043808501213788986, -0.023588750511407852, -0.012686295434832573, -0.01782093197107315, -0.010825956240296364, 0.021384473890066147, 0.010956068523228168, -0.001901097595691681, 0.016023820266127586, -0.006847314536571503, -0.04490461200475693, -0.017001165077090263, -0.04429120942950249, -0.029496390372514725, 0.013182537630200386, -0.013899569399654865, 0.03236740082502365, 0.036615267395973206, 0.003173081437125802, 0.037765901535749435, -0.05125753581523895, 0.04378170520067215, -0.015692640095949173, -0.03198886290192604, 0.015202762559056282, 0.027906067669391632, -0.012473300099372864, -0.03180467709898949, -0.022868864238262177, -0.001958607230335474, -0.027781199663877487, 0.03481512516736984, 0.02143794856965542, -0.01712779514491558, 0.012963870540261269, -0.026428524404764175, -0.038784209638834, 0.01176262553781271, -0.006726738531142473, 0.029185455292463303, -0.05550488829612732, 0.025879880413413048, -0.08704797923564911, 0.035967595875263214, 0.0001750555238686502, -0.04842274263501167, -0.014372223056852818, -0.022400232031941414, -0.01064632460474968, 0.0003505632630549371, -0.08174601197242737, 0.08185198158025742, 0.03855055570602417, -0.07615005224943161, -0.042710788547992706, -0.021085141226649284, 0.013587559573352337, -0.05494564026594162, 0.011961243115365505, 0.06224178522825241, 0.07674083858728409, 0.05379147455096245, 0.113644078373909, -0.004803129937499762, 0.0275564044713974, -0.011830269359052181, -0.003504945896565914, 0.05100901052355766, -0.021211791783571243, 0.018392616882920265, -0.03074069321155548, 0.052357133477926254, 0.010175594128668308, 0.006988310255110264, -0.021240243688225746, 0.036177393049001694, -0.044294487684965134, 0.006579347886145115, -0.02939010038971901, -0.051175788044929504, -0.05250554159283638, 0.019865110516548157, 0.05011183023452759, -0.03462694585323334, 0.023847009986639023, -0.04215880483388901, 0.042081087827682495, -0.006207636091858149, 0.0030437626410275698, -0.04475506767630577, -0.025035101920366287, 0.03863001987338066, -0.011074651964008808, 0.006591065786778927, 0.011943517252802849, -0.038266245275735855, 0.0003661749651655555, 0.008555442094802856, -0.0742105096578598, -0.07173317670822144, 0.08659357577562332, 0.014978700317442417, -5.696691375872524e-33, 0.0029862234368920326, 0.023978421464562416, -0.01310720108449459, 0.003550437279045582, -0.005547501612454653, -0.04187287390232086, 0.042524419724941254, -0.049936626106500626, -0.0026625392492860556, -0.08233574777841568, -0.003797677345573902, 0.041790883988142014, 0.03661433607339859, 0.004571450874209404, -0.01913248375058174, -0.0066822064109146595, 0.022861825302243233, -0.018127627670764923, -0.006107698660343885, -0.052790917456150055, -0.04648532718420029, -0.01014843862503767, -0.0074066403321921825, -0.015005938708782196, -0.07295160740613937, -0.0024164291098713875, 0.012115894816815853, -0.08773001283407211, -0.003339187940582633, -0.011340883560478687, 0.03513922542333603, 0.03496935963630676, -0.04465807229280472, -0.011841165833175182, 9.157595923170447e-05, 0.03343159705400467, -0.018570996820926666, -0.019417867064476013, -0.0018843273865059018, 0.058569252490997314, 0.01959298923611641, -0.01772392727434635, 0.020494170486927032, 0.09432034939527512, -0.12981897592544556, 0.04197827726602554, 0.019405286759138107, -0.01261308416724205, -0.021624427288770676, 0.019421564415097237, -0.04072505608201027, -0.01637963578104973, -0.005873735528439283, 0.047973450273275375, 0.0027178418822586536, -0.06833162903785706, -0.05472102016210556, -0.07483098655939102, -0.07351263612508774, 0.013190988451242447, 0.04068345949053764, 0.0242813378572464, -0.04155750572681427, 0.0007375358254648745, 0.01849069446325302, 0.04197757691144943, -0.004326152615249157, -0.03606168180704117, 0.041471295058727264, 0.01557378564029932, 0.055455293506383896, -0.020966699346899986, -0.02465973235666752, -0.041410647332668304, 0.010511001572012901, -0.0427650548517704, -0.008503014221787453, 0.035733867436647415, 0.016571268439292908, -0.010997749865055084, -0.02410673163831234, 0.014739301055669785, -0.021659206598997116, 0.012225992046296597, 0.016314294189214706, 0.031468477100133896, 0.015805914998054504, -0.04778178408741951, -0.0029429413843899965, 0.012474901042878628, 0.008879496715962887, -0.0001585052377777174, -0.04377970099449158, -0.047693200409412384, 0.09188541024923325, -0.032376036047935486, -0.02444295771420002, 0.054552678018808365, -0.002370749367401004, -0.00929862167686224, 0.030365528538823128, -0.004828786477446556, 0.05024275183677673, 0.1052086353302002, 0.004791869781911373, 0.010828161612153053, -0.03207843750715256, 0.09526174515485764, -0.011666035279631615, 0.012424113228917122, 0.006301674526184797, -0.025271061807870865, 0.061696138232946396, 0.004870527423918247, -0.010830232873558998, -0.019293246790766716, -0.0063590253703296185, -0.023488009348511696, -0.07381577044725418, -0.10923466086387634, 0.010484365746378899, -0.05904027074575424, 0.021777216345071793, 0.02762548252940178, -0.14125992357730865, -0.015766935423016548, -0.03866737335920334, 0.024455834180116653, 0.06611516326665878, 0.006821807939559221, -0.01902140863239765, -0.03940152749419212, 2.9729409334322554e-07, -0.06510362029075623, 0.04871154576539993, 0.021426638588309288, -0.0002482478157617152, -0.02077976055443287, -0.04685121029615402, -0.04979213699698448, 0.038012273609638214, 0.0715908408164978, -0.0033243249636143446, -0.005614542867988348, -0.06791569292545319, 0.03770915046334267, 0.017053993418812752, -0.031023036688566208, 0.026373814791440964, -0.015128786675632, 0.045990198850631714, -0.035569511353969574, 0.0482906699180603, 0.06377606838941574, 0.027259422466158867, 0.01749933511018753, -0.021110335364937782, 0.09253804385662079, 0.01584053784608841, -0.024737726897001266, 0.04835128039121628, -0.007710260804742575, -0.007267653476446867, 0.027834288775920868, 0.04871859401464462, -0.038104020059108734, 0.016223523765802383, -0.006920061074197292, 0.034116651862859726, -0.012087215669453144, 0.04262357950210571, -0.012772330082952976, 0.012322871014475822, -0.026650255545973778, -0.031479522585868835, 0.06811758130788803, 0.01740523800253868, 0.01553793903440237, 0.02175346575677395, -0.043322887271642685, -0.0017283313209190965, 0.024043623358011246, -0.04285590350627899, -0.05855020508170128, 0.011993040330708027, 0.043140072375535965, -0.05609655752778053, -0.006542714312672615, 0.013878893107175827, 0.00950775295495987, -0.016547897830605507, 0.03795825317502022, -0.004142505582422018, 0.019650552421808243, -0.0332370363175869, -0.013801713474094868, 0.019943153485655785, 0.04286348074674606, 0.01102477964013815, 0.05852442607283592, 2.2152682361150453e-34, -0.036732207983732224, 0.04742314666509628, 0.051523372530937195, 0.02071707509458065, 0.009164543822407722, 0.005237803794443607, 0.015297203324735165, -0.0014962725108489394, 0.022001445293426514, -0.01109202392399311, 0.0007996727945283055]

['Aleksandrs Slivkins']

0907.3986v5

In a multi-armed bandit (MAB) problem, an online algorithm makes a sequence of choices. In each round it chooses from a time-invariant set of alternatives and receives the payoff associated with this alternative. While the case of small strategy sets is by now well-understood, a lot of recent work has focused on MAB problems with exponentially or infinitely large strategy sets, where one needs to assume extra structure in order to make the problem tractable. In particular, recent literature considered information on similarity between arms. We consider similarity information in the setting of "contextual bandits", a natural extension of the basic MAB problem where before each round an algorithm is given the "context" -- a hint about the payoffs in this round. Contextual bandits are directly motivated by placing advertisements on webpages, one of the crucial problems in sponsored search. A particularly simple way to represent similarity information in the contextual bandit setting is via a "similarity distance" between the context-arm pairs which gives an upper bound on the difference between the respective expected payoffs. Prior work on contextual bandits with similarity uses "uniform" partitions of the similarity space, which is potentially wasteful. We design more efficient algorithms that are based on adaptive partitions adjusted to "popular" context and "high-payoff" arms.

Contextual Bandits with Similarity Information

http://arxiv.org/pdf/0907.3986v5

Title Contextual Bandits Similarity Information Summary multiarmed bandit MAB problem online algorithm make sequence choice round chooses timeinvariant set alternative receives payoff associated alternative case small strategy set wellunderstood lot recent work focused MAB problem exponentially infinitely large strategy set one need assume extra structure order make problem tractable particular recent literature considered information similarity arm consider similarity information setting contextual bandit natural extension basic MAB problem round algorithm given context hint payoff round Contextual bandit directly motivated placing advertisement webpage one crucial problem sponsored search particularly simple way represent similarity information contextual bandit setting via similarity distance contextarm pair give upper bound difference respective expected payoff Prior work contextual bandit similarity us uniform partition similarity space potentially wasteful design efficient algorithm based adaptive partition adjusted popular context highpayoff arm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.003646060125902295, 0.05602133646607399, -0.029970219358801842, 0.0022792676463723183, -0.05265825614333153, -0.012222242541611195, 0.059779874980449677, 0.03904580697417259, -0.031126180663704872, -0.026701753959059715, -0.01191089116036892, 0.01484981644898653, -0.03912053257226944, 0.0311236921697855, 0.01133265532553196, -0.04622872546315193, -0.0029400803614407778, -0.03523043170571327, 0.0013963239034637809, -0.011176534928381443, 0.025912920013070107, -0.04953499510884285, -0.007355156354606152, 0.012440147809684277, 0.0623905174434185, 0.01194586232304573, -0.06409064680337906, -0.013308098539710045, 0.014291347935795784, -0.12562908232212067, 0.03939560428261757, 0.013504178263247013, 0.004419546574354172, 0.09367324411869049, 2.31162584896083e-06, -0.0774645283818245, -0.06815508008003235, -0.03744486719369888, 0.020941760390996933, 0.01090770773589611, 0.06450449675321579, 0.027143282815814018, 0.038535866886377335, 0.014679704792797565, -0.02371818944811821, 0.008456934243440628, 0.022475989535450935, 0.03760649636387825, -0.007588128559291363, 0.005032565910369158, 0.003986002877354622, -0.01711825095117092, -0.0008178625139407814, -0.029234644025564194, 0.039180248975753784, -0.028894834220409393, -0.0017617861740291119, -0.008316602557897568, 0.04798416793346405, -0.04065481945872307, 0.011873561888933182, -0.004684264771640301, -0.03144693374633789, 0.030815361067652702, 0.02673938125371933, 0.007904315367341042, -0.019763952121138573, 0.004756358917802572, -0.011411829851567745, 0.0016164977569133043, -0.04195940122008324, -0.0021409180480986834, 0.04254191368818283, -0.025747481733560562, -0.040809545665979385, 0.002810142934322357, -0.0057212538085877895, 0.03936132788658142, -0.06433567404747009, 0.011627997271716595, 0.007889091037213802, 0.10518103837966919, -0.0202175360172987, 0.020886104553937912, -0.01524825394153595, 0.032712992280721664, -0.02358960546553135, -0.01859523355960846, -0.000480419781524688, -0.021102318540215492, -0.028596535325050354, -0.044073596596717834, 0.030170505866408348, 0.004895851481705904, -0.06617464125156403, -0.021029848605394363, 0.013514474034309387, 0.020177248865365982, 0.050218481570482254, -0.0175008624792099, 0.07399551570415497, -0.027567658573389053, 0.03419126197695732, 0.0409863106906414, -0.0033554022666066885, 0.010682173073291779, -0.048347536474466324, -0.008631253615021706, -0.029323911294341087, 0.025250958278775215, -0.023436585441231728, 0.011339973658323288, -0.00031587929697707295, 0.0408802293241024, 0.03741057589650154, -0.019789284095168114, -0.04785764589905739, 0.02587948553264141, -0.0473749116063118, 0.010389283299446106, -0.003383708419278264, 0.031005393713712692, 0.012282625772058964, 0.00933818705379963, -0.03200871869921684, -0.07470831274986267, -0.08870396763086319, 0.02831101045012474, 0.004954560659825802, 0.025582237169146538, 0.024148868396878242, 0.0042978450655937195, -0.003852464724332094, -0.0250517800450325, 0.0024730435106903315, 0.06584674119949341, 0.02329082600772381, -0.0347868949174881, -0.06117910146713257, -0.04427996277809143, 0.016914494335651398, 0.009761674329638481, -0.051914457231760025, -0.09348424524068832, 0.010493375360965729, -0.09252959489822388, -0.024496400728821754, 0.07513487339019775, 0.001521841622889042, -0.015804335474967957, -0.020837027579545975, 0.08160998672246933, 0.04831160604953766, -0.007966287434101105, 0.03282568231225014, 0.011913226917386055, -0.007647355552762747, -0.0006372190546244383, -0.019195279106497765, 0.04132602736353874, 0.0323038324713707, 0.026541784405708313, -0.034982990473508835, -0.006725153885781765, -0.027662649750709534, -0.034757427871227264, 0.030726300552487373, 0.00778010580688715, 0.04002130404114723, 0.08037896454334259, -0.006116536911576986, -0.02609298937022686, -0.04795068874955177, -0.0469711609184742, 0.028519753366708755, 0.04016074910759926, 0.06542723625898361, -0.012658304534852505, 0.007723646238446236, 0.016991732642054558, -0.053028129041194916, -0.006337195169180632, 0.00895552895963192, 0.023956196382641792, -0.058388616889715195, 0.0018958812579512596, 0.04443337768316269, 0.010095971636474133, -0.012243310920894146, 0.007953008636832237, 0.005216821096837521, -0.015413756482303143, -0.02733541838824749, -0.007645015139132738, -0.025362707674503326, -0.04434073716402054, -0.04811124503612518, -0.11931541562080383, 0.013575284741818905, 0.052953023463487625, -0.07272820174694061, 0.008388927206397057, 0.03422941640019417, -0.0035919868387281895, 0.027507420629262924, -0.05857551842927933, 0.0034590240102261305, 0.017278071492910385, -0.04153946414589882, -0.07958811521530151, 0.028372136875987053, -0.03676031157374382, 0.0053406162187457085, -0.029508909210562706, -0.03211424872279167, 0.014439551159739494, -0.021187644451856613, 0.04095356911420822, 0.00755032803863287, 0.0350504033267498, -0.0014286345103755593, 0.024152155965566635, 0.07482196390628815, 0.0001724025933071971, -0.00963771715760231, -0.03590170294046402, 0.04089094698429108, 0.01096922904253006, 0.06971291452646255, -0.023815641179680824, 0.03525637835264206, -0.0021517197601497173, 0.04842497780919075, -0.03292687237262726, -0.019978417083621025, 0.03345651924610138, 0.006501583382487297, -0.03291641175746918, 0.035721130669116974, -0.02364402823150158, 0.05230165272951126, 0.028476569801568985, -0.015383293852210045, -0.00931163877248764, -0.0028250827454030514, -0.017606645822525024, 0.03850679472088814, -0.019930684939026833, 0.03359092399477959, 0.0027570691891014576, 0.018572725355625153, -0.05125799775123596, 0.06520247459411621, 0.008607743307948112, 0.06315071135759354, -0.004639571998268366, -0.004690135829150677, 0.026881227269768715, -0.07559424638748169, 0.05017644912004471, 0.002657004166394472, 0.009144380688667297, -0.037698742002248764, 0.0148036302998662, 0.03694615885615349, -0.002926799701526761, 0.00236067408695817, -0.019441131502389908, 0.01130493450909853, 0.03668030723929405, 0.011323315091431141, 0.004690865520387888, -0.030947621911764145, 0.005289169494062662, -0.024772174656391144, -0.00814037211239338, 0.001996442209929228, -0.016393110156059265, 0.01269711647182703, 0.04809928312897682, 0.001903480850160122, -0.033247824758291245, -0.0305218156427145, -0.031758636236190796, -0.00774774607270956, 0.0450718067586422, 0.03596486151218414, -0.011676179245114326, -0.05557195469737053, -0.057910941541194916, -0.049778152257204056, 0.016984207555651665, -0.006054108031094074, 0.04990164563059807, -0.023417694494128227, -0.01756235770881176, -0.013324753381311893, 0.038741812109947205, 0.07308203727006912, 0.018707547336816788, 0.04199932888150215, 0.03396870195865631, -0.02539532072842121, 0.003618406131863594, 0.011168998666107655, -0.00895683653652668, 0.03744477778673172, -0.03919452428817749, 0.059514451771974564, 0.0545981340110302, 0.009953559376299381, 0.012235783040523529, 0.001786238164640963, -0.0032911906018853188, 0.04928804188966751, -0.017356568947434425, -0.062091223895549774, 9.230036084773019e-05, -0.01976979523897171, 0.03059048391878605, 0.014828975312411785, -0.009455793537199497, 0.0978752076625824, 0.013822723180055618, 0.03940202668309212, 0.014066170901060104, -0.05359663441777229, -0.023634353652596474, -0.008167955093085766, 0.03322280943393707, 0.04470330476760864, 0.004783987067639828, -0.021066861227154732, -0.010760553181171417, 0.010880941525101662, 0.07836273312568665, -0.02706100605428219, -0.05425610393285751, 0.0007180782267823815, -0.014259710907936096, 0.021220987662672997, -0.05609078332781792, -0.0022753130178898573, -0.03798015043139458, 0.042694419622421265, -0.029090549796819687, 0.03052726946771145, -0.004388342145830393, -0.05285852029919624, 0.016200842335820198, -0.006847146898508072, 0.06950407475233078, 0.021490896120667458, -0.03425932303071022, 0.015003918670117855, 0.07865718752145767, 0.008419491350650787, -0.025752464309334755, 0.0227432269603014, -0.04315419867634773, 0.045902155339717865, 0.04210194945335388, 0.052285533398389816, -0.01529622171074152, -0.012082383036613464, 0.05705809220671654, 0.026345159858465195, -0.08962386846542358, -0.05998895317316055, 0.041798051446676254, -0.004978542681783438, -1.9332785086589865e-05, -0.0034378040581941605, 0.05029523745179176, 0.05316322669386864, -0.03700911998748779, 0.025043556466698647, -0.03855776786804199, 0.06071590259671211, 0.0015250478172674775, 0.037306636571884155, -0.05776701495051384, -0.0038845359813421965, -0.03904379531741142, 0.07474106550216675, -0.06804855912923813, -0.0937582328915596, -0.009452590718865395, -0.06849537044763565, 0.016459455713629723, -0.0018211916321888566, -0.06649666279554367, 0.025993285700678825, -0.05188797041773796, -0.027341360226273537, -0.05165537819266319, -0.09580353647470474, 0.05546349287033081, -0.020332304760813713, -0.005060379393398762, 0.022269083186984062, -0.0156853087246418, 0.0734095573425293, 0.02477804571390152, -0.06299708038568497, 0.005019386298954487, 0.00503184087574482, -0.0007836801814846694, 0.034530337899923325, -0.02958252839744091, -0.036862704902887344, -0.005705350078642368, 0.017573300749063492, 0.010627176612615585, 0.012822834774851799, 0.002264314563944936, 0.040505290031433105, -0.002672978211194277, 0.0206469539552927, -0.0014458798104897141, -0.03599124401807785, 0.04066293686628342, 0.022914165630936623, 0.012962033972144127, 0.000968519423622638, -0.027647318318486214, 0.0017458153888583183, 0.02444644272327423, 0.019219938665628433, -0.047645024955272675, -0.015315985307097435, -0.031072204932570457, 0.009798490442335606, -8.185754995793104e-05, -0.012399197556078434, 0.03664654493331909, -0.027229439467191696, 0.0038271816447377205, 0.016175169497728348, -0.09601021558046341, -0.0011025117710232735, -0.05855995789170265, 0.0782003179192543, -0.042928315699100494, -0.003973944112658501, -0.04077600687742233, -0.025663621723651886, -0.07954603433609009, -0.06115660071372986, 0.023972393944859505, 0.0063334577716887, -0.03334103524684906, 0.05145116522908211, 0.01166518684476614, -0.02366892620921135, -0.03585821017622948, -0.003515159245580435, -0.09434525668621063, -0.05753340944647789, 0.012059573084115982, 0.04588999226689339, 0.0162963829934597, 0.01035468652844429, -0.01262653898447752, 0.013154478743672371, 0.026811381801962852, -0.007692879065871239, 0.07411698997020721, 0.010555156506597996, -0.01330764964222908, 0.025594167411327362, -0.014573757536709309, 0.009026740677654743, -0.00980222225189209, 0.00951353833079338, -0.050198670476675034, -0.0004382529004942626, -0.04856457561254501, 0.0007553942268714309, 0.010917424224317074, 0.016517922282218933, 0.030755775049328804, 0.025521740317344666, -0.0351334884762764, 0.010303406044840813, 0.029412714764475822, 0.021649019792675972, -0.022075070068240166, -0.005139156710356474, -0.02783946320414543, 0.006061577703803778, 0.0026272647082805634, 0.021490944549441338, 0.01953371800482273, 0.02305448427796364, -0.03678230941295624, -0.03803250566124916, -0.0011873150942847133, 0.002129842760041356, 0.08580737560987473, -0.03125999867916107, 0.005140678957104683, 0.03752932325005531, 0.015629658475518227, 0.00894279032945633, 0.0754462257027626, -0.013599541038274765, 0.013367507606744766, 0.02691226825118065, 0.03322815150022507, -0.010166941210627556, -0.006728137377649546, -0.04172561690211296, -0.026671795174479485, -0.03955436870455742, 0.016426095739006996, 0.01722213625907898, -0.055490393191576004, -0.024752091616392136, -0.015582443214952946, 0.017921317368745804, 0.001450593350455165, 0.02093391679227352, -0.04926000535488129, -0.04821677505970001, 0.03319660201668739, 0.03403782099485397, -0.00999344140291214, 0.060376834124326706, 0.08591543883085251, 0.023777611553668976, 0.025502456352114677, -0.03571018949151039, -0.04466653987765312, -0.0304208192974329, 0.0072881076484918594, 0.041817329823970795, 0.09180191159248352, -0.029268650338053703, -0.03657243400812149, -0.008998566307127476, 0.04438787326216698, 0.009709151461720467, 0.014738542959094048, 0.060507964342832565, 0.015373209491372108, 0.04098781570792198, -0.019910912960767746, -0.030616601929068565, 0.03598165884613991, -0.02272588014602661, 0.007949775084853172, -0.014545203186571598, -0.03408545255661011, -0.05756302922964096, -6.466414995024543e-33, -0.0034982203505933285, -0.053679682314395905, -0.032012391835451126, -0.06867802143096924, -0.046565983444452286, -0.04080232232809067, 0.016526537016034126, -8.974614502221812e-06, 0.050760623067617416, -0.07436659187078476, 0.010684275068342686, -0.030061256140470505, 0.011163676157593727, -0.010096005164086819, 0.014321734197437763, 0.020172158256173134, -0.02359003759920597, 0.03538069501519203, -0.027391456067562103, -0.027320479974150658, 0.034349989145994186, 0.014054443687200546, -0.013104940764605999, -0.0229718629270792, -0.01912863925099373, -6.0992933867964894e-05, -0.010802011936903, -0.006100830622017384, -0.008259125053882599, 0.040958307683467865, 0.0015551825053989887, -0.020018715411424637, -0.025834646075963974, -0.04677742347121239, -0.0035845350939780474, -0.0690019503235817, 0.024242395535111427, -0.0369294211268425, -0.041758254170417786, 0.010921605862677097, 0.01831025630235672, -0.020714271813631058, 0.04729795083403587, -0.01316139753907919, -0.018880613148212433, 0.011824384331703186, 0.04502444714307785, -0.020813792943954468, -0.07933320850133896, 0.014477952383458614, 0.030002785846590996, 0.012853911146521568, -0.03985593467950821, 0.05243375524878502, 0.030251462012529373, 0.03583882749080658, 0.00048616144340485334, 0.0491006039083004, 0.00511672580614686, 0.084355928003788, 0.020211871713399887, 0.022635290399193764, 0.015313426963984966, 0.0012618249747902155, 0.07113415747880936, 0.042634882032871246, 0.016307810321450233, -0.06417648494243622, 0.053210243582725525, -0.04105775058269501, -0.046279024332761765, 0.006030632648617029, 0.01426604576408863, 0.05157521367073059, 0.0919196754693985, 0.006180315278470516, 0.0005326831596903503, 0.07350514829158783, -0.004709239117801189, -0.049009889364242554, 0.005736691411584616, 0.053228627890348434, -0.012504145503044128, 0.004502380266785622, 0.0352252833545208, -0.02853568270802498, -0.008873257786035538, -0.02535184659063816, 0.013945875689387321, 0.019561652094125748, 0.014204282313585281, 0.03978875279426575, -0.03504617139697075, -0.014848296530544758, -0.002295931102707982, -0.04104916378855705, 0.026505431160330772, 0.02616007998585701, -0.009808273054659367, -0.021442724391818047, -0.04416806623339653, -0.03165818750858307, -0.013550953008234501, -0.04367950186133385, 0.03862699121236801, -0.02242104336619377, 0.0005929028266109526, -0.005220759194344282, -0.06326871365308762, 0.01691117323935032, 0.013157015666365623, -0.04597904905676842, -0.02251574955880642, -0.04340168088674545, 0.05076874792575836, -0.06472594290971756, -0.0007961799274198711, 0.04500556364655495, 0.04126064479351044, -0.0884619802236557, -0.035162996500730515, -0.007473777513951063, -0.03321666270494461, 0.009613795205950737, 0.004329974297434092, 0.03864744305610657, -0.02881488762795925, 0.018933990970253944, -0.014446470886468887, -0.011406836099922657, -0.033783916383981705, -0.014786078594624996, 2.920805002304405e-07, -0.026758948341012, 0.034077342599630356, 0.002492679515853524, -0.031408295035362244, -0.009659925475716591, 0.03061831183731556, -0.019126562401652336, 0.034894876182079315, -0.06296660751104355, 0.06021779775619507, 0.06434482336044312, -0.03737984225153923, 0.027915308251976967, 0.018141744658350945, -0.01906699500977993, 0.012469965033233166, -0.044259801506996155, 0.034674789756536484, -0.07655955851078033, -0.034152787178754807, -0.0041892495937645435, 0.05787847191095352, 0.04259468615055084, -0.002552617574110627, 0.05062336102128029, -0.024693239480257034, 0.013763262890279293, -0.04154221713542938, 0.0013217246159911156, -0.04074406251311302, -0.01936703734099865, -0.03725204989314079, -0.047652341425418854, -0.01447315700352192, -0.01408699993044138, 0.007565225008875132, 0.031168172135949135, -0.006711877882480621, 0.04027146100997925, -1.7150880012195557e-05, 0.01617210917174816, 0.009460899978876114, -0.0013090081047266722, -0.05238574370741844, 0.0045464602299034595, 0.02773471549153328, -0.020565342158079147, 0.011473770253360271, -0.01500802580267191, -0.026953471824526787, 0.030492456629872322, 0.028846504166722298, -0.011738091707229614, 0.023382076993584633, -0.020911267027258873, 0.02085881121456623, 0.022821592167019844, 0.012837483547627926, 0.005064826924353838, 0.055671580135822296, 0.01247569639235735, 0.02056625857949257, -0.024424834176898003, 0.07109026610851288, 0.04730643332004547, -0.09960174560546875, -0.013958079740405083, 2.914562708168272e-34, -0.007196048274636269, 0.014680230058729649, -0.018498040735721588, -0.006773373577743769, 0.0034822067245841026, 0.025715220719575882, 0.019851908087730408, 0.01398882083594799, 0.04951232671737671, 0.0063837673515081406, -0.02163468673825264]

['Adhistya Erna Permanasari', 'Dayang Rohaya Awang Rambli', 'Dhanapal Durai Dominic']

0910.0820v2

Zoonosis refers to the transmission of infectious diseases from animal to human. The increasing number of zoonosis incidence makes the great losses to lives, including humans and animals, and also the impact in social economic. It motivates development of a system that can predict the future number of zoonosis occurrences in human. This paper analyses and presents the use of Seasonal Autoregressive Integrated Moving Average (SARIMA) method for developing a forecasting model that able to support and provide prediction number of zoonosis human incidence. The dataset for model development was collected on a time series data of human tuberculosis occurrences in United States which comprises of fourteen years of monthly data obtained from a study published by Centers for Disease Control and Prevention (CDC). Several trial models of SARIMA were compared to obtain the most appropriate model. Then, diagnostic tests were used to determine model validity. The result showed that the SARIMA(9,0,14)(12,1,24)12 is the fittest model. While in the measure of accuracy, the selected model achieved 0.062 of Theils U value. It implied that the model was highly accurate and a close fit. It was also indicated the capability of final model to closely represent and made prediction based on the tuberculosis historical dataset.

Prediction of Zoonosis Incidence in Human using Seasonal Auto Regressive Integrated Moving Average (SARIMA)

http://arxiv.org/pdf/0910.0820v2

Title Prediction Zoonosis Incidence Human using Seasonal Auto Regressive Integrated Moving Average SARIMA Summary Zoonosis refers transmission infectious disease animal human increasing number zoonosis incidence make great loss life including human animal also impact social economic motivates development system predict future number zoonosis occurrence human paper analysis present use Seasonal Autoregressive Integrated Moving Average SARIMA method developing forecasting model able support provide prediction number zoonosis human incidence dataset model development collected time series data human tuberculosis occurrence United States comprises fourteen year monthly data obtained study published Centers Disease Control Prevention CDC Several trial model SARIMA compared obtain appropriate model diagnostic test used determine model validity result showed SARIMA90141212412 fittest model measure accuracy selected model achieved 0062 Theils U value implied model highly accurate close fit also indicated capability final model closely represent made prediction based tuberculosis historical dataset Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[5.425167182693258e-05, 0.03215879201889038, -0.022759003564715385, -0.05324310436844826, 0.027129273861646652, -0.006991364061832428, 0.04751018434762955, -0.007590348366647959, 0.03183417022228241, 0.0034877455327659845, 0.032336413860321045, -0.015062850899994373, 0.02476087585091591, 0.09344718605279922, -0.023327579721808434, -0.006046612747013569, 0.016811486333608627, -0.044820841401815414, -0.039398182183504105, 0.026342887431383133, -0.004554023500531912, -0.01564325951039791, 0.025404788553714752, 0.025926411151885986, 0.043076254427433014, -0.005170868709683418, 0.019806690514087677, -6.009997014189139e-05, 0.03425829857587814, -0.09702655673027039, 0.05059429630637169, -0.037679821252822876, 0.02012009173631668, -0.009233707562088966, 2.0858212792518316e-06, -0.011166985146701336, -0.020131627097725868, -0.0027127256616950035, 0.027625523507595062, -0.002120294375345111, 0.0890667736530304, -0.016550278291106224, 0.05425896495580673, 0.02068333700299263, -0.04304615408182144, 0.028340892866253853, 0.003980736248195171, 0.05337933078408241, 0.012243104167282581, -0.03328719362616539, 0.008160200901329517, 0.014768343418836594, 0.019303619861602783, -0.03475901857018471, -0.04845624789595604, -0.010569906793534756, 0.0053451647982001305, -0.005908985622227192, 0.02081538364291191, -0.007982162758708, -0.020192179828882217, 0.04576446861028671, 0.0044792648404836655, 0.013097560033202171, -0.0126746641471982, 0.05467994883656502, 0.038648732006549835, -0.030332744121551514, 0.0010324902832508087, -0.023214517161250114, 0.025612829253077507, -0.04461934044957161, 0.019894791767001152, 0.049142904579639435, -0.012235547415912151, 0.00016194985073525459, -0.0570468045771122, 0.010369694791734219, 0.005354660097509623, 0.01216069981455803, 0.044384270906448364, 0.0718308761715889, -0.013907967135310173, 0.019551077857613564, 0.0012130795512348413, 0.020570427179336548, -0.03456088900566101, -0.02078319527208805, -0.029493073001503944, -0.05981143191456795, -0.03634609654545784, -0.00325203244574368, 0.003913168795406818, 0.03133660927414894, -0.06665653735399246, -0.007160713896155357, 0.04964327812194824, -0.06000254303216934, 0.07295728474855423, 0.00640174699947238, -0.03232866898179054, 0.0004436981398612261, 0.014003772288560867, -0.0297609381377697, -0.007788683287799358, -0.016460593789815903, -0.06332387775182724, 0.017989350482821465, 0.014790493994951248, 0.03950989991426468, -0.023717578500509262, 0.008705341257154942, 0.03126286342740059, -0.022614335641264915, 0.05463184416294098, 0.040914878249168396, -0.08236712217330933, -0.040429096668958664, -0.00293877930380404, -0.056808698922395706, 0.0991113930940628, 0.04661446437239647, -0.03807847946882248, 0.03342599421739578, 0.027771135792136192, 0.018272826448082924, -0.013914666138589382, 0.055235058069229126, 0.012557481415569782, 0.006983415689319372, -0.002696644514799118, -0.062388356775045395, 0.029155448079109192, 0.03057974763214588, 0.002502470277249813, 0.005483753513544798, -0.0007478008046746254, 0.05224531516432762, -0.030620208010077477, 0.029183564707636833, -0.024389268830418587, -0.021046064794063568, -0.09831811487674713, 0.030958881601691246, -0.006926168687641621, 0.04493687301874161, 0.017780030146241188, 0.051610976457595825, 0.011610293760895729, -0.0038631290663033724, -0.056072503328323364, -0.04516832157969475, -0.08680261671543121, 0.022722136229276657, 0.01931481622159481, 0.03133758530020714, 0.043276604264974594, -0.06963072717189789, 0.009043621830642223, 0.029531436040997505, -0.04027876257896423, 0.03106089122593403, -0.009734231978654861, -0.013003495521843433, -0.029311295598745346, 0.027155717834830284, -0.02808680571615696, 0.021593639627099037, 0.03621789067983627, -0.017040297389030457, -0.045205093920230865, 0.007947348058223724, 0.02710821107029915, 0.014018111862242222, 0.03755500912666321, 0.001674228347837925, -0.042586538940668106, -0.04450562223792076, 0.017674969509243965, -0.001632551895454526, -0.006378562655299902, -0.08352673798799515, 0.04080136865377426, 0.03826352581381798, -0.03593285381793976, 0.026630248874425888, -0.012666764669120312, 0.014329364523291588, 0.019316494464874268, -0.05319731682538986, 0.0070023005828261375, -0.014716066420078278, 0.0147913359105587, -0.06603121012449265, -0.003955519292503595, 0.006705439183861017, 0.032071005553007126, -0.007703827694058418, 0.07098362594842911, 0.03261232748627663, -0.0552440881729126, -0.04883333295583725, 0.024890555068850517, -0.043184973299503326, -0.0031881763134151697, 0.03456852585077286, -0.047367606312036514, -0.05299199000000954, 0.02541671320796013, -0.05290011316537857, -0.05185035616159439, 0.0017747171223163605, -0.023766404017806053, -0.03529077023267746, 0.023810766637325287, 0.08613360673189163, 0.01943317987024784, -0.012019428424537182, -0.011693463660776615, 0.054281048476696014, 0.02310246415436268, 0.03909117355942726, -0.013502920977771282, 0.004445724654942751, -0.06840705871582031, 0.011338960379362106, 0.02073769085109234, -0.02654515951871872, 0.08323347568511963, -0.0459173321723938, 0.030508358031511307, 0.006549477111548185, -0.0036105772014707327, -0.023555874824523926, -0.007237234152853489, 0.10995044559240341, 0.013605003245174885, -0.017896169796586037, -0.047034941613674164, 0.06645029783248901, 0.009365268051624298, 0.05485140532255173, 0.01544979214668274, -0.024380752816796303, 0.05557514354586601, -0.012376870028674603, 0.0026453614700585604, -0.0253478791564703, 0.0018507124623283744, 0.02089930884540081, -0.0084711704403162, 0.016108214855194092, -0.006880350410938263, 0.009330343455076218, -0.053102124482393265, 0.014235766604542732, -0.08820436894893646, 0.015076933428645134, -0.014991204254329205, 0.006434155628085136, -0.016877366229891777, -0.008552119135856628, -0.014325886964797974, -0.04240528121590614, -0.02326488308608532, -0.03361799567937851, 0.024084659293293953, -0.04402455314993858, 0.011655555106699467, 0.031075304374098778, -0.006017492618411779, -0.018390990793704987, 0.006445901934057474, 0.0038376268930733204, -0.011600662022829056, 0.02176596410572529, -0.009971863590180874, 0.03201902285218239, 0.006053656339645386, 0.0756319910287857, 0.01660531759262085, -0.009734747000038624, -0.05007480829954147, 0.0334865003824234, -0.06582061201334, 0.013557247817516327, 0.029196036979556084, -0.0154804028570652, 0.07651813328266144, -0.016826746985316277, -0.014000060968101025, -0.008882738649845123, -0.022911882027983665, -0.03505904600024223, -0.07651682943105698, -0.03717253357172012, -0.024482740089297295, -0.02008046582341194, 0.005915974732488394, -0.06703687459230423, 0.013085816986858845, 0.042472295463085175, -0.0371389240026474, 0.011655994690954685, 0.004299956373870373, 0.019869254902005196, 0.04343019798398018, -0.028225023299455643, -0.02064405009150505, 0.08304622769355774, 0.023838816210627556, -0.017821215093135834, 0.040431346744298935, 0.04863540455698967, -0.013942524790763855, -0.010062431916594505, -0.039643947035074234, 0.022224733605980873, -0.02026999182999134, 0.022846151143312454, -0.011082760989665985, -0.07991653680801392, -0.027867073193192482, 0.035145774483680725, -0.03038977086544037, -0.010984396561980247, -0.02455703727900982, -0.009685984812676907, -0.0942208394408226, -0.0013857083395123482, -0.031657811254262924, -0.005415087100118399, 0.013749943114817142, 0.021726027131080627, -0.004605249967426062, -0.04016043245792389, -0.020596839487552643, -0.04756128787994385, -0.00875034648925066, 0.010569869540631771, 0.021046876907348633, 0.015167185105383396, 0.013372594490647316, 0.025724250823259354, -0.03478272259235382, -0.039639513939619064, -0.008280517533421516, 0.035255067050457, -0.039811816066503525, 0.05556943640112877, -0.026630675420165062, -0.004092132672667503, -0.04808804392814636, -0.02431955747306347, 0.02124054543673992, -0.07232890278100967, 0.028096474707126617, -0.07729892432689667, -0.09167908877134323, 0.014543202705681324, 0.05762400105595589, -0.038443632423877716, -0.010605597868561745, 0.05076110363006592, -0.06392035633325577, 0.06537257134914398, -0.02999534085392952, -0.010878047905862331, -0.03637862578034401, 0.020160011947155, -0.04578494280576706, -0.004754721187055111, 0.009373682551085949, 0.03959078714251518, 0.0074732499197125435, 0.0002866232243832201, -0.011873883195221424, -0.07180608808994293, -0.04335089772939682, -0.0579356886446476, -0.006173009984195232, 0.0279887393116951, -0.00800873339176178, 0.006999273784458637, -0.024796253070235252, -0.017490165308117867, -0.057837944477796555, -0.009778749197721481, 0.04336443170905113, 0.016227101907134056, 0.00574645446613431, 0.016680365428328514, -0.007968603633344173, -0.0562376044690609, 0.0018863690784201026, -0.05910104885697365, -0.012907597236335278, -0.01324320025742054, 0.01895485632121563, 0.02223515696823597, 0.025617973878979683, -0.09330698847770691, -0.013352873735129833, 0.0466516874730587, -0.013016829267144203, -0.007009953260421753, 0.010806952603161335, 0.0196402408182621, -0.016822269186377525, 0.017367636784911156, -0.041030146181583405, 0.09572432190179825, 0.03712226450443268, -0.06512115895748138, 0.06314060837030411, 0.036499764770269394, -0.004421950783580542, -0.04491207376122475, -0.01545314397662878, -0.0474378876388073, 0.04977524280548096, 0.03130658343434334, 0.07145121693611145, 0.031996265053749084, -0.013830911368131638, -0.048201292753219604, 0.030316445976495743, -0.003448102157562971, 0.017650360241532326, 0.016559001058340073, 0.03592842444777489, 0.005657397676259279, 0.04322499781847, 0.007056693080812693, -0.033255435526371, -0.03789756819605827, 0.004327487666159868, -0.07969673722982407, -0.05405215919017792, 0.0013110717991366982, 0.0034009981900453568, 0.011966842226684093, 0.016816170886158943, 0.0235858503729105, 0.06536230444908142, 0.01511926855891943, -0.02984570525586605, -0.016588913276791573, -0.058036744594573975, 0.02246043272316456, 0.013708553276956081, -0.007654810324311256, 0.047924719750881195, 0.05745122954249382, 0.006983068771660328, -0.001189119298942387, -0.025003310292959213, -0.06416507810354233, 0.01583678647875786, 0.03939080610871315, 0.00843888521194458, 0.017497017979621887, -0.0585172064602375, 0.02184392511844635, 0.06047540158033371, 0.03468026965856552, -0.013440159149467945, 0.07968694716691971, -0.04177767038345337, -0.03795774653553963, 0.01609252765774727, 0.01915019378066063, -0.015248904004693031, 0.05132027715444565, 0.03464654088020325, 0.027089372277259827, -0.006570050027221441, -0.0388430692255497, 0.023722641170024872, -0.030788475647568703, 0.016819020733237267, 0.037406258285045624, 0.0005416754866018891, -0.06876111775636673, -0.03901468962430954, 0.016973210498690605, 0.0017588771879673004, -0.003280035452917218, -0.013547786511480808, 0.027020655572414398, 0.042274441570043564, 0.0476413331925869, -0.08061354607343674, 0.007484120782464743, -0.003638068912550807, -0.03823618218302727, 0.012665904127061367, 0.09759274870157242, 0.009790723212063313, 0.06194591149687767, 0.02498755045235157, 0.038576316088438034, 0.00396754639223218, -0.07303310185670853, 0.03770020604133606, 0.0388374924659729, 0.03584667667746544, 0.04771897941827774, -0.06442797183990479, -0.0019527869299054146, 0.02474341355264187, 0.03473401814699173, 0.0193997360765934, 0.06150919944047928, -0.0037439463194459677, 0.02031775936484337, -0.08451393991708755, -0.01970209740102291, -0.005120450630784035, -0.007956952787935734, 0.021886805072426796, -0.04528161883354187, 0.07876325398683548, -0.01584576442837715, 0.0903860554099083, 0.017834017053246498, -0.030813388526439667, -0.06581224501132965, -0.017805686220526695, 0.015056367963552475, 0.019349737092852592, -0.02891414798796177, 0.008331422694027424, -0.02863464504480362, -0.039264995604753494, 0.05838362127542496, 0.01189135666936636, -0.08157685399055481, -0.006842563860118389, 0.005571239627897739, 0.011176178231835365, -0.026471108198165894, 0.05624184012413025, -0.044378943741321564, 0.01739497110247612, 0.014882544055581093, -0.09326111525297165, -0.028458300977945328, 0.010024947114288807, 0.033654700964689255, 0.012186755426228046, 0.023989317938685417, -0.016384869813919067, 0.014786199666559696, -0.04821694269776344, -5.330569333971522e-33, -0.009956032037734985, 0.002039445796981454, 0.016440298408269882, -0.058315783739089966, 0.017069997265934944, 0.06063175946474075, -0.022622177377343178, -0.007587159518152475, -0.004006776958703995, -0.019003335386514664, -0.04123833402991295, -0.030808547511696815, 0.008381875231862068, -0.01231074146926403, 0.08396731317043304, 0.01691417768597603, -0.02192792296409607, 0.020847301930189133, 0.045120783150196075, -0.0418056957423687, 0.00838924665004015, 0.037033043801784515, -0.007911366410553455, 0.03485937789082527, -0.010955801233649254, -0.005963318049907684, -0.01184073556214571, -0.03139751777052879, -0.012238411232829094, 0.008660353720188141, 0.032643094658851624, -0.04189351201057434, 0.01753283478319645, -0.02886483073234558, 0.006946976762264967, 0.022607695311307907, 0.01119641587138176, -0.02492862194776535, -0.006619265768676996, -0.0649624913930893, -0.013967202976346016, -0.017983926460146904, 0.06316869705915451, 0.005592320580035448, -0.013152978383004665, 0.04124942421913147, -0.004162521567195654, -0.06068607047200203, 0.02826741337776184, -0.03641067445278168, 0.0035684637259691954, 0.022979650646448135, 0.01653306558728218, 0.02950599603354931, -0.021900992840528488, 0.04710158705711365, -0.03448094427585602, 0.07406217604875565, 0.024292727932333946, 0.0007872919086366892, 0.03842157870531082, 0.019351430237293243, -0.006713175680488348, 0.0026499778032302856, 0.026824332773685455, -0.042560920119285583, 0.006200898438692093, -0.02217782288789749, -0.0250259842723608, -0.02555689960718155, -0.01720043085515499, -0.023429594933986664, 0.006089738104492426, 0.011120191775262356, 0.017011316493153572, -0.05792791023850441, -0.019031032919883728, 0.08329442888498306, 0.008425307460129261, 0.03352837264537811, -0.041229624301195145, -0.022899355739355087, 0.0036778664216399193, 0.021418210119009018, -0.023360682651400566, 0.022965142503380775, -0.004314458463340998, -0.008019346743822098, 0.04042048752307892, 0.029788481071591377, 0.04067021980881691, 0.05231029912829399, 0.031811393797397614, 0.012104805558919907, 0.03788452222943306, -0.03364172205328941, 0.029140982776880264, -0.008118927478790283, 0.031343162059783936, 0.019863249734044075, -0.001626181649044156, 0.033314865082502365, -0.008773604407906532, 0.015947233885526657, 0.008226117119193077, -0.035325899720191956, 0.06858064234256744, 0.00031263817800208926, -0.017315363511443138, -0.022701244801282883, 0.03242398798465729, 0.00696725444868207, -0.022198421880602837, 0.012028371915221214, -0.014696327969431877, -0.07601818442344666, 0.011773963458836079, 0.0169206615537405, 0.019771577790379524, 0.03562527149915695, -0.02973308227956295, 0.005797737743705511, -0.016363872215151787, -0.04566532000899315, -0.037172652781009674, -0.03220929205417633, -0.002875148318707943, 0.006931382697075605, -0.05539855733513832, -0.05181111767888069, 0.043080367147922516, -0.0256681926548481, 2.7869680252479156e-07, 0.041742827743291855, 0.04774077609181404, -0.08577821403741837, 0.0610995851457119, -0.0003626046236604452, -0.0008401203667744994, -0.052985116839408875, -0.03204633295536041, 0.02595527097582817, 0.03941788151860237, 0.08370703458786011, -0.0380505807697773, -0.018649736419320107, 0.02645118162035942, 0.026815691962838173, -0.07009483873844147, -0.10575877130031586, 0.027119217440485954, 0.007259252015501261, -0.03909246250987053, -0.01290321908891201, 0.039880361407995224, 0.02776476740837097, -0.011870848014950752, -0.002831164514645934, -0.018524939194321632, 0.0027065114118158817, -0.04506341367959976, -0.04373070225119591, 0.006848508957773447, 0.05065171793103218, 0.05683894827961922, -0.00882971752434969, -0.013598894700407982, -0.03969958424568176, -0.03492884710431099, -0.015229013748466969, 0.0006189885316416621, 0.012153812684118748, 0.03964448347687721, 0.05745092034339905, 0.008798038586974144, 0.019916227087378502, -0.020765358582139015, 0.029071150347590446, 0.01593165658414364, -0.011814683675765991, -0.014090565033257008, -0.007505818270146847, 0.08085291087627411, 0.032269436866045, -0.012772809714078903, 0.011148667894303799, 0.017315007746219635, -0.025353651493787766, -0.009927192702889442, 0.004937071818858385, 0.006937902420759201, -0.015625493600964546, -0.02949622832238674, -0.0355948731303215, -0.05154458433389664, -0.008654091507196426, 0.0037517400924116373, 0.022838937118649483, -0.0833192765712738, 0.021828122437000275, 2.8185914004408056e-34, 0.051942624151706696, -0.008314927108585835, 0.0069736638106405735, -0.025163324549794197, -0.0016645170981064439, -0.004235705826431513, 0.01053921040147543, -0.0036555659025907516, -0.00567966140806675, -0.004766376689076424, -0.04365398362278938]

['Raghunandan H. Keshavan', 'Andrea Montanari', 'Sewoong Oh']

0910.0921v2

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and wireless sensor networks. In this paper, we focus on the matrix completion problem in the case when the observed samples are corrupted by noise. We compare the performance of three state-of-the-art matrix completion algorithms (OptSpace, ADMiRA and FPCA) on a single simulation platform and present numerical results. We show that in practice these efficient algorithms can be used to reconstruct real data matrices, as well as randomly generated matrices, accurately.

Low-rank Matrix Completion with Noisy Observations: a Quantitative Comparison

http://arxiv.org/pdf/0910.0921v2

Title Lowrank Matrix Completion Noisy Observations Quantitative Comparison Summary consider problem significant practical importance namely reconstruction lowrank data matrix small subset entry problem appears many area collaborative filtering computer vision wireless sensor network paper focus matrix completion problem case observed sample corrupted noise compare performance three stateoftheart matrix completion algorithm OptSpace ADMiRA FPCA single simulation platform present numerical result show practice efficient algorithm used reconstruct real data matrix well randomly generated matrix accurately Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.010159709490835667, 0.03778974711894989, 0.006451854482293129, 0.0054736873134970665, 9.295624477090314e-05, -0.014220255427062511, -0.030436091125011444, 0.03407227620482445, 0.012284649536013603, 0.029040003195405006, 0.0324060320854187, 0.031044401228427887, 0.05703485757112503, -0.008886492811143398, 0.002922563813626766, -0.01702454686164856, -0.018820302560925484, 0.006295102182775736, -0.0797359049320221, -0.06388881802558899, -0.02513253130018711, -0.034332793205976486, 0.027296409010887146, 0.005402248818427324, -0.04622192680835724, 0.019824324175715446, -0.0048331511206924915, -0.018689919263124466, -0.035129159688949585, -0.0189809612929821, -0.021253349259495735, -0.002988547785207629, 0.024451853707432747, -0.018493277952075005, 2.513976369300508e-06, 0.005859793163836002, 0.004230814520269632, -0.023221412673592567, 0.05249772220849991, -0.02028633840382099, 0.0029485009144991636, 0.05736197158694267, 0.04021550342440605, 0.0003698132641147822, 0.0021451839711517096, -0.01311258040368557, 0.020186761394143105, 0.009336535818874836, 0.01066440250724554, -0.05784181132912636, -0.002227365504950285, -0.01966642029583454, -0.010360142216086388, -0.013090813532471657, 0.0028305985033512115, -0.03750414773821831, 0.05274050310254097, -0.0024588124360889196, 0.03736976906657219, -0.016970044001936913, -0.006049877963960171, 0.040148817002773285, -0.014087074436247349, 0.010082561522722244, 0.10687782615423203, 0.014515371061861515, 0.022207247093319893, -0.02464241534471512, -0.0038250284269452095, 0.043270472437143326, -0.032734327018260956, 0.012080920860171318, 0.04810662567615509, 0.021914167329669, -0.008418158628046513, -0.022053886204957962, -0.023513391613960266, -0.013577369973063469, -0.012883997522294521, 0.0026721751783043146, -0.09147708117961884, 0.018371321260929108, 0.0040181586518883705, 0.017326615750789642, -0.010499791242182255, 0.12030404061079025, 0.01382200513035059, 0.019817570224404335, -0.0575089156627655, 0.023539308458566666, 0.046783991158008575, -0.02186901681125164, 0.04320048540830612, -0.020665045827627182, -0.05962323769927025, 0.0030619422905147076, -0.04352032393217087, -0.032541099935770035, -0.005549529101699591, -0.015912620350718498, 0.04719295725226402, -0.013062950223684311, 0.03311939537525177, 0.03265109285712242, 0.008541474118828773, -0.022702723741531372, -0.059908147901296616, -0.017689408734440804, -0.03410040959715843, -0.029755916446447372, 0.015146465972065926, 0.022948071360588074, 0.035197846591472626, 0.11029764264822006, -0.027918275445699692, -0.012075069360435009, -0.039487324655056, 0.023719986900687218, -0.012619762681424618, 0.010377521626651287, -0.04854744300246239, 0.06131703406572342, -0.012951215729117393, -0.0656682550907135, -0.028157958760857582, -0.00974078755825758, 0.06198234111070633, 0.053396400064229965, -0.013598713092505932, 0.0758834108710289, 0.012281433679163456, 0.005423744209110737, 0.0467674657702446, 0.0009960939642041922, 0.01784440688788891, 0.050884172320365906, -0.020069772377610207, -0.006833716295659542, -0.008874042890965939, 0.010664551518857479, -0.037457097321748734, -0.009777901694178581, -0.017958058044314384, -0.06073455885052681, 0.024991100654006004, -0.0012112172553315759, 0.012959887273609638, 0.0287731122225523, 0.009627663530409336, 0.009910606779158115, -0.08493348956108093, 0.09506960213184357, -0.07090307027101517, 0.0034489042591303587, 0.05659957230091095, -0.0227179154753685, 0.041885871440172195, -0.07615617662668228, 0.009895416907966137, 0.08929342776536942, 0.004350624047219753, -0.01494602207094431, 0.004994173999875784, -0.021862978115677834, 0.02156165800988674, -0.029490826651453972, -0.03950543329119682, -0.007656008470803499, -0.03512047976255417, -0.024194147437810898, -0.020424777641892433, 0.01014005672186613, 0.022868996486067772, 0.034395482391119, 0.04160289466381073, 0.04471202194690704, 0.032576970756053925, 0.03287852928042412, -0.06174272298812866, 0.022704429924488068, -0.01228555291891098, 0.010519732721149921, 0.025897718966007233, 0.05738786235451698, -0.02405574545264244, -0.03457698971033096, 0.0384681262075901, 0.01423647254705429, -0.01838965155184269, -0.022748781368136406, 0.019077928736805916, -0.03931561857461929, -0.0016910545527935028, -0.0004856191808357835, 0.10160990804433823, -0.014232046902179718, -0.02529868856072426, -0.08605077117681503, 0.06182948872447014, -0.009295662865042686, -0.009114204905927181, -0.024535750970244408, 0.08816983550786972, -0.0347176119685173, -0.002865147078409791, -0.04971566051244736, 0.035005319863557816, -0.02820582687854767, -0.01647154800593853, -0.12757354974746704, -0.07207531481981277, 0.010063095949590206, -0.0004817384178750217, -0.010323158465325832, -0.05967938154935837, 0.09039292484521866, 0.0058966586366295815, 0.0073037357069551945, -0.04472680389881134, -0.012287246063351631, -0.008274752646684647, -0.006776368245482445, -0.02106468752026558, -0.003959885332733393, 0.04053768143057823, 0.0759955644607544, 0.04950675740838051, 0.013593059964478016, 0.06039244309067726, 0.035291168838739395, 0.067042276263237, -0.03771376982331276, 0.06531314551830292, -0.021537376567721367, -0.010796408168971539, -0.03569979965686798, -0.0011861519888043404, 0.003197190584614873, 0.028088480234146118, -0.04425552114844322, -0.009212818928062916, 0.10501336306333542, 0.028265710920095444, -0.052159033715724945, 0.037018369883298874, -0.034466635435819626, -0.08219364285469055, -0.03095509484410286, 0.020402375608682632, -0.026207024231553078, -0.006542485672980547, -0.023322835564613342, 0.03833432495594025, -0.03525547310709953, 0.01731780357658863, 0.016413867473602295, -0.010880072601139545, 0.03863473981618881, -0.03269358351826668, -0.017166834324598312, -0.0025310448836535215, -0.02170119807124138, -0.009829294867813587, 0.024359414353966713, 0.007594540249556303, 0.015674594789743423, -0.010574501007795334, 0.0584784597158432, 0.010380486957728863, 0.01477060653269291, -0.05343465134501457, 0.0030084738973528147, 0.015231614001095295, 0.05579274892807007, -0.05069717392325401, 0.002523549599573016, 0.09115514159202576, 0.016243550926446915, -0.05253488942980766, 0.03950532153248787, 0.028047850355505943, -0.002897904720157385, -0.02796844020485878, -0.02424832060933113, 0.02119928039610386, 0.006366843357682228, 0.003343952586874366, -0.09234711527824402, -0.030645569786429405, 0.03333592042326927, 0.00640858756378293, 0.004871391225606203, -0.01807192713022232, -0.013128644786775112, -0.022508393973112106, 0.010206322185695171, -0.006367276888340712, -0.008603711612522602, 0.005959947127848864, -0.011859636753797531, 0.05556896701455116, 0.03538569062948227, -0.01894104667007923, 0.032819248735904694, -0.04990481212735176, 0.03723471984267235, 0.04025491327047348, 0.017889102920889854, -0.011584760621190071, -0.04191594198346138, 0.0016543755773454905, -0.02018132619559765, 0.001897001639008522, 0.008695492520928383, 0.014115232974290848, -0.00668510003015399, -0.10663724690675735, -0.017746079713106155, -0.03114374540746212, 0.028345130383968353, -0.028224872425198555, 0.002395153045654297, -0.008552519604563713, 0.005233502481132746, 0.011019772849977016, 0.0047918036580085754, -0.02818533591926098, 0.0807570070028305, -0.043833449482917786, 0.04801006615161896, 0.018345534801483154, -0.07705193758010864, -0.004014882259070873, -0.018276002258062363, -0.01715322583913803, -0.02158033661544323, -0.06452479213476181, -0.04707161337137222, 0.021734539419412613, 0.0002023399865720421, 0.022714665159583092, -0.016250383108854294, -0.029205137863755226, 0.008247461169958115, 0.05335920676589012, -0.08601228892803192, -0.010168048553168774, 0.017039943486452103, 0.03418603539466858, -0.016164103522896767, 0.036886367946863174, -0.010406170040369034, 0.01801776885986328, -0.014245320111513138, -0.037953875958919525, 0.04948220029473305, 0.007680098991841078, -0.012603836134076118, 0.026015499606728554, 0.003436662256717682, 0.007836111821234226, 0.037284839898347855, 0.0668812170624733, 0.023833585903048515, -0.07096856087446213, 0.017032090574502945, 0.034878991544246674, 0.08327601104974747, -0.022005220875144005, 0.016248710453510284, 0.011935572139918804, 0.009354211390018463, 0.0719907283782959, -0.02984844148159027, -0.014750681817531586, -0.10423320531845093, -0.02766723744571209, 0.02763429284095764, -0.01999426633119583, 0.03654031082987785, -0.009789926931262016, 0.01793437823653221, 0.04594164341688156, 0.02550594136118889, 0.05180465430021286, 0.00530779454857111, -0.01647634617984295, 0.01382701937109232, -0.04476715996861458, 0.05438484624028206, -0.014787641353905201, 0.03092663176357746, -0.11335590481758118, -0.046724867075681686, 0.02629554644227028, 0.005641597788780928, 0.00676084915176034, 0.023395521566271782, 0.030808890238404274, -0.010435606352984905, 0.005870855413377285, -0.0630846917629242, 0.005026842001825571, -0.038861796259880066, -0.02112768031656742, 0.05223854258656502, -0.019930295646190643, 0.022422457113862038, -0.04299148544669151, -0.014406086876988411, -0.03668152168393135, 0.016354570165276527, -0.025905489921569824, -0.024235788732767105, 0.017644885927438736, 0.07403574883937836, -0.02972484566271305, -0.03545549884438515, 0.06050185114145279, 0.01633361726999283, 0.006940365768969059, -0.023231303319334984, 0.031057016924023628, -0.002617896068841219, 0.030659906566143036, 0.01598619855940342, 0.0008023421396501362, 0.0025989769492298365, -0.008838562294840813, -0.026904955506324768, -0.013860423117876053, 0.028562400490045547, 0.03183356672525406, 0.026155035942792892, 0.018865738064050674, 0.004281301982700825, 0.049458567053079605, -0.021512622013688087, 0.0027484854217618704, -0.04889484494924545, -0.003578465897589922, 0.04306352511048317, 0.03820636123418808, -0.022373022511601448, 0.04890035092830658, 0.01566663756966591, -0.04266590625047684, 0.002009607618674636, -0.029746972024440765, 0.018316470086574554, -0.005321925040334463, 0.03137773275375366, 0.07700571417808533, -0.04051043838262558, -0.05181717500090599, -0.028528131544589996, -0.028277432546019554, -0.043957583606243134, -0.007490780670195818, 0.01434226892888546, 0.06692304462194443, 0.010616408661007881, 0.022250819951295853, -0.039590783417224884, -0.06413555890321732, -0.028248758986592293, 0.005845134146511555, 0.018050646409392357, 0.012322713620960712, -0.008975423872470856, -0.02726804092526436, -0.0015346846776083112, 0.03093772754073143, -0.034841619431972504, 0.010222175158560276, 0.01121267769485712, -0.049209315329790115, -0.038047049194574356, 0.002013980410993099, 0.029052285477519035, 0.019084028899669647, 0.056931622326374054, 0.040025610476732254, -0.0073152570985257626, -0.030828194692730904, 0.02559492737054825, -0.0561506561934948, -0.01109398901462555, -0.03681676462292671, -0.008103646337985992, 0.002115890383720398, 0.024938685819506645, -0.009740577079355717, -0.07172843813896179, 0.008710604161024094, 0.00012806148151867092, -0.028360383585095406, -0.05053696781396866, -0.03641000762581825, -0.05885700508952141, 0.012876441702246666, 0.016360005363821983, 0.01593373529613018, -0.02080325037240982, 0.07830323278903961, 0.007437462452799082, 0.008739849552512169, -0.06610792130231857, -0.0004104800464119762, -0.04647291824221611, -0.03364107012748718, 0.014774896204471588, 0.0037956174928694963, -0.032530635595321655, -0.008995166048407555, 0.05912955105304718, 0.05519494041800499, 0.029224146157503128, -0.011110789142549038, 0.016521098092198372, 0.02491641789674759, -0.026136666536331177, 0.02416723594069481, 0.018351862207055092, 0.04842958226799965, 0.01958967000246048, -0.008813311345875263, -0.02491900324821472, 0.07736845314502716, 0.05482468381524086, 0.013477233238518238, -0.0007949318387545645, -0.03097515180706978, -0.006549281533807516, -0.014590028673410416, 0.06867808848619461, -0.007617170922458172, 0.07510613650083542, -0.06158873438835144, 0.003257300704717636, 0.04836180806159973, -0.0388122983276844, 0.017183907330036163, -0.02327621914446354, 0.012761130928993225, -0.03896493464708328, -0.028265463188290596, 0.02212423086166382, -0.013535303995013237, 0.06776593625545502, -0.006113427225500345, -0.05960873141884804, 0.034145280718803406, -0.03443639352917671, -0.005191505420953035, -6.679451305592005e-33, -0.02122759260237217, -0.046658359467983246, -0.05902472138404846, -0.021717045456171036, -0.02474980615079403, -0.03618315979838371, 0.015190270729362965, 0.02765757590532303, 0.046764250844717026, -0.0058661820366978645, -0.056035302579402924, 0.03232063725590706, 0.01983943209052086, 0.03987677022814751, -0.0014567745383828878, 0.06906818598508835, 0.014159572310745716, 0.013195640407502651, 0.037122149020433426, -0.011599909514188766, 0.00799641478806734, 0.050722185522317886, -0.030411815270781517, -0.07899332046508789, -0.06306755542755127, 0.005059346091002226, -0.023447591811418533, -0.03957169130444527, -0.009243655018508434, -0.029695535078644753, -0.010404218919575214, 0.027419425547122955, 0.009671502746641636, 0.005230221897363663, -0.044195257127285004, -0.030601950362324715, -0.030340610072016716, 0.025877488777041435, -0.03350106254220009, 1.0210557775280904e-05, -0.040064726024866104, 0.009436220861971378, 0.049722667783498764, 0.00947125256061554, -0.032900284975767136, 0.011660749092698097, 0.03919631987810135, -0.04840519651770592, -0.07150696218013763, 0.004997562151402235, 0.049148328602313995, -0.0003380298148840666, -0.01959117129445076, -0.007112142164260149, 0.009351763874292374, 0.006754422094672918, -0.034546174108982086, 0.012118116952478886, -0.05587564781308174, 0.013725697062909603, -0.021426133811473846, 0.07180079072713852, -0.03710739314556122, -0.019053153693675995, 0.0024445054586976767, 0.02551901340484619, 0.04153204709291458, -0.0039795441552996635, 0.015426112338900566, -0.0459224209189415, -0.055358145385980606, 0.056307658553123474, 0.026172401383519173, 0.05712691694498062, 0.0186690054833889, -0.05952834337949753, -0.03570724278688431, 0.05784965306520462, -0.08222267031669617, 0.02579750493168831, 0.016011105850338936, -0.005946991499513388, 0.014575338922441006, -0.01687728986144066, 0.02657175436615944, -0.009873717091977596, -0.022008810192346573, 0.029651900753378868, -0.01957721821963787, 0.015819508582353592, -0.043026071041822433, 0.019312867894768715, -0.003247812855988741, -0.05878178030252457, 0.030941614881157875, -0.05987359583377838, -0.006569291464984417, 0.0204013641923666, 0.028672637417912483, -0.0011167958145961165, -0.005658529233187437, -0.02612936496734619, -0.04402269423007965, 0.0076240114867687225, -0.03761943057179451, 0.028406450524926186, -0.014215001836419106, 0.010845641605556011, 0.004853039048612118, -0.009939925745129585, -0.0009858194971457124, -0.0073996614664793015, 0.02631686069071293, -0.022296734154224396, 0.02415129914879799, -0.03766540810465813, 0.00835809763520956, 0.08267621695995331, 0.011444931849837303, 0.07365890592336655, 0.007425353862345219, -0.09933856874704361, -0.023874688893556595, -0.007607019040733576, -0.018685949966311455, -0.007534348405897617, -0.10194045305252075, 0.026144128292798996, 0.04492667317390442, 0.014721523970365524, -0.0064584133215248585, -0.05115066096186638, 3.187614652233606e-07, -0.05851871520280838, 0.05582045391201973, -0.04057575389742851, -0.046896424144506454, -0.0007070329738780856, -0.017333876341581345, 0.00852472148835659, 0.050476644188165665, -0.0054101841524243355, -0.024915527552366257, -0.006756081245839596, -0.07331027090549469, 0.03282543271780014, -0.007993954233825207, -0.052892208099365234, 0.0034604601096361876, -0.042037803679704666, 0.013552041724324226, -0.015668274834752083, -0.021222352981567383, -0.0034685502760112286, 0.022926222532987595, 0.0016149814473465085, -0.014726143330335617, 0.03235235437750816, 0.020017677918076515, 0.019754398614168167, -0.014277305454015732, -0.033736344426870346, -0.04098615050315857, 0.07030483335256577, -0.011610280722379684, 0.010053605772554874, -0.0070311445742845535, -0.008654664270579815, 0.016306394711136818, 0.04321069270372391, -0.02707032859325409, -0.0281753558665514, 0.00691481726244092, 0.04269770532846451, 0.02832760661840439, 0.021305358037352562, -0.042650703340768814, 0.019586360082030296, -0.0024362436961382627, -0.009478817693889141, -0.007290351670235395, -0.018171101808547974, 0.026605406776070595, -0.0029884378891438246, 0.029620131477713585, 0.0333842933177948, -0.034036293625831604, -0.0430058129131794, 0.016260439530014992, 0.049143560230731964, 0.009501608088612556, 0.06551874428987503, -0.029609529301524162, -0.026154102757573128, -0.025766873732209206, 0.02120289020240307, -0.03691675141453743, 0.06606557220220566, 0.015613149851560593, -0.020832743495702744, 2.574873998550661e-34, -0.02036532200872898, 0.04196372255682945, 0.013405723497271538, -0.0004992897738702595, -0.058269236236810684, -0.02746276929974556, -0.02546272985637188, 0.009303293190896511, -0.0031189105939120054, -0.027738351374864578, -0.030990462750196457]

['Hugo Zanghi', 'Franck Picard', 'Vincent Miele', 'Christophe Ambroise']

0910.2034v2

In this paper we adapt online estimation strategies to perform model-based clustering on large networks. Our work focuses on two algorithms, the first based on the SAEM algorithm, and the second on variational methods. These two strategies are compared with existing approaches on simulated and real data. We use the method to decipher the connexion structure of the political websphere during the US political campaign in 2008. We show that our online EM-based algorithms offer a good trade-off between precision and speed, when estimating parameters for mixture distributions in the context of random graphs.

Strategies for online inference of model-based clustering in large and growing networks

http://arxiv.org/pdf/0910.2034v2

Title Strategies online inference modelbased clustering large growing network Summary paper adapt online estimation strategy perform modelbased clustering large network work focus two algorithm first based SAEM algorithm second variational method two strategy compared existing approach simulated real data use method decipher connexion structure political websphere US political campaign 2008 show online EMbased algorithm offer good tradeoff precision speed estimating parameter mixture distribution context random graph Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.029717423021793365, 0.06034715846180916, -0.03896050527691841, -0.019062520936131477, -0.023394877091050148, -0.03398086130619049, 0.014753274619579315, -0.04419015720486641, 0.027625836431980133, 0.014884169213473797, 0.05155450105667114, -0.0005044295685365796, 0.0011246451176702976, 0.08655693382024765, 0.014013294130563736, -0.05969274044036865, 0.029995325952768326, 0.021489610895514488, 0.007689894642680883, -0.027122097089886665, 0.018340162932872772, -0.008100764825940132, 0.003665492171421647, -0.0015985845820978284, -0.0037961762864142656, -0.010795029811561108, -0.026318384334445, -0.032844629138708115, 0.02328294888138771, 0.014440197497606277, 0.004863492213189602, -0.0068961018696427345, 0.0017049340531229973, -0.00391761539503932, 2.1777666461275658e-06, -0.028764359652996063, -0.07655981183052063, -0.029442014172673225, 0.012123075313866138, -0.00032161897979676723, 0.0678817480802536, 0.0024453040678054094, -0.0007300687138922513, 0.03372488170862198, 0.007696922868490219, 0.026522785425186157, 0.016847047954797745, -0.02841140702366829, -0.009751448407769203, -0.02592756599187851, -0.004835807252675295, 0.048743799328804016, 0.0005704881623387337, -0.007141151465475559, -0.04989638924598694, 0.023999473080039024, 0.04085756838321686, 0.03263748809695244, -0.0047285426408052444, -0.02538496069610119, -0.021939806640148163, 0.03189228102564812, -0.004505703691393137, -0.01191033236682415, 0.05462750792503357, 0.027691835537552834, 0.027828330174088478, -0.003666166216135025, -0.013386786915361881, 0.04087065905332565, 0.013101802207529545, 0.0310707725584507, 0.059827204793691635, 0.007312985602766275, -0.05022669956088066, 0.09082497656345367, -0.04152308776974678, 0.01348763145506382, -0.0565616674721241, 0.004450646694749594, 0.01439750101417303, 0.013240215368568897, 0.0013448602985590696, 0.0493304580450058, -0.0009353925124742091, 0.0687447339296341, -0.009391131810843945, 0.028448043391108513, -0.02524096891283989, -0.02891959436237812, -0.041636593639850616, -0.023648986592888832, 0.07879307121038437, -0.021060727536678314, -0.012306110933423042, -0.0061799464747309685, 0.041722703725099564, 0.037117164582014084, 0.02814353257417679, -0.030807429924607277, 0.01666511781513691, -0.05366504564881325, 0.05901914834976196, 0.06248641386628151, 0.05075840279459953, -0.03757011145353317, -0.06828939914703369, -0.04724719747900963, 0.036903541535139084, 0.006119305733591318, -0.04420613870024681, 0.014453480951488018, 0.023034289479255676, 0.01345229521393776, -0.027680909261107445, -0.012911549769341946, -0.04682723060250282, 0.08497830480337143, -0.0454653799533844, -0.006299607455730438, -0.005731157958507538, 0.005418288987129927, 0.07316523045301437, -0.012895614840090275, -0.02913426049053669, 0.0177676510065794, -0.030140504240989685, 0.051255110651254654, -0.03109505958855152, 0.011241643689572811, 0.031035762280225754, 0.027656463906168938, 0.08031868934631348, 0.025104496628046036, -0.027262380346655846, 0.055324096232652664, 0.009721451438963413, -0.004142352379858494, -0.0006448395433835685, -0.025526082143187523, -0.02279715985059738, 0.03905020281672478, -0.005322292912751436, -0.07310277968645096, 0.01509749423712492, -0.044504083693027496, 0.01049718540161848, 0.0359082892537117, -0.023786302655935287, -0.05131420120596886, -0.035106733441352844, -0.0030939795542508364, -0.057362139225006104, 0.0305989570915699, 0.03939003497362137, 0.00039204442873597145, 0.009996849112212658, 0.03668970987200737, -0.01914779469370842, 0.05223216861486435, 0.05342596396803856, 0.011579611338675022, -0.012993701733648777, 0.008885561488568783, 0.022899406030774117, 0.0666065439581871, -0.008849612437188625, -0.012155571952462196, -0.03334059566259384, -0.03942831605672836, -0.005320596043020487, -0.00892199669033289, -0.03163231909275055, 0.030954398214817047, 0.03844156861305237, 0.014388125389814377, 0.012064529582858086, 0.008150434121489525, -0.03375609591603279, 0.04679625481367111, -0.03270506486296654, -0.028466185554862022, -0.009089196100831032, 0.00247611990198493, -0.05343164876103401, -0.02904091775417328, 0.050519660115242004, 0.038782861083745956, -0.015819769352674484, 0.01345872227102518, 0.008231095969676971, 0.008307290263473988, 0.0047155627980828285, -0.01943107321858406, 0.0709681287407875, -0.0617104209959507, 0.0026829533744603395, -0.02571979910135269, 0.05533897876739502, 0.030607422813773155, 0.010683783330023289, -0.0534307137131691, 0.012921447865664959, -0.02074509486556053, 0.01406380906701088, -0.027186434715986252, -0.05432070791721344, 0.005795267876237631, 0.015327314846217632, -0.06719394773244858, -0.025970596820116043, -0.01682497002184391, -0.018695231527090073, 0.0263555608689785, -0.0024785371497273445, 0.05841819569468498, 0.02717767469584942, 0.004987584892660379, -0.0041876062750816345, 0.04757433757185936, -0.025674697011709213, -0.03194744512438774, 0.05579773336648941, -0.014113787561655045, 0.007742464076727629, 0.07554765045642853, 0.030936775729060173, 0.0017888844013214111, 0.06155881658196449, 0.008926068432629108, 0.028076672926545143, -0.03788946941494942, 0.023969050496816635, 0.011586037464439869, -0.04251615330576897, 0.007494162768125534, 0.06548918783664703, 0.034223172813653946, 0.00228572404012084, -0.004254610277712345, 0.0037737509701400995, -0.033350978046655655, 0.006148965563625097, -0.015194667503237724, 0.09318243712186813, 0.0105160316452384, 0.043781086802482605, 0.012851675041019917, 0.009764841757714748, -0.016524242237210274, 0.006851209327578545, 0.0037607995327562094, 0.038531653583049774, -0.0034734036307781935, 0.010289909318089485, 0.010506097227334976, -0.009049098938703537, 0.019980521872639656, -0.020030738785862923, 0.03743988275527954, -0.08980990201234818, -0.047876983880996704, -0.0300380140542984, 0.00945193599909544, -0.04820574074983597, -0.043157145380973816, -0.03286700323224068, -0.05065634101629257, 0.013138220645487309, 0.004663010127842426, 0.018284710124135017, 0.04448355361819267, 0.021628236398100853, -0.0237126424908638, 0.03839969262480736, 0.08176285773515701, 0.02312915027141571, -0.024376410990953445, -0.014427212066948414, -0.0037025772035121918, -0.03311358019709587, -0.048794228583574295, -0.03258831053972244, -0.036965783685445786, -0.04383867606520653, 0.040253475308418274, 0.005181964486837387, -0.09837997704744339, 0.03919472545385361, 2.369250614719931e-05, -0.07588616758584976, -0.013945703394711018, -0.03381071612238884, -0.04301507771015167, -0.039961136877536774, -0.012919504195451736, 0.05187308415770531, 0.009859198704361916, 0.038980357348918915, 0.04129903018474579, 0.014472490176558495, -0.038222040981054306, 0.005988936871290207, 0.0022068528924137354, -0.054942741990089417, 0.022477054968476295, 0.030248746275901794, -0.017896847799420357, 0.027808818966150284, 0.03142398223280907, 0.0412457101047039, 0.0008739308686926961, 0.06306608021259308, 0.013917863368988037, -0.03796956688165665, 0.038873519748449326, -0.07592705637216568, 0.0004689208581112325, 0.02159719727933407, 0.005228741094470024, -0.0006222281372174621, -0.020220201462507248, -0.009057778865098953, 0.02676854282617569, 0.053708113729953766, 0.03277060016989708, -0.07365114986896515, 0.04236229509115219, -0.018260866403579712, 0.032837968319654465, 0.02814185433089733, -0.009667676873505116, -0.008210095576941967, -0.01053338497877121, 0.007902074605226517, 0.06109881401062012, -0.036241691559553146, -0.02941776067018509, 0.02270331233739853, -0.002993689849972725, 0.0014799941563978791, 0.013871485367417336, -0.03782851621508598, 0.003112124279141426, 0.008585398085415363, -0.012061826884746552, 0.048318974673748016, -0.05044252425432205, 0.04144926741719246, 0.033735502511262894, -0.0008819068898446858, -0.0006034908001311123, -0.016848454251885414, -0.012261833995580673, 0.003771543735638261, 0.09075303375720978, 0.002033999189734459, -0.05245968699455261, -0.0032271286472678185, -0.022509854286909103, -0.02028738148510456, -0.016024012118577957, -0.010327504016458988, 0.012172575108706951, -0.0397922620177269, -0.01551726646721363, -0.006270848214626312, -0.018384475260972977, 0.014181834645569324, 0.013973374851047993, 0.04627271369099617, 0.005858748219907284, 0.03913803771138191, 0.055880993604660034, 0.022545762360095978, -0.04992954805493355, -0.004294475074857473, 0.020741134881973267, -0.0012173341820016503, 0.01734851486980915, 0.03152148798108101, -0.02350327931344509, 0.04322480782866478, -0.00459339888766408, -0.021478289738297462, -0.021101808175444603, -0.057160884141922, -0.005486247595399618, -0.029081027954816818, 0.04311957210302353, -0.0028116749599575996, 0.01500733196735382, 0.018963593989610672, -0.10038543492555618, 0.017265012487769127, -0.054805733263492584, -0.0637303963303566, -0.004133850336074829, -0.005175269208848476, -0.01464740838855505, 0.006606900133192539, -0.07925789058208466, -0.025765875354409218, -0.041923634707927704, -0.08274415880441666, 0.05357198789715767, -0.05243846774101257, 0.06249859929084778, -0.014840726740658283, 0.01884838193655014, 0.08734837919473648, -0.026580601930618286, -0.019445637241005898, -0.011518805287778378, 0.0609387643635273, 0.02799411676824093, 0.025633208453655243, -0.05403373762965202, 0.0019519077613949776, 0.008185025304555893, -0.014360964298248291, 0.03896413370966911, 0.042435213923454285, -4.19132447859738e-05, -0.003138287691399455, -0.022019343450665474, 0.01889331452548504, 0.03127957135438919, -0.03279346972703934, -0.005697839427739382, -0.017270425334572792, 0.031728096306324005, -0.006166705396026373, 0.032987792044878006, 0.05887774005532265, 0.023417849093675613, -0.0018681223737075925, -0.019873544573783875, -0.024255236610770226, -0.04159665107727051, 0.06041383370757103, -0.03209928423166275, 0.05377475544810295, -0.0252890195697546, 0.03646611049771309, 0.08175479620695114, -0.047359250485897064, -0.0379546619951725, -0.030870143324136734, -0.010900271125137806, -0.005732344463467598, 0.004551420453935862, -0.011067543178796768, -0.01233956590294838, 0.027374591678380966, -0.05944127216935158, -0.048720456659793854, -0.10357819497585297, -0.042566679418087006, 0.00044944480760023, -0.050988681614398956, 0.019781485199928284, 0.0349571630358696, -0.07791374623775482, 0.003672670805826783, 0.016093434765934944, 0.00140906882006675, -0.0020068930462002754, -0.04909819737076759, 0.013987052254378796, 0.024667484685778618, 0.003128340467810631, 0.02098049968481064, -0.004348515998572111, 0.030258936807513237, 0.015678275376558304, -0.09943173825740814, -0.07021589577198029, -0.002271985402330756, -0.04118906334042549, 0.03375355899333954, 0.09237544238567352, 0.042741525918245316, -0.06468735635280609, -0.04908541217446327, -0.03814511373639107, -0.001611260580830276, -0.007732787169516087, 0.020556369796395302, 0.003823451930657029, 0.0041706194169819355, 0.04218894988298416, -0.030012980103492737, 0.012257051654160023, 0.055774152278900146, 0.005706931464374065, -0.014276365749537945, 0.007515127770602703, -0.014525233767926693, -0.01358268316835165, -0.009582236409187317, 0.0241757333278656, 0.03547380119562149, -0.03047487698495388, 0.020227445289492607, 0.07859267294406891, -0.00875027570873499, -0.01800706423819065, -0.01055857539176941, -0.03593878075480461, 0.0017304271459579468, 0.03793559595942497, -0.014913096092641354, -0.05109899863600731, -0.018108181655406952, 0.07597317546606064, 0.01806758902966976, 0.031070483848452568, 0.039866287261247635, -0.013746711425483227, 0.008798674680292606, -0.020158803090453148, 0.0455898754298687, -0.02390417642891407, -0.022097976878285408, 0.015468710102140903, 0.01754956878721714, -0.032443515956401825, 0.1102445125579834, 0.04216410592198372, 0.02965432032942772, -0.05038972571492195, -0.008414983749389648, -0.05787993595004082, -0.004966825246810913, 0.06985063850879669, 0.00031296955421566963, 0.053620580583810806, -0.03020353429019451, 0.014037820510566235, 0.010785292834043503, -0.014108535833656788, 0.025780845433473587, -0.019839417189359665, -0.0015390722546726465, 0.03922780603170395, -0.020596874877810478, -0.0002058466343441978, -0.024719564244151115, 0.056364841759204865, -0.06962898373603821, 0.010974997654557228, -0.03452708199620247, -0.020190011709928513, 0.03873731568455696, -6.606347311914367e-33, 0.014553096145391464, -0.06602169573307037, -0.06166048347949982, -0.10222482681274414, -0.07709626853466034, 0.03221649304032326, -0.023174002766609192, -0.012085957452654839, -0.005574420560151339, -0.020064808428287506, -0.0024483725428581238, 0.01629304327070713, 0.01113183330744505, -0.007106036879122257, 0.0037083986680954695, 0.0029903945978730917, -0.0029902018141001463, 0.061651427298784256, -0.00044529300066642463, 0.051685355603694916, 0.029464658349752426, -0.005190168973058462, -0.04571162909269333, -0.029255632311105728, -0.03537965938448906, 0.03404403105378151, -0.018828924745321274, 0.03394763916730881, 0.022625144571065903, 0.030186187475919724, -0.02167012169957161, 0.004497142042964697, 0.0016095219179987907, 0.0019290727796033025, 0.006857031956315041, -0.0004274934181012213, -0.020131567493081093, -0.0006157011375762522, -0.040521711111068726, -0.017613783478736877, 0.008749780245125294, -0.011749417521059513, 0.019017256796360016, 0.0626855343580246, 0.03034750185906887, -0.02399212308228016, 0.0756368488073349, -0.0038422048091888428, -0.02804272435605526, 0.021052168682217598, 0.048410940915346146, 0.03232249617576599, -0.06076179817318916, 0.08019641786813736, -0.05664924904704094, -0.02243942581117153, 6.185143138282001e-05, 0.029398426413536072, -0.05581693723797798, 0.03826870769262314, -0.012781589291989803, 0.022997893393039703, 0.013852846808731556, 0.0204676054418087, 0.06502929329872131, 0.043742965906858444, -0.024423133581876755, 0.0003555946168489754, -0.03247663751244545, -0.0025211689062416553, 0.012705768458545208, 0.006014108657836914, -0.025383176282048225, -0.015043397434055805, -0.0038235133979469538, -0.06030871719121933, -0.06568558514118195, -0.00354039017111063, 0.023915845900774002, -0.02310262992978096, 0.01455792598426342, -0.010844775475561619, -0.00650889752432704, -0.03314719349145889, 0.04715895652770996, -0.11224906146526337, -0.008403763175010681, -0.020257264375686646, -0.03814687579870224, 0.010820767842233181, -0.032044097781181335, -0.004055914934724569, -0.0003046981291845441, -0.04755397513508797, -0.012344235554337502, 0.01164940930902958, -0.008017664775252342, 0.03836047276854515, -0.0002596708945930004, -0.025521835312247276, -0.06022084504365921, -0.05739225819706917, -0.0590268112719059, 0.0033120138105005026, -0.028520090505480766, -0.005580485332757235, -0.024872994050383568, 0.002458340022712946, -0.034756433218717575, 0.011449804529547691, 0.033653050661087036, -0.041385047137737274, -0.00476536201313138, -1.3171693353797309e-05, 0.04016385227441788, -0.03531956300139427, 0.014515237882733345, 0.04411802068352699, 0.08617442846298218, 0.0495588555932045, 0.004837265703827143, -0.02035650797188282, -0.07061373442411423, -0.03647230938076973, -0.0402081161737442, -0.027625421062111855, -0.0334523543715477, 0.006192917004227638, -0.029007066041231155, -0.053111039102077484, -0.01803216151893139, -0.07393119484186172, 2.760210691121756e-07, 0.0030413824133574963, 0.05870732292532921, -0.016032343730330467, 0.004172480199486017, 0.026132849976420403, -0.021060124039649963, 0.01420009508728981, -0.00876338966190815, -0.031312424689531326, -0.07090181857347488, 0.011576104909181595, 0.006338843610137701, 0.006740476470440626, 0.029026832431554794, -0.048816606402397156, 0.006887511815875769, -0.042457759380340576, 0.01440064050257206, -0.04932323843240738, 0.010090623050928116, -0.013783767819404602, 0.03567594662308693, 0.060652002692222595, 0.020412549376487732, 0.020940309390425682, 0.005803863983601332, 0.02200615406036377, -0.027321122586727142, -0.06560129672288895, 0.028697190806269646, 0.008798965252935886, -0.03864581510424614, -0.04066234827041626, 0.012166679836809635, -0.03030708059668541, -0.0017951835179701447, -0.05099206790328026, 0.015733938664197922, 0.030009370297193527, 0.08934712409973145, -0.002203160896897316, -0.050413113087415695, 0.037900615483522415, -0.01379962358623743, 0.07032451778650284, -0.007933259010314941, -0.017388705164194107, -0.03598681837320328, 0.014104954898357391, 0.012377169914543629, 0.02092648856341839, 0.01825850084424019, -0.020665336400270462, 0.024732783436775208, -0.05285831540822983, -0.008645092137157917, 0.03558548539876938, 0.01148783415555954, 0.0469776950776577, 0.0374482236802578, -0.03137525916099548, -0.09825584292411804, 0.03716832771897316, 0.03665821999311447, 0.13969075679779053, 0.03805018588900566, 0.012564625591039658, 2.8373605095568354e-34, 0.01261154469102621, 0.031066713854670525, 0.002824893919751048, -0.0276612751185894, 0.000973486399743706, -0.014021839015185833, -0.023064028471708298, -0.033667851239442825, 0.016797268763184547, -0.058047596365213394, -0.02238345518708229]

['Brendan Juba']

0910.3713v1

We examine the complexity of learning the distributions produced by finite-state quantum sources. We show how prior techniques for learning hidden Markov models can be adapted to the quantum generator model to find that the analogous state of affairs holds: information-theoretically, a polynomial number of samples suffice to approximately identify the distribution, but computationally, the problem is as hard as learning parities with noise, a notorious open question in computational learning theory.

On Learning Finite-State Quantum Sources

http://arxiv.org/pdf/0910.3713v1

Title Learning FiniteState Quantum Sources Summary examine complexity learning distribution produced finitestate quantum source show prior technique learning hidden Markov model adapted quantum generator model find analogous state affair hold informationtheoretically polynomial number sample suffice approximately identify distribution computationally problem hard learning parity noise notorious open question computational learning theory Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04062831401824951, 0.026398353278636932, -0.03489036113023758, 0.0280333012342453, -0.05865168571472168, -0.027205293998122215, -0.04476537927985191, 0.03672144189476967, -0.015081299468874931, -0.011899416334927082, 0.0114328907802701, 0.003227982670068741, -0.019630063325166702, 0.02226361632347107, 0.041197389364242554, 0.010046626441180706, 0.03316481038928032, 0.02987915836274624, -0.09310111403465271, -0.06516856700181961, -0.03481012210249901, -0.08669336140155792, -0.008891553618013859, 0.0138412369415164, 0.02699429914355278, 0.004074025899171829, -0.029725071042776108, -0.0043858373537659645, -0.025043150410056114, -0.0410163551568985, -0.05203049257397652, -0.011492319405078888, -0.007406633347272873, -0.008946911431849003, 2.069060656140209e-06, -0.035837654024362564, -0.034352339804172516, 0.016362588852643967, -0.007716943975538015, -0.00965572614222765, -0.059261709451675415, -0.017295949161052704, -0.024898646399378777, -0.022944869473576546, -0.03215900436043739, 0.007406746502965689, 0.05894492194056511, 0.01711347885429859, -0.004622886888682842, 0.045882344245910645, -0.013679596595466137, 0.006048952229321003, 0.009197387844324112, -0.020856399089097977, 0.01667565479874611, -0.06755875051021576, 0.0342225655913353, -0.01929202489554882, -0.02333998866379261, -0.0366382896900177, -0.0333511084318161, -0.013410976156592369, 0.03315327689051628, -0.0003364408330526203, 0.035225559026002884, 0.01248997449874878, 0.06460891664028168, 0.06328606605529785, -0.03967633470892906, 0.08424369990825653, -0.012827993370592594, -0.01168245542794466, -0.017272617667913437, 0.0034946086816489697, -0.05540413782000542, 0.03867626190185547, 0.009029574692249298, 0.007964923046529293, -0.023858070373535156, 0.06043534725904465, 0.010687563568353653, -0.015142411924898624, 0.002000145148485899, -0.0019624591805040836, 0.018098652362823486, 0.06191311776638031, 0.023637231439352036, -0.023959778249263763, -0.003117230487987399, -0.020214859396219254, -0.03237262740731239, 0.015995047986507416, 0.010915583930909634, -0.02249564230442047, 0.0373053140938282, 0.005180463660508394, 0.006755214184522629, 0.020915469154715538, -0.002838457701727748, -0.0015754547202959657, 0.008627633564174175, 0.022307518869638443, -0.002467511221766472, 0.014004601165652275, 0.010305609554052353, -0.03754447028040886, -0.024669090285897255, -0.011109360493719578, -0.040578026324510574, 0.03915328532457352, -0.03287634998559952, 0.0367201492190361, -0.0071078198961913586, 0.06962963938713074, 0.02012842707335949, -0.06266184151172638, -0.08825568109750748, -0.001872274442575872, 0.01169534120708704, 0.0010087598348036408, -0.0008297934546135366, 0.013421609997749329, -0.01692809723317623, -0.0015712847234681249, -0.018005209043622017, 0.036231983453035355, -0.0007222526473924518, 0.021398501470685005, -0.056063827127218246, -0.015260248444974422, -0.04126434400677681, 0.02312355861067772, -0.0002381119702477008, 0.032468032091856, -0.07091069221496582, 0.027276689186692238, 0.008585643023252487, -0.03867426514625549, 0.013492396101355553, 0.02814168483018875, -0.014964664354920387, 0.0015048112254589796, 0.004781672731041908, -0.033191900700330734, -0.026487868279218674, 0.021001022309064865, 8.38244377519004e-05, -0.04395043104887009, 0.03222760185599327, -0.07355358451604843, 0.004159853793680668, 0.038110606372356415, 0.007255694828927517, -0.051851049065589905, 0.05887505039572716, 0.040744125843048096, 0.04190627485513687, 0.0154280886054039, -0.02520478330552578, 0.022849611937999725, 0.0006066728965379298, -0.026344969868659973, 0.0583127923309803, -0.02434934861958027, 0.06397755444049835, 0.0022891107946634293, -0.04958998039364815, -0.038873229175806046, -0.03135675564408302, -0.022312575951218605, -0.007509666960686445, 0.06909427046775818, -0.04090499505400658, -0.01003732718527317, -0.022073201835155487, 0.08456336706876755, 0.03401687368750572, 0.04144907370209694, -0.00883819442242384, 0.01303396187722683, 0.010989278554916382, 0.03669775649905205, -0.005517102312296629, 0.06653265655040741, -0.04623771831393242, -0.00567694753408432, 0.050748828798532486, -0.06816776096820831, -0.03602977469563484, -0.05113139748573303, -0.007415276486426592, -0.028374558314681053, -0.013890382833778858, -0.0640304833650589, 0.08226074278354645, 0.03574742376804352, -0.0329509861767292, 0.021107973530888557, 0.02296939492225647, -0.010426760651171207, 0.008218266069889069, -0.0633450299501419, 0.0806431919336319, -3.967200825627515e-07, 0.01771629974246025, -0.04069388657808304, 0.06243550032377243, 0.02177603170275688, -0.06896178424358368, -0.01280138734728098, -0.009345640428364277, -0.013077530078589916, 0.04691595211625099, 0.013151734136044979, -0.021367797628045082, 0.010558868758380413, 0.013907150365412235, 0.0024062921293079853, 0.010782793164253235, -0.042175181210041046, 0.015907464548945427, 0.004446235951036215, -0.005106288939714432, -0.01096207182854414, -0.024958226829767227, -0.046937402337789536, 0.056923408061265945, 0.014927509240806103, 0.03405018150806427, -0.013103057630360126, -0.024975469335913658, 0.03970981761813164, 0.010918772779405117, -0.014131109230220318, -0.02275947295129299, -0.03586442396044731, -0.009145609103143215, 0.007386813871562481, 0.030862441286444664, -0.05461360141634941, 0.10738126933574677, -0.01707281731069088, 0.014124923385679722, -0.020255552604794502, 0.0816456601023674, 0.0014435884077101946, 0.013737400993704796, -0.04561721906065941, -0.0599188394844532, 0.027882855385541916, 0.04801999777555466, -0.0013751874212175608, 0.06977978348731995, -0.017280977219343185, 0.0766167864203453, -0.03994611278176308, 0.0024220210034400225, 0.01339568942785263, -0.049832046031951904, 0.03265281766653061, -0.06105155497789383, -0.041650861501693726, -0.029219867661595345, 0.009216124191880226, -0.005206373054534197, 0.018106840550899506, 0.01385406032204628, -0.009729202836751938, -0.02693885564804077, -0.029176803305745125, -0.008594818413257599, 0.019538098946213722, -0.029902391135692596, 0.0188067015260458, -0.028705773875117302, -0.017563369125127792, -0.01818188652396202, 0.01599053665995598, -0.06229596585035324, 0.00010521584044909105, 0.005307755898684263, -0.00484582781791687, -0.061297930777072906, -0.01492974255234003, -0.014810786582529545, -0.003637707093730569, -0.03612329810857773, 0.008008555509150028, -0.05582430586218834, 0.05314754322171211, 0.02738918922841549, 0.012420249171555042, -0.021031387150287628, -0.006779357325285673, 0.001137219020165503, -0.051768023520708084, 0.005657265894114971, 0.0384046845138073, 0.06734251230955124, 0.027919238433241844, 0.03630232438445091, 0.08469271659851074, -0.010427665896713734, -0.016116410493850708, -0.07384743541479111, 0.03079800121486187, 0.010506715625524521, -0.015542399138212204, 0.03923555463552475, 0.008202954195439816, 0.04339572787284851, 0.0097882691770792, -0.013417558744549751, 0.009425335563719273, -0.028221210464835167, -0.03810939937829971, -0.029423750936985016, 0.027257902547717094, 0.006300576962530613, -0.003751389216631651, 0.011732026003301144, -0.0060007767751812935, 0.06322721391916275, 0.016413269564509392, 0.04889010637998581, -0.029630377888679504, -0.04833318293094635, 0.04017705097794533, -0.039386484771966934, -0.005361632443964481, 0.0806426852941513, -0.08680978417396545, 0.03424939885735512, 0.0233767107129097, -0.035465944558382034, 0.034591786563396454, -0.016270766034722328, -0.049165431410074234, 0.03554346412420273, -0.0074205645360052586, -0.01634271629154682, -0.03100830875337124, -0.0037108175456523895, 0.010012578219175339, 0.03886447474360466, -0.01071892399340868, -0.028201252222061157, 0.023504693061113358, 0.06680209934711456, -0.02717973291873932, 0.022745409980416298, 0.04174399748444557, -0.008717193268239498, -0.02770468033850193, 0.004152141511440277, 0.05286863073706627, 0.029447924345731735, -0.03613273799419403, 0.047256939113140106, -0.005215045530349016, 0.05528317764401436, 0.022369494661688805, 0.03091094084084034, 0.08667417615652084, -0.009957762435078621, -0.021324560046195984, 0.03832188993692398, -0.015909451991319656, 0.017924370244145393, 0.06141131743788719, -0.0014829180436208844, 0.02267327718436718, -0.007782460190355778, -0.009204110130667686, 0.018825216218829155, -0.035488300025463104, 0.015398848801851273, 0.0276300348341465, -0.11281737685203552, 0.012572990730404854, 0.001538337441161275, -0.07103724777698517, 0.03737138211727142, -0.045777007937431335, 0.025888703763484955, -0.010342932306230068, 0.0031924331560730934, -0.012944304384291172, -0.026961706578731537, -0.011990781873464584, 0.02446603775024414, 0.014113863930106163, -0.04935724288225174, -0.04410789534449577, 0.009152520447969437, -0.025200724601745605, -0.008187645114958286, 0.026640648022294044, -0.007121588569134474, 0.004756275564432144, 0.050564706325531006, 0.0009885417530313134, -0.0117489043623209, -0.023222407326102257, -0.001430726028047502, -0.009209820069372654, 0.033288151025772095, 0.002658449811860919, -0.040578048676252365, -0.08380555361509323, -0.051354456692934036, -0.035067908465862274, -0.010231859982013702, -0.01718887686729431, 0.0017275819554924965, 0.07117567211389542, -0.026167532429099083, -0.009705880656838417, 0.05936300382018089, 0.028052419424057007, 0.0010963344248011708, 0.007102431263774633, -0.005796800367534161, -0.01187511533498764, 0.03158162906765938, 0.04670703411102295, 0.0031515927985310555, 0.030102957040071487, 0.017063681036233902, -0.0379764623939991, 0.0016565786208957434, -0.036680418998003006, -0.0031998164486140013, 0.08234494179487228, -0.019704952836036682, -0.0002574667742010206, -0.02998722344636917, 0.020682144910097122, -0.03921600431203842, -0.12695515155792236, 0.0703730583190918, -0.06172509491443634, 0.051612257957458496, 0.023290282115340233, 0.002504626289010048, 0.046844229102134705, -0.03135012462735176, 0.01960454136133194, -0.058120641857385635, 0.01753326877951622, -0.045457761734724045, -0.05957777425646782, -0.06005954369902611, 0.031027797609567642, -0.08748915046453476, -0.007362356875091791, -0.07027227431535721, -0.002559117041528225, -0.03747928887605667, 0.027141083031892776, 0.028221748769283295, 0.007184373680502176, -0.04234401136636734, 0.03024045005440712, 0.01754063554108143, 0.019891763105988503, 0.021174583584070206, -0.011199160479009151, 0.010605724528431892, 0.021923987194895744, 0.032621804624795914, -0.03560373932123184, 0.016016900539398193, 0.009869375266134739, 0.019189996644854546, 0.02486133947968483, 0.022053943946957588, -0.0899319276213646, -0.03392616659402847, 0.026640627533197403, -0.02036762610077858, 0.07216522842645645, 0.025200527161359787, 0.04660680145025253, 0.009141899645328522, 0.013911072164773941, -0.010962539352476597, 0.04641544818878174, -0.06458403170108795, 0.013798284344375134, 0.0652792751789093, 0.008579997345805168, 0.03467553108930588, -0.021097149699926376, 0.08197810500860214, -0.0063319941982626915, -0.0062148915603756905, -0.007287426386028528, 0.030647268518805504, -0.012091265060007572, -0.011867210268974304, -0.017372433096170425, -0.017704254016280174, 0.030168062075972557, 0.030448270961642265, 0.04019469395279884, -0.008073298260569572, 0.07870950549840927, -0.011498476378619671, -0.006293176207691431, -0.019048338755965233, 0.007858740165829659, -0.06839799135923386, -0.04023128002882004, -0.006116792559623718, 0.07026127725839615, 0.07840358465909958, 0.052182480692863464, -0.003679287154227495, -0.02410455234348774, -0.006564939394593239, -0.02326091006398201, 0.10452655702829361, 0.01290110033005476, -0.0035390141420066357, 0.022753583267331123, 0.01978030800819397, -0.036529265344142914, -0.007789970375597477, 0.05177205428481102, 0.0801028460264206, 0.03800957649946213, -0.049552954733371735, 0.020730795338749886, -0.012928444892168045, 0.012612288817763329, -0.03149738162755966, 0.044230006635189056, -0.0011317464523017406, 0.0644136592745781, -0.014566640369594097, 0.016042103990912437, 0.018446726724505424, 0.0007103336392901838, -0.004062032792717218, -0.023310326039791107, 0.04174460098147392, 0.02610260434448719, -0.02161143161356449, -0.037804413586854935, -0.036114294081926346, -0.055432453751564026, 0.07225032895803452, -0.008986041881144047, -0.01351429894566536, -5.827376592983207e-33, -0.05223051831126213, -0.019966401159763336, -0.008987789042294025, 0.0263459924608469, 0.05429047718644142, -0.009446239098906517, -0.007961871102452278, -0.03009333461523056, 0.008786292746663094, -0.0702504962682724, 0.012046238407492638, 0.039947230368852615, 0.015439231880009174, -0.002906359499320388, -0.018436862155795097, 0.008426117710769176, 0.030017297714948654, 0.041014909744262695, 0.01168668083846569, 0.027953192591667175, 0.04607425630092621, -0.02230612374842167, 0.04396071657538414, 0.007163916248828173, -0.046925731003284454, 0.039051756262779236, -0.009464098140597343, 0.02659391611814499, -0.009512534365057945, -0.012655927799642086, -0.04176260158419609, -0.02441975846886635, -0.06475208699703217, -0.01587178371846676, 0.046435657888650894, -0.09000398963689804, -0.002901165746152401, 0.014640755951404572, 0.0029060898814350367, -0.04537418484687805, 0.001218178658746183, 0.003197278594598174, -0.029516451060771942, 0.013946779072284698, -0.06726507097482681, 0.02569473162293434, 0.010251116007566452, 0.01365223340690136, -0.020922772586345673, -0.0662011057138443, 0.0027588815428316593, -0.007541302125900984, -0.022329235449433327, 0.023000067099928856, -0.0001575065398355946, -0.03399674594402313, -0.04482161998748779, -0.0942138135433197, 0.00046576670138165355, 0.06786467134952545, 0.05118174850940704, 0.07257156819105148, 0.0041357059963047504, -0.0020436865743249655, 0.04509761556982994, 0.0067182076163589954, 0.04678715020418167, -0.03562138229608536, -0.019295359030365944, -0.037895865738391876, -0.008823055773973465, 0.010456579737365246, -0.00401795981451869, 0.0025731693021953106, 0.06068440526723862, -0.09748058766126633, -0.0530572272837162, 0.004445947706699371, 0.08442436158657074, 0.016067933291196823, 0.041677165776491165, -0.02629057690501213, -0.012793166562914848, -0.04335424676537514, 0.026814904063940048, 0.031493667513132095, 0.03692198544740677, 0.012580604292452335, 0.011801384389400482, 0.04439929872751236, -0.015008894726634026, -0.03396618738770485, 0.04346511885523796, -0.030738279223442078, 0.012673646211624146, 0.04930603876709938, 0.027530113235116005, -0.015823351219296455, -0.027248043566942215, -0.08516955375671387, -0.0245515163987875, -0.027212494984269142, 0.014863047748804092, -0.014290178194642067, -0.021095501258969307, 0.057164374738931656, -0.00931368488818407, 0.014417437836527824, -0.02673671953380108, 0.01429564319550991, -0.008794717490673065, -0.014445590786635876, 0.02917572855949402, -0.0188122671097517, 0.01920521818101406, -0.010025893338024616, -0.02560817450284958, 0.022027762606739998, 0.0016417652368545532, 0.03702973946928978, -0.014688902534544468, 0.009151251055300236, -0.011259370483458042, 0.08497167378664017, -0.030742216855287552, -0.020451439544558525, -0.07389217615127563, 0.017675835639238358, 0.02046770043671131, -0.052243199199438095, -0.022164562717080116, 0.007306247483938932, 2.5922852842086286e-07, -0.027956118807196617, -0.03088780865073204, -0.062102463096380234, -0.036839503794908524, 0.02179020643234253, -0.05612600967288017, -0.012773590162396431, -0.012133984826505184, -0.02163543365895748, 0.021131422370672226, 0.00562211824581027, -0.005882876925170422, -0.017097290605306625, 0.024333352223038673, -0.03254750370979309, -0.04820750653743744, -0.03479654714465141, 0.029826948419213295, 0.03582540154457092, 0.019180364906787872, 0.01158920768648386, 0.05104760453104973, 0.02884856052696705, 0.05119815468788147, 0.03790067136287689, -0.021351169794797897, 0.07695312798023224, 0.07411056756973267, 0.04640267789363861, 0.011126389726996422, -0.011967659927904606, -0.027431702241301537, 0.0316811166703701, -0.048652052879333496, 0.009398423135280609, 0.013187614269554615, -0.02072129026055336, -0.012193921022117138, 0.0500219352543354, -0.03457679972052574, -0.05928431451320648, 0.043481145054101944, 0.03449363261461258, 0.04258076101541519, 0.01281130313873291, 0.0303040761500597, 5.620185038424097e-05, -0.02135883830487728, -0.04544698819518089, 0.02760317549109459, -0.02163698524236679, 0.027156006544828415, 0.012207948602735996, -0.05249422416090965, -0.07738059014081955, 0.008015722967684269, 0.07529491931200027, 0.021099187433719635, -0.019138861447572708, -0.00022451896802522242, 0.03543572127819061, -0.0633930116891861, 0.007209926377981901, -0.034803103655576706, 0.017199525609612465, 0.018900979310274124, -0.022257743403315544, 2.5308900764320123e-34, -0.032275330275297165, -0.0052855126559734344, 0.02004098705947399, 0.021494898945093155, -0.03331676125526428, -0.003778699319809675, -0.027954529970884323, -0.034956879913806915, 0.014570368453860283, 0.024057190865278244, 0.0038012261502444744]

['Raghunandan H. Keshavan', 'Sewoong Oh']

0910.5260v2

We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local manifold optimization, for solving the low-rank matrix completion problem. It has been shown that if the number of revealed entries is large enough, the output of singular value decomposition gives a good estimate for the original matrix, so that local optimization reconstructs the correct matrix with high probability. We present numerical results which show that this algorithm can reconstruct the low rank matrix exactly from a very small subset of its entries. We further study the robustness of the algorithm with respect to noise, and its performance on actual collaborative filtering datasets.

A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion

http://arxiv.org/pdf/0910.5260v2

Title Gradient Descent Algorithm Grassman Manifold Matrix Completion Summary consider problem reconstructing lowrank matrix small subset entry paper describe implementation efficient algorithm called OptSpace based singular value decomposition followed local manifold optimization solving lowrank matrix completion problem shown number revealed entry large enough output singular value decomposition give good estimate original matrix local optimization reconstructs correct matrix high probability present numerical result show algorithm reconstruct low rank matrix exactly small subset entry study robustness algorithm respect noise performance actual collaborative filtering datasets Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.012535160407423973, 0.004797298926860094, 0.0032052230089902878, 0.035979826003313065, 0.01471778191626072, -0.03163836896419525, -0.01252596452832222, 0.04568515345454216, 0.0598321370780468, 0.030912531539797783, -0.0045005097053945065, 0.041569385677576065, 0.03789518028497696, -0.01075640507042408, 0.0031119659543037415, -0.04327104613184929, -0.026740480214357376, 0.006199972704052925, -0.08216354995965958, -0.08316905051469803, 0.010573330335319042, -0.008891045115888119, 0.023484298959374428, 0.015001341700553894, -0.02017541229724884, -0.011721336282789707, 0.0057804337702691555, -0.0038207094185054302, -0.005675888154655695, 0.0015424044104292989, -0.015537327155470848, -0.011611554771661758, 0.04761767014861107, 0.018460649996995926, 2.248053533548955e-06, 0.009786956012248993, -0.02401401288807392, -0.023642703890800476, 0.04558549076318741, -0.013582155108451843, -0.010035856626927853, 0.04175814613699913, 0.015191115438938141, 0.005339992698282003, -0.019139224663376808, -0.02353297732770443, -0.023825572803616524, -0.0018603125354275107, 0.028413083404302597, 0.00824143085628748, -0.012185346335172653, -0.04546089097857475, -0.02853969857096672, -0.025291472673416138, -0.018868185579776764, -0.04986779764294624, 0.04139226675033569, -0.002329779788851738, -0.01322861947119236, -0.02921738661825657, -0.044993285089731216, 0.029612917453050613, -0.017676856368780136, 0.010516050271689892, 0.09205543249845505, 0.038312848657369614, 0.05783228576183319, -0.0025726412422955036, -0.0057562412694096565, 0.039334479719400406, -0.020516378805041313, 0.011579344049096107, 0.01726633310317993, 0.013346666470170021, 0.029442256316542625, -0.007618833798915148, -0.03604663163423538, -0.01233966089785099, 0.002273505786433816, 0.020921969786286354, -0.0853692814707756, -0.025079546496272087, -0.007056748028844595, -0.0016686345916241407, 0.013568134047091007, 0.11950615048408508, 0.020090797916054726, 0.004157498013228178, -0.039877116680145264, -0.007398005574941635, 0.023750418797135353, 0.00036462387652136385, 0.05803133174777031, -0.010133308358490467, -0.05155569314956665, -0.03231550008058548, -0.007488469127565622, -0.06516849994659424, -0.0031483741477131844, -0.02554255910217762, 0.07942220568656921, -0.023533347994089127, 0.06490103900432587, 0.026834310963749886, -0.008458541706204414, 0.023961620405316353, -0.060711558908224106, 0.021485166624188423, -0.03564458340406418, 0.007168550975620747, 0.012032990343868732, -0.0013239486142992973, 0.035219088196754456, 0.09773816168308258, -0.002401199424639344, 0.019595565274357796, -0.06601258367300034, 0.012185107916593552, -0.023178933188319206, 0.044106677174568176, -0.01336238719522953, 0.05893906578421593, -0.0001495928008807823, -0.0441942997276783, -0.05929988622665405, -0.0013285952154546976, -0.01746806688606739, 0.05153639614582062, -0.058199796825647354, 0.0970185250043869, 0.00289817713201046, 0.004163558594882488, 0.014677782543003559, -0.0070411828346550465, 0.03429035469889641, 0.008724091574549675, -0.006272448692470789, 0.030523434281349182, 0.014502818696200848, 0.0008031322504393756, -0.02973211370408535, -0.04748305678367615, -0.03763177618384361, -0.04617466405034065, 0.029965568333864212, -0.017080694437026978, 0.031041357666254044, -0.0011587671469897032, -0.006527170538902283, -0.019451728090643883, -0.07085910439491272, 0.05274735391139984, -0.005695566534996033, 0.004105399362742901, 0.0532657764852047, -0.024148274213075638, 0.024195976555347443, -0.05554763600230217, -0.021686328575015068, 0.10992221534252167, 0.015254425816237926, -0.0253612007945776, -0.006460544187575579, -0.017183640971779823, 0.0034587073605507612, -0.03857119008898735, -0.038576189428567886, -0.022144827991724014, -0.019910212606191635, -0.008261469192802906, 0.008399998769164085, 0.03562694787979126, 0.0036278252955526114, -0.02856753207743168, 0.014965999871492386, 0.05792217329144478, 0.06529710441827774, 0.05838451534509659, -0.0136769013479352, 0.035100411623716354, -0.03696070611476898, 0.04037727415561676, 0.04410882294178009, 0.0606592632830143, -0.02350030653178692, -0.04339004307985306, 0.042076680809259415, 0.026320073753595352, -0.016239214688539505, -0.01789565198123455, 0.0360913909971714, -0.022638441994786263, -0.015462557785212994, 0.017065009102225304, 0.09981278330087662, -0.021301640197634697, -0.040373295545578, -0.07791528105735779, 0.022571690380573273, -0.026662200689315796, 0.00014170476060826331, 0.004740711767226458, 0.09021267294883728, -0.03379189223051071, 0.016004623845219612, -0.038908883929252625, 0.0475449413061142, -0.01672111265361309, -0.02968866564333439, -0.10977443307638168, -0.06043390557169914, -0.0013161435490474105, -0.01733505353331566, 0.002295625628903508, -0.025405611842870712, 0.06279166042804718, -0.0013961949152871966, 0.02045556716620922, -0.03558780625462532, -0.032174065709114075, -0.009036167524755001, -0.014533829875290394, 0.004983704537153244, 0.018359998241066933, 0.04160546883940697, 0.039410002529621124, 0.06928794831037521, 0.008697903715074062, 0.05892260745167732, 0.027418507263064384, 0.04887046292424202, -0.05614432692527771, 0.05357235297560692, -0.007800545077770948, -0.03268018737435341, -0.07576552778482437, 0.02874377742409706, -0.019018979743123055, 0.03785926103591919, -0.06326655298471451, 0.021113282069563866, 0.11707387119531631, 0.00806721393018961, -0.059625934809446335, 0.016886811703443527, -0.018451901152729988, -0.08935580402612686, -0.05213828757405281, 0.0009139301837421954, -0.0150203388184309, 0.01051690336316824, 0.007736481260508299, 0.05672468990087509, -0.022750701755285263, 0.015645276755094528, 0.014753374271094799, -0.021334301680326462, 0.018122859299182892, -0.02875801920890808, -0.02615077793598175, 0.009292949922382832, -0.023352524265646935, 0.0038776216097176075, 0.008433517999947071, 0.00549775967374444, 0.01331411860883236, -0.0023472656030207872, -0.025129692628979683, 0.011422405019402504, 0.01037407387048006, -0.026153098791837692, 0.0022394508123397827, -0.0016373303951695561, 0.06481403112411499, -0.05304590240120888, 0.019862791523337364, 0.0944547951221466, -0.016264626756310463, -0.0478396862745285, 0.042144060134887695, 0.01349526084959507, 0.0031290564220398664, 0.0015167688252404332, -0.014934581704437733, 0.014318641275167465, 0.02291625179350376, -0.03289059177041054, -0.032631248235702515, -0.01967858336865902, 0.03840199112892151, -0.007464003749191761, 0.001824257313273847, -0.021901266649365425, -0.0378803089261055, -0.043239887803792953, 0.018214449286460876, 0.030346473678946495, 0.03206583485007286, 0.01837545819580555, 0.007584971841424704, 0.05848725885152817, 0.05992930755019188, -0.0067528653889894485, 0.006073752883821726, -0.05407872423529625, 0.004388116300106049, 0.04285072162747383, 0.04114433377981186, -0.01628238335251808, -0.04811534285545349, 0.011647646315395832, -0.012868826277554035, -0.0073995827697217464, 0.006067323498427868, 0.0167847890406847, -0.017863484099507332, -0.10419147461652756, 0.032351668924093246, -0.04855284467339516, 0.011385169811546803, 0.006691950839012861, 0.006621242500841618, 0.012493493035435677, 0.012490679509937763, -0.025443973019719124, 0.012100119143724442, -0.026515237987041473, 0.018669933080673218, -0.06136411055922508, 0.005283973179757595, 0.009875178337097168, -0.09712424129247665, -0.0035851080901920795, -0.02055840566754341, 0.03866950049996376, 0.015341725200414658, -0.05352130904793739, -0.04314437881112099, 0.04358688369393349, 0.001377844368107617, 0.007404028903692961, -0.028432223945856094, -0.011656076647341251, -0.008475708775222301, 0.06509777158498764, -0.04937838762998581, 0.0008922486449591815, 0.005845549516379833, 0.02703186497092247, -0.0354149304330349, 0.012775681912899017, 0.01084891613572836, -0.03685201704502106, 0.0034120846539735794, 0.00763979647308588, 0.04433804377913475, -0.0025123278610408306, -0.014291344210505486, -0.011643556877970695, -0.021024350076913834, 0.05333629250526428, 0.04981086030602455, 0.050014954060316086, -0.013910687528550625, -0.025792649015784264, 0.006163747515529394, 0.03193150833249092, 0.058591827750205994, -0.0068998783826828, 0.03721156343817711, 0.005370536353439093, -0.005755582358688116, 0.04781140014529228, -0.0051185027696192265, -0.010210047475993633, -0.09783115983009338, -0.02759486623108387, -0.004181576892733574, 0.0037309913896024227, 0.04378322884440422, 0.008275902830064297, 0.011331571266055107, 0.058314815163612366, -0.0023513464257121086, 0.034774914383888245, 0.029472991824150085, -0.003219590289518237, 0.03786967322230339, -0.01713504083454609, 0.06450466811656952, 0.02102874219417572, -0.0036368579603731632, -0.014364221133291721, -0.03462522104382515, 0.0009378507384099066, 0.012240155600011349, -0.02033098228275776, 0.021850407123565674, -0.009828283451497555, -0.02165036089718342, 0.0018906493205577135, -0.056564368307590485, -0.019445795565843582, -0.01621616631746292, -0.014046026393771172, 0.0007634630310349166, -0.03239268437027931, 0.05089443176984787, -0.03713005781173706, -0.0256304033100605, -0.015267545357346535, 0.046986740082502365, -0.021500442177057266, -0.05695786699652672, 0.05425800010561943, 0.01466692890971899, -0.011003181338310242, -0.034371137619018555, 0.08377354592084885, -0.002758623566478491, 0.041422683745622635, -0.011501166969537735, 0.06345372647047043, -0.02216644026339054, -0.003543557832017541, 0.018000861629843712, -0.03277834132313728, -0.04576987028121948, -0.012125520035624504, -0.02272455208003521, -0.022547980770468712, -0.00874540489166975, 0.005211225710809231, 0.044659387320280075, 0.034852284938097, -0.03524956479668617, 0.029559634625911713, -0.030399462208151817, -0.03534574434161186, -0.015722226351499557, 0.03069356642663479, 0.05013721063733101, 0.04618239402770996, -0.014471562579274178, 0.034436069428920746, -0.021208375692367554, -0.03582455590367317, -0.018766356632113457, -0.015281984582543373, 0.008490440435707569, 0.023956961929798126, 0.02535324916243553, 0.0011591570219025016, 0.015909912064671516, -0.0322490893304348, -0.028120752424001694, -0.08255641907453537, -0.01833437755703926, -0.006584439426660538, -0.049567706882953644, 0.05302216112613678, 0.0032554713543504477, 0.010387470945715904, -0.0196841973811388, -0.055786557495594025, 0.010900299996137619, -0.0001499197824159637, 0.039037078619003296, 0.04832024872303009, 0.017700809985399246, -0.029373010620474815, -0.014574672095477581, 0.039960477501153946, -0.014239056035876274, 0.0009488263167440891, 0.03117074817419052, -0.033658258616924286, -0.01277702022343874, 0.07305804640054703, 0.0287780798971653, 0.005289670079946518, 0.05212332680821419, 0.012528161518275738, -0.043657634407281876, -0.03167686238884926, 0.016576094552874565, -0.046552032232284546, -0.03163107484579086, 0.007235382683575153, -0.00712560722604394, 0.017281554639339447, 0.031230829656124115, -0.023124583065509796, -0.04944344609975815, 0.02771706134080887, 0.011794962920248508, -0.075213722884655, -0.03401840850710869, 0.001996307633817196, -0.04800019413232803, 0.017378689721226692, 0.048325587064027786, -0.003317944472655654, -0.033035509288311005, 0.05780680850148201, 0.008623740635812283, 0.020075833424925804, -0.04263163357973099, -0.0017199983121827245, 0.02097383141517639, -0.04865117371082306, 0.0008833666215650737, 0.01323741115629673, -0.03558267652988434, -0.043078649789094925, 0.01991111971437931, 0.08049662411212921, 0.02832314930856228, 0.004314122721552849, 0.0466189906001091, -0.0036748340353369713, -0.04874105378985405, 0.016128061339259148, -0.01116222981363535, -0.005163715686649084, 0.03285016492009163, -0.027875293046236038, -0.006823115050792694, 0.0725659728050232, 0.0854596346616745, 0.007385373115539551, -0.04208165407180786, -0.026232080534100533, -0.030904356390237808, -0.05239439383149147, 0.02860507182776928, -0.027403827756643295, 0.11854749172925949, -0.025879302993416786, -0.003815250936895609, 0.017562009394168854, -0.032059818506240845, 0.004057895392179489, -0.055376335978507996, 0.016371099278330803, -0.011961759999394417, 0.004385513719171286, 0.013485689647495747, -0.02169172093272209, 0.0402810201048851, -0.04152347892522812, -0.03813239187002182, 0.027858473360538483, -0.032124076038599014, -0.01597200706601143, -6.176190582594305e-33, -0.02563420869410038, -0.057114921510219574, -0.0768299475312233, 0.012061920948326588, -0.0210300013422966, -0.029662687331438065, 0.003040449693799019, 0.024467315524816513, 0.057132694870233536, 0.02426476776599884, -0.03242110833525658, 0.008541888557374477, 0.005687565542757511, 0.013185416348278522, 0.024452369660139084, 0.0448254831135273, 0.02710229530930519, -0.0052155060693621635, 0.0018922287272289395, 0.009896538220345974, 0.028113044798374176, 0.06627996265888214, -0.006642801687121391, -0.06923668086528778, -0.07691831886768341, 0.00968807004392147, -0.02120831236243248, -0.037844013422727585, -0.011191904544830322, -0.019243504852056503, -0.04422895610332489, 0.03144451230764389, 0.031010987237095833, 0.018504619598388672, -0.02150031365454197, -0.029719172045588493, -0.018015561625361443, 0.03680167347192764, -0.022146929055452347, -0.006773113738745451, -0.05034589767456055, 0.01030983030796051, 0.030743267387151718, 0.029678355902433395, -0.05036154016852379, -0.0174027681350708, 0.06046559289097786, -0.022340133786201477, -0.038550667464733124, -0.03210525959730148, 0.03534999489784241, -0.0015178980538621545, -0.000683323189150542, 0.0021343794651329517, 0.06537643820047379, 0.013899975456297398, -0.03560313209891319, 0.02948899194598198, -0.006378608290106058, 0.020172972232103348, -0.07299825549125671, 0.041962724179029465, -0.004466329235583544, -0.02712448127567768, -0.027560889720916748, 0.03803038224577904, 0.023428376764059067, -0.015752825886011124, -0.013862157240509987, -0.0369853675365448, -0.020248427987098694, 0.026207566261291504, 0.008439799770712852, 0.02089739218354225, -0.007951261475682259, -0.0668504536151886, -0.031492892652750015, 0.05230359733104706, -0.03169658035039902, 0.03145236894488335, 0.03875317424535751, 0.036938343197107315, 0.015773341059684753, -0.022107413038611412, 0.020961346104741096, -0.035783253610134125, -0.028661120682954788, 0.01617252267897129, -0.001564372912980616, 0.009479131549596786, -0.04280365630984306, -0.026701131835579872, -0.019693955779075623, -0.03973318636417389, 0.024539977312088013, -0.06538061797618866, -0.005946919787675142, 0.03076622635126114, 0.05069873481988907, -0.03750576078891754, 0.012176874093711376, 0.006766375154256821, -0.021063726395368576, -0.02626354992389679, -0.008169909007847309, -0.0046234577894210815, -0.047941941767930984, 0.011897851713001728, 0.011777417734265327, -0.005646914709359407, -0.009590058587491512, -0.08712050318717957, 0.004442221485078335, 0.03219112381339073, 0.01337975263595581, -0.004585918504744768, 0.0030096627306193113, 0.12227509170770645, 0.0009328066371381283, 0.11689426749944687, -0.020965972915291786, -0.10523562133312225, 0.014192532747983932, -0.00013459874026011676, -0.04103603586554527, -0.0131904948502779, -0.028363380581140518, -0.0175618939101696, 0.06379806250333786, 0.007833713665604591, -0.005353071726858616, -0.04959602653980255, 2.840597801423428e-07, -0.05449311435222626, 0.059134721755981445, -0.05957631394267082, -0.07601738721132278, -0.004844131413847208, 0.0022289843764156103, -0.01459091529250145, 0.049542512744665146, -0.016384681686758995, -0.031273458153009415, 0.023988302797079086, -0.07798586040735245, 0.03968800976872444, -0.018544556573033333, -0.06032254174351692, -0.013405583798885345, -0.05607839673757553, 0.021168455481529236, -0.02938062511384487, -0.03598228469491005, -0.020988520234823227, 0.04519250616431236, 0.04486275091767311, -0.02481711097061634, 0.007500409614294767, 0.07835466414690018, 0.032627202570438385, -0.018200531601905823, -0.011242534033954144, -0.051481686532497406, 0.04471125081181526, 0.005908961407840252, -0.014523458667099476, -0.008757799863815308, -0.0025086370296776295, 0.04666396975517273, 0.03251242637634277, -0.0028178810607641935, -0.01699989289045334, -0.0007904231897555292, 0.015015930868685246, 0.07676790654659271, 0.031054968014359474, -0.0515701025724411, 0.0115519929677248, 0.03505965322256088, -0.023151271045207977, -0.030092479661107063, -0.038050513714551926, 0.028768029063940048, 0.0263548381626606, -0.005475190933793783, 0.03538278490304947, 0.0059438287280499935, -0.01467637624591589, -0.0016076850006356835, 0.04255211725831032, -0.03799097239971161, 0.08700507134199142, 0.02053024433553219, -0.07269918918609619, -0.02890305034816265, 0.04152387008070946, 0.02584882825613022, 0.022408200427889824, 0.003985535819083452, -0.004511408973485231, 2.614733358948114e-34, -0.0001689469354460016, 0.02880113758146763, 0.006056143436580896, 0.04405954107642174, -0.045758895576000214, -0.03688163682818413, -0.01684136688709259, -0.008193771354854107, 0.008922901004552841, -0.04841744154691696, -0.030588064342737198]

['Frederic Thouin', 'Mark Coates', 'Michael Rabbat']

1001.1009v1

Knowing the largest rate at which data can be sent on an end-to-end path such that the egress rate is equal to the ingress rate with high probability can be very practical when choosing transmission rates in video streaming or selecting peers in peer-to-peer applications. We introduce probabilistic available bandwidth, which is defined in terms of ingress rates and egress rates of traffic on a path, rather than in terms of capacity and utilization of the constituent links of the path like the standard available bandwidth metric. In this paper, we describe a distributed algorithm, based on a probabilistic graphical model and Bayesian active learning, for simultaneously estimating the probabilistic available bandwidth of multiple paths through a network. Our procedure exploits the fact that each packet train provides information not only about the path it traverses, but also about any path that shares a link with the monitored path. Simulations and PlanetLab experiments indicate that this process can dramatically reduce the number of probes required to generate accurate estimates.

Multi-path Probabilistic Available Bandwidth Estimation through Bayesian Active Learning

http://arxiv.org/pdf/1001.1009v1

Title Multipath Probabilistic Available Bandwidth Estimation Bayesian Active Learning Summary Knowing largest rate data sent endtoend path egress rate equal ingres rate high probability practical choosing transmission rate video streaming selecting peer peertopeer application introduce probabilistic available bandwidth defined term ingres rate egress rate traffic path rather term capacity utilization constituent link path like standard available bandwidth metric paper describe distributed algorithm based probabilistic graphical model Bayesian active learning simultaneously estimating probabilistic available bandwidth multiple path network procedure exploit fact packet train provides information path traverse also path share link monitored path Simulations PlanetLab experiment indicate process dramatically reduce number probe required generate accurate estimate Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.011541265062987804, -0.008343292400240898, -0.01341888029128313, -0.03785132244229317, -0.06858315318822861, -0.02429545857012272, 0.015478917397558689, -0.022226354107260704, -0.03355409577488899, -0.0292286928743124, 0.04909469187259674, -0.00710442615672946, -0.012512819841504097, 0.0898139551281929, 0.013935853727161884, -0.03574391081929207, 0.030664915218949318, -0.008805114775896072, 0.02098987251520157, 0.004233414772897959, 0.015055365860462189, 0.0011701303301379085, 0.024461030960083008, -0.00647965632379055, -0.005504803266376257, -0.009125607088208199, -0.036388006061315536, 0.02405804768204689, -0.025631267577409744, -0.03188859298825264, 0.02445795387029648, 0.009431547485291958, -0.009989854879677296, -0.003009084379300475, 1.964615194083308e-06, -0.022200318053364754, -0.04030705988407135, -0.012374297715723515, 0.048670586198568344, 0.04682089388370514, 2.62622743321117e-05, 0.04633917659521103, -0.0005547197652049363, 0.006567913573235273, 0.03222186863422394, 0.00395539402961731, 0.07871019840240479, -0.009923633188009262, -0.014593291096389294, -0.018788324669003487, -0.026041986420750618, 0.009016991592943668, -0.012304335832595825, -0.0076429531909525394, 0.02022514119744301, -0.06510141491889954, 0.02791239134967327, 0.07562881708145142, 0.01854337565600872, -0.026379838585853577, -0.03446201607584953, -0.015803903341293335, 0.02134997770190239, -0.01746288686990738, 0.06381047517061234, 0.003775988472625613, 0.029762068763375282, 0.010707260109484196, -0.041321247816085815, -0.009803000837564468, 0.01786339096724987, 0.00818127952516079, 0.013580666854977608, -0.03249141946434975, -0.05676129832863808, 0.06050898879766464, -0.010645256377756596, -0.019491979852318764, -0.023128420114517212, -0.009434771724045277, -0.09739033132791519, 0.016467537730932236, 0.011092993430793285, 0.06062987074255943, 0.024132205173373222, 0.02575884386897087, -0.006199181545525789, 0.009916269220411777, 0.043450936675071716, 0.02375791408121586, -0.03376079723238945, 0.024077311158180237, 0.07921624928712845, -0.05195168778300285, -0.005357095971703529, 0.010482629761099815, 0.01790236495435238, 0.013899028301239014, 0.005932213738560677, -0.04078150540590286, 0.0529353953897953, -0.04392870515584946, 0.016757745295763016, -0.0011022723047062755, 0.03413386642932892, -0.06702477484941483, -0.07579585909843445, -0.011878054589033127, 0.008956712670624256, 0.06490593403577805, 0.004213217180222273, -0.04727468267083168, 0.03127846121788025, 0.05306627228856087, 0.034338854253292084, -0.016682056710124016, -0.04085369408130646, 0.060085561126470566, -0.048251308500766754, -0.04892895743250847, 0.05184950679540634, 0.0021564094349741936, 0.012818869203329086, 0.029373761266469955, -0.041544824838638306, -0.028205137699842453, -0.06576261669397354, 0.05053715780377388, -0.004676126874983311, -0.0214456245303154, 0.03544798493385315, 0.011676941066980362, -0.0007016860763542354, -0.03561926633119583, -0.008831208571791649, 0.03516535088419914, -0.014799831435084343, 0.04304800182580948, -0.008317084051668644, -0.04267285019159317, 0.030397316440939903, 0.016044389456510544, -0.05736621096730232, -0.042632799595594406, -0.034391138702631, -0.017131809145212173, -0.0007560267113149166, 0.06619991362094879, -0.044319238513708115, -0.03808055445551872, -0.04617831110954285, 0.0020100583788007498, 0.004679282195866108, -0.029214361682534218, 0.06967010349035263, -0.019472874701023102, -0.022737402468919754, 0.01550302840769291, -0.035045769065618515, 0.022409997880458832, 0.019808191806077957, 0.0080714775249362, -0.047443561255931854, -0.0028959421906620264, 0.01990816928446293, 0.006863543763756752, 0.02304954268038273, -0.04324091598391533, 0.04181190952658653, -0.03234460577368736, -0.0036946837790310383, 0.040716078132390976, -0.0036047198809683323, -0.021507026627659798, -0.010456843301653862, 0.0009768311865627766, 0.019342731684446335, -0.05721793696284294, 0.012820575386285782, 0.07700248807668686, -0.0022977625485509634, -0.03565533086657524, 0.02903475984930992, 0.07062241435050964, 0.042198557406663895, -0.01894805207848549, 0.033308111131191254, 0.05932111293077469, 0.00799604132771492, 0.0014043139526620507, -0.01984039694070816, -0.03738215193152428, -0.052073366940021515, -0.01919291913509369, 0.09408199042081833, -0.020249053835868835, -0.013362763449549675, 0.0024449301417917013, 0.08094905316829681, 0.0003653275780379772, -0.003687711199745536, -0.016493085771799088, -0.020846042782068253, -0.04599078744649887, 0.013751408085227013, -0.014745679683983326, -0.020080994814634323, -0.01582392491400242, -0.004137091338634491, -0.08856768906116486, 0.034862685948610306, 0.01011294312775135, -0.040618859231472015, -0.05123455822467804, -0.02541974186897278, 0.06588355451822281, 0.028237774968147278, 0.003983919508755207, -0.048855241388082504, 0.0014130386989563704, -0.007853714749217033, 0.014736122451722622, -0.02927948720753193, 0.005229055415838957, 0.056482888758182526, 0.06627707928419113, 0.06384863704442978, -0.02587343566119671, 0.08160636574029922, -0.01661856658756733, -0.012801372446119785, -0.007901649922132492, -0.01649503968656063, 0.058943938463926315, -0.04263806343078613, 0.0693502202630043, 0.040757425129413605, 0.03224741294980049, 0.008664274588227272, -0.023147454485297203, 0.05074184387922287, -0.0023655446711927652, 0.005984865128993988, -0.009961145929992199, 0.012986378744244576, -0.035184346139431, -0.07832855731248856, -0.004987992346286774, 0.00551266735419631, -0.005584897007793188, 0.027642061933875084, -0.005403804127126932, -0.009713352657854557, 0.04594976454973221, 0.02255125157535076, -0.019801737740635872, -0.0060601565055549145, 0.06142180413007736, -0.01920258067548275, 0.02118169330060482, -0.0384882315993309, -0.04653361812233925, -0.0007139352383092046, 0.03275853395462036, 0.027057696133852005, 0.04365254193544388, 0.009539395570755005, 0.020988846197724342, 0.017018163576722145, -0.013745780102908611, 0.04136789217591286, -0.017845114693045616, -0.01186797022819519, -0.004609399940818548, -0.04454926773905754, 0.014573846012353897, 0.04837822541594505, -0.03139152005314827, -0.03983939066529274, -0.030289165675640106, 0.011039293371140957, -0.013588819652795792, -0.009078145027160645, -0.052504077553749084, -0.017118925228714943, 0.033874403685331345, 0.07447511702775955, -0.07659735530614853, 0.0331762321293354, -0.02685602381825447, -0.030378881841897964, -0.04017314687371254, -0.01307053305208683, -0.010372001677751541, -0.03232412412762642, -0.026696670800447464, -0.0554586797952652, -0.04889388382434845, -0.020557710900902748, -0.028358491137623787, 0.02028893120586872, 0.014375668950378895, -0.03773486241698265, 0.027639489620923996, -0.04536834731698036, -0.006568192038685083, 0.0029696631245315075, -0.04557689651846886, 0.02043476328253746, 0.0010428961832076311, 0.03352896124124527, -0.0020148155745118856, 0.018879540264606476, -0.0543975904583931, -0.015326051041483879, -0.007571682799607515, -0.08845039457082748, 0.012545867823064327, -0.01058236788958311, -0.0008292236598208547, 0.041241519153118134, -0.016805049031972885, 0.030993202701210976, 0.04024544730782509, -0.007029958534985781, -0.0025836999993771315, -0.05425874888896942, 0.040158338844776154, 0.005596162285655737, 0.042667485773563385, 0.07333029806613922, -0.06727549433708191, -0.029503455385565758, 0.0015320178354158998, 0.031180070713162422, 0.06468147039413452, -0.03677208721637726, -0.09747671335935593, -0.021877877414226532, 0.030212311074137688, 0.005878830794245005, -0.005463854875415564, -0.014470470137894154, 0.01894020289182663, 0.03941173478960991, -0.05836759880185127, -0.04035608097910881, -0.010304808616638184, 0.03160659223794937, 0.04899946227669716, -0.02090827003121376, 0.00923569779843092, -0.015720902010798454, -0.010201997123658657, 0.026407919824123383, 0.011826254427433014, 0.025570474565029144, -0.0406838022172451, -0.02756178006529808, 0.007476884871721268, -0.008695426397025585, 0.023829428479075432, 0.0032879761420190334, 0.04486655816435814, 0.028204167261719704, 0.07390832901000977, 0.024456439539790154, -0.04696797579526901, -0.015769517049193382, 0.05435091629624367, 0.01869320310652256, 0.012372512370347977, 0.013169247657060623, 0.025846058502793312, 0.016764547675848007, -0.09859185665845871, -0.03536166995763779, -0.005066331941634417, -0.027880532667040825, -0.004139799624681473, 0.04698062315583229, -0.05715634673833847, 0.010122215375304222, -0.04847070202231407, -0.002814801409840584, -0.016536906361579895, -0.041435807943344116, -0.010530106723308563, -0.04735148325562477, 0.0551828108727932, 0.006396299693733454, 0.0365951806306839, 0.049893055111169815, -0.052067577838897705, -0.03450143709778786, -0.014754856936633587, -0.0003032343811355531, -0.027403265237808228, 0.07377277314662933, -0.004635756369680166, 0.05940685048699379, -0.041097499430179596, -0.0329626239836216, -0.03596804291009903, -0.03815570846199989, 0.04815895855426788, -0.08881207555532455, -0.01181112416088581, -0.03069550357758999, -0.02354826033115387, 0.02397969178855419, -0.02675621025264263, -0.036265093833208084, -0.013625925406813622, 0.043277326971292496, 0.04317495599389076, 0.009092743508517742, -0.016451217234134674, 0.011253139935433865, 0.06754244118928909, -0.01619846746325493, 0.018676361069083214, 0.037461407482624054, -0.027141975238919258, 0.015190022997558117, -0.007712931372225285, 0.03390222787857056, 0.015958083793520927, -0.0323268286883831, -0.04314883053302765, 0.022754725068807602, -0.025280727073550224, -0.023510780185461044, -0.010008423589169979, 0.014494343660771847, -0.027874663472175598, 0.03053046017885208, -0.03147776797413826, -0.0512256845831871, -0.02449197880923748, 0.07345423102378845, -0.0044672223739326, 0.09222334623336792, 0.016356395557522774, 0.04666014388203621, 0.035837989300489426, 0.023035243153572083, -0.03268054500222206, -0.056932881474494934, 0.06819068640470505, 0.00999996904283762, -0.018401535227894783, -0.02124679461121559, 0.005267344880849123, -0.0072221532464027405, -0.05650640279054642, -0.03571837767958641, -0.010169114917516708, -0.06645311415195465, 0.018710805103182793, 0.035485681146383286, 0.020389113575220108, -0.006903153378516436, -0.032904502004384995, -0.012334863655269146, -0.035199396312236786, -0.04220486804842949, 0.030533822253346443, -0.00792820192873478, 0.03292442858219147, -0.0023731233086436987, -0.018055861815810204, 0.0100712226703763, -0.01743524894118309, 0.023266945034265518, -0.00854677613824606, -0.06973562389612198, -0.02170712873339653, -0.000876592705026269, -0.03375637158751488, 0.016335854306817055, 0.02530466578900814, 0.0017557977698743343, -0.033730894327163696, -0.04319550469517708, -0.0069639720022678375, 0.0013455828884616494, 0.027574915438890457, -0.007566521409898996, 0.008693361654877663, 0.04681721702218056, 0.018292073160409927, 0.017004942521452904, -0.00998021848499775, 0.09518525004386902, -0.11057148873806, 0.026896802708506584, -0.04394524171948433, 0.017223332077264786, -0.04689355567097664, -0.04725657403469086, -0.007952684536576271, 0.045477110892534256, -0.1159181073307991, 0.06421922892332077, 0.051286645233631134, 0.002732579130679369, 0.004335520789027214, -0.03450261056423187, -0.022221582010388374, -0.015934322029352188, -0.027831802144646645, 0.01789833791553974, -0.009580339305102825, 0.023809947073459625, 0.07682180404663086, 0.028901129961013794, 0.020297855138778687, 0.013027910143136978, -0.05140881612896919, 0.04394560307264328, -0.02787320502102375, -0.0013211951591074467, -0.031713999807834625, 0.024294057860970497, 0.03996528685092926, 0.009322374127805233, -0.015091477893292904, 0.053421877324581146, -0.031795624643564224, 0.0356217585504055, -0.011917064897716045, -0.08595550805330276, -0.07043445855379105, 0.008078480139374733, 0.02966885268688202, -0.02066555805504322, 0.036745816469192505, -0.026573048904538155, 0.03482285141944885, 0.023442666977643967, 0.016775496304035187, -0.05533799156546593, -0.00037721582339145243, 0.059077080339193344, -0.025928035378456116, 0.04184679687023163, 0.012616739608347416, -0.009983873926103115, 0.013798589818179607, -0.052187200635671616, -0.07169836014509201, -0.025717569515109062, 0.07074686884880066, -0.005893123801797628, -6.244503702108373e-33, 0.06719515472650528, -0.0011370501015335321, -0.04005276411771774, 0.01011495478451252, -0.001708024530671537, 0.028034163638949394, 0.01100861094892025, -0.017204463481903076, -8.393569441977888e-05, -0.009226754307746887, 0.030643977224826813, -0.010636789724230766, 0.030153430998325348, 0.0004198080860078335, -0.0009556550066918135, 0.0366036519408226, -0.007751211058348417, 0.02711310051381588, -0.0022601180244237185, -0.023970317095518112, 0.03704100102186203, 0.042510319501161575, -0.0067732445895671844, 0.01378006674349308, -0.004855158273130655, 0.020038561895489693, -0.02928611822426319, 0.0065643577836453915, -0.014856995083391666, -0.017749255523085594, 0.029103660956025124, -0.010853049345314503, -0.047660116106271744, -0.0038465794641524553, -0.017144979909062386, -0.02267325669527054, 0.004712010268121958, 0.013761489652097225, -0.0126168979331851, 0.04362022504210472, -0.02135077491402626, 0.052889589220285416, -0.02172941528260708, 0.07715845108032227, -0.06746912002563477, 0.0010884650982916355, 0.02945806458592415, 0.05964789167046547, -0.024746209383010864, 0.013250049203634262, 0.07909844070672989, 0.009973013773560524, -0.024521058425307274, 0.08818040043115616, -0.007460490334779024, -0.05834526568651199, -0.055368661880493164, -0.03904438018798828, 0.017270134761929512, 0.04232373088598251, -0.03606337308883667, 0.030547602102160454, 0.013088131323456764, -0.029028940945863724, 0.043411266058683395, 0.07170473039150238, 0.0024512908421456814, -0.05311738699674606, 0.027927547693252563, 0.03238252177834511, -0.005139086861163378, -0.0013551346492022276, -0.01524994894862175, -0.016776956617832184, -0.014070563018321991, -0.041699234396219254, -0.0343787707388401, 0.01219717226922512, 0.14572365581989288, -0.054342396557331085, -0.019690170884132385, -0.024824824184179306, -0.02005503885447979, -0.019955608993768692, -0.0028012150432914495, 0.01745828241109848, 0.046636372804641724, -0.06359630078077316, -0.012362348847091198, -0.005482632201164961, -0.01966652274131775, 0.009174452163279057, 0.001202429411932826, -0.011882960796356201, -0.009845367632806301, -0.007977491244673729, 0.007068241015076637, 0.07434933632612228, -0.0034760197158902884, -0.040960028767585754, -0.06250856071710587, -0.04814767464995384, -0.031263381242752075, -0.0033696768805384636, -0.02621527388691902, 0.0014371956931427121, 0.006069312337785959, 0.017659222707152367, 0.002027045236900449, 0.037763118743896484, 0.003179834922775626, -0.0030933020170778036, 0.03887644037604332, 0.015085439197719097, 0.03726649656891823, -0.028379717841744423, -0.026732472702860832, 0.061109524220228195, 0.01410557609051466, -0.03167034313082695, 0.0033425558358430862, -0.030053328722715378, -0.051275189965963364, 0.008551513776183128, -0.06298872828483582, -0.01773020252585411, -0.06329304724931717, 0.0010729347122833133, 0.03361362963914871, -0.04052497819066048, 0.010986622422933578, 0.0060643283650279045, 2.790066275792924e-07, 0.03469091281294823, 0.0447223000228405, -0.05262944847345352, 0.017473723739385605, -0.032059602439403534, -0.010123086161911488, -0.04073938727378845, -0.000681226490996778, 0.04901864379644394, 0.018606625497341156, 0.002916372613981366, -0.03840068727731705, -0.0016066450625658035, -0.007519329432398081, -0.04988815262913704, -0.03256033733487129, -0.06281129270792007, 0.07955396175384521, 0.00566107826307416, -0.021127648651599884, 0.011006227694451809, 0.03415984660387039, 0.05346707999706268, 0.027640042826533318, 0.07513526827096939, -0.0547645203769207, -0.02512560598552227, 0.01414716150611639, -0.03233373165130615, 0.025738367810845375, -0.005906354635953903, -0.017869392409920692, -0.021102532744407654, 0.04753715172410011, -0.037937384098768234, -0.023896541446447372, 0.018357284367084503, 0.04879525676369667, 0.02109132893383503, 0.03792590647935867, 0.006057135760784149, 0.0052325832657516, 0.05113398656249046, 0.04021130129694939, 0.006928256247192621, 0.05860580876469612, -0.057404033839702606, 0.040789805352687836, 0.021451260894536972, -0.04731769859790802, 0.032321538776159286, 0.06324536353349686, -0.014865366742014885, -0.013903248123824596, -0.05059635639190674, 0.0013270688941702247, 0.010244019329547882, -0.03271320462226868, 0.03754030540585518, -0.0008430886664427817, 0.013522695749998093, -0.0661667063832283, 0.018580742180347443, 0.04488192871212959, 0.09417355805635452, -0.029947979375720024, 0.03920222446322441, 2.3065371072617417e-34, 0.01438671164214611, 0.028162924572825432, 0.03274310752749443, 0.02528482861816883, -0.0010714209638535976, -0.016310060396790504, 0.04359220713376999, -0.030157819390296936, -0.010589388199150562, 0.0093521848320961, 0.005079665686935186]

['Cem Tekin', 'Mingyan Liu']

1010.0056v1

We consider an opportunistic spectrum access (OSA) problem where the time-varying condition of each channel (e.g., as a result of random fading or certain primary users' activities) is modeled as an arbitrary finite-state Markov chain. At each instance of time, a (secondary) user probes a channel and collects a certain reward as a function of the state of the channel (e.g., good channel condition results in higher data rate for the user). Each channel has potentially different state space and statistics, both unknown to the user, who tries to learn which one is the best as it goes and maximizes its usage of the best channel. The objective is to construct a good online learning algorithm so as to minimize the difference between the user's performance in total rewards and that of using the best channel (on average) had it known which one is the best from a priori knowledge of the channel statistics (also known as the regret). This is a classic exploration and exploitation problem and results abound when the reward processes are assumed to be iid. Compared to prior work, the biggest difference is that in our case the reward process is assumed to be Markovian, of which iid is a special case. In addition, the reward processes are restless in that the channel conditions will continue to evolve independent of the user's actions. This leads to a restless bandit problem, for which there exists little result on either algorithms or performance bounds in this learning context to the best of our knowledge. In this paper we introduce an algorithm that utilizes regenerative cycles of a Markov chain and computes a sample-mean based index policy, and show that under mild conditions on the state transition probabilities of the Markov chains this algorithm achieves logarithmic regret uniformly over time, and that this regret bound is also optimal.

Online Learning in Opportunistic Spectrum Access: A Restless Bandit Approach

http://arxiv.org/pdf/1010.0056v1

Title Online Learning Opportunistic Spectrum Access Restless Bandit Approach Summary consider opportunistic spectrum access OSA problem timevarying condition channel eg result random fading certain primary user activity modeled arbitrary finitestate Markov chain instance time secondary user probe channel collect certain reward function state channel eg good channel condition result higher data rate user channel potentially different state space statistic unknown user try learn one best go maximizes usage best channel objective construct good online learning algorithm minimize difference user performance total reward using best channel average known one best priori knowledge channel statistic also known regret classic exploration exploitation problem result abound reward process assumed iid Compared prior work biggest difference case reward process assumed Markovian iid special case addition reward process restless channel condition continue evolve independent user action lead restless bandit problem exists little result either algorithm performance bound learning context best knowledge paper introduce algorithm utilizes regenerative cycle Markov chain computes samplemean based index policy show mild condition state transition probability Markov chain algorithm achieves logarithmic regret uniformly time regret bound also optimal Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.010369249619543552, 0.03464570641517639, 0.005439855623990297, -0.08773569017648697, -0.006326572969555855, -0.02456473372876644, -0.03040509857237339, 0.009271861985325813, -0.06942259520292282, -0.004514485131949186, -0.009591730311512947, 0.01682262495160103, -0.05016084015369415, 0.04604250565171242, -0.049870409071445465, 0.010675568133592606, 0.02652311511337757, -0.05901598185300827, 0.0036115196999162436, 0.011663033626973629, -0.004042292945086956, -0.04864373058080673, -0.020511053502559662, -0.005858323071151972, 0.005458803381770849, 0.016177669167518616, -0.03342057764530182, -0.02222251705825329, -0.01340997964143753, -0.07236073911190033, 0.021343396976590157, -0.02024710737168789, 0.06268429011106491, 0.06788899749517441, 1.8664367189558106e-06, -0.015260761603713036, -0.04508013650774956, -0.015146227553486824, 0.023120425641536713, 0.0003560966579243541, 0.03179376199841499, 0.032391633838415146, -0.025813059881329536, 0.02186638116836548, -0.0337274931371212, 0.007944652810692787, 0.0330035574734211, 0.018845954909920692, 0.00225218222476542, 0.03643418848514557, 0.0011960361152887344, 0.038276538252830505, -0.0075201913714408875, -0.018143821507692337, 0.03752654418349266, -0.0484006367623806, 0.029092907905578613, 0.01386681105941534, 0.01110840868204832, -0.07071588933467865, 0.030624262988567352, 0.012726342305541039, 0.011202149093151093, -0.01113688014447689, 0.06548476964235306, -0.05046023800969124, -0.008118264377117157, -0.017242109403014183, -0.008338275365531445, -0.027291757985949516, 0.008636625483632088, -0.009082261472940445, 0.015280540101230145, 0.018021995201706886, -0.03785134106874466, 0.008185266517102718, -0.00982147827744484, -0.007955948822200298, -0.04036744311451912, 0.038025226444005966, -0.008970675989985466, 0.07196933776140213, -0.01357301976531744, 0.04081091284751892, -0.00733354315161705, 0.06964714825153351, -0.03168183192610741, -0.04580891132354736, 0.0692048892378807, 0.006920481100678444, 0.03272506222128868, -0.00860354769974947, -0.00839193444699049, 0.017424043267965317, -0.06789861619472504, 0.02250598557293415, 0.005182111635804176, 0.023026594892144203, 0.0012334404746070504, 0.015064947307109833, 0.07148296386003494, -0.043034251779317856, 0.050832245498895645, -0.0038421947974711657, 0.004429773427546024, -0.07947689294815063, -0.01810254529118538, -0.03696972131729126, 0.0030087768100202084, 0.03094780072569847, -0.04100343957543373, -0.01174464076757431, 0.015536104328930378, 0.06729782372713089, 0.08709341287612915, -0.04763954505324364, -0.05193265154957771, 0.040362194180488586, -0.0065664974972605705, 0.0029067567083984613, -0.01473606564104557, -0.00789948832243681, -0.04432401806116104, 0.02169252187013626, -0.025157537311315536, -0.08644108474254608, 0.006416410207748413, 0.07112514972686768, -0.0024279893841594458, -0.026937993243336678, 0.011653012596070766, 0.012491798959672451, -0.032859548926353455, 0.015167100355029106, -0.0521351620554924, 0.052558425813913345, -0.004714906681329012, 0.010163934901356697, -0.02997524105012417, -0.0516134649515152, 0.09050752967596054, -0.01052453275769949, -0.04139208793640137, -0.024826860055327415, -0.0764048621058464, -0.039580605924129486, -0.03375610336661339, 0.04772946238517761, 0.00022511494171340019, -0.03406191244721413, 0.029167480766773224, -0.04544322192668915, 0.0010793874971568584, 0.005482023116201162, 0.08734150975942612, 0.004714081063866615, 0.006347621325403452, 0.033109791576862335, -0.0245494581758976, 0.013893088325858116, 0.011884565465152264, -0.01509893499314785, -0.002761676674708724, 0.0003862470621243119, 0.04591783508658409, 0.008951036259531975, 0.07292715460062027, -0.029470883309841156, 0.009195596911013126, 0.04418100416660309, 0.014784766361117363, -0.011219487525522709, -0.04844672232866287, 0.06433729827404022, -0.014633375220000744, 0.006334011442959309, 0.09008421003818512, 0.004036695696413517, -0.034307509660720825, 0.06683316081762314, -0.017671411857008934, -0.041702818125486374, 0.031080402433872223, 0.03240172192454338, -0.031357310712337494, -0.006755361333489418, 0.03993885591626167, 0.001649247482419014, -0.00497306976467371, 0.008365108631551266, 0.009089075028896332, -0.019144592806696892, -0.04492151364684105, 0.01958974450826645, 0.048915550112724304, -0.039773810654878616, -0.022572986781597137, -0.06551635265350342, 0.038308702409267426, 0.06553051620721817, -0.037668488919734955, -0.07597532868385315, -0.007555489428341389, -0.04912690445780754, 0.015188571996986866, -0.01707839034497738, 0.034272633492946625, -0.026824239641427994, -0.0014785748207941651, -0.03061695210635662, 0.03473077714443207, -0.030737893655896187, 0.021799715235829353, 0.00111483468208462, -0.010606384836137295, 0.03504732996225357, 0.03692879155278206, 0.07514414936304092, 0.017094237729907036, 0.02816939726471901, -0.02935345284640789, 0.019240237772464752, -0.0028162586968392134, 0.018142398446798325, -0.0020088946912437677, -0.0346054807305336, 0.027956971898674965, -0.006470783613622189, 0.05029807984828949, -0.0574556402862072, 0.03609362244606018, 0.014464706182479858, -0.00437332084402442, 0.007346321363002062, -0.045462846755981445, 0.002000270877033472, -0.016443893313407898, 0.02265959046781063, -0.004203524440526962, -0.018157489597797394, 0.04264222830533981, 0.031797878444194794, 0.022195778787136078, -0.03258849307894707, 0.024357475340366364, -0.025838853791356087, 0.03274692967534065, 0.009450029581785202, -0.021749058738350868, -0.00780465779826045, 0.00630350923165679, 0.006997172255069017, 0.03601153567433357, 0.04026854410767555, 0.021394824609160423, -0.031088266521692276, -0.0453127957880497, 0.027240166440606117, -0.08431819826364517, 0.06753994524478912, -0.05939171090722084, -0.06263024359941483, -0.023813538253307343, -0.04974987357854843, 0.023181453347206116, 0.017217271029949188, 0.0011408699210733175, 0.05128013715147972, -0.00817058701068163, -0.022193286567926407, 0.05616232380270958, 0.005289175547659397, -0.032706983387470245, 0.008780588395893574, -0.020670536905527115, 0.0021213870495557785, 0.01510705891996622, -0.0034861385356634855, -0.0008460041135549545, -0.026412952691316605, 0.04188214987516403, -0.02675434574484825, -0.023078208789229393, -0.022528016939759254, 0.021064549684524536, -0.014817987568676472, 0.012016617693006992, -0.038361772894859314, -0.03963412344455719, -0.05049639195203781, -0.001365851378068328, 0.004257765132933855, -0.011793356388807297, 0.04305608570575714, 0.016492146998643875, 0.010369873605668545, -0.030342623591423035, -0.0038047104608267546, 0.025251541286706924, 0.03562907129526138, 0.013574805110692978, 0.013374692760407925, -0.029200779274106026, -0.02119607850909233, 0.007884431630373001, -0.0548413060605526, 0.005928749218583107, 0.011119529604911804, 0.0600055456161499, -0.0018722348613664508, -0.0005375435575842857, 0.040423642843961716, 0.01850358583033085, -0.04241861402988434, 0.002844720846042037, -0.07885777205228806, -0.04072271287441254, 0.030293693765997887, -0.013394605368375778, -0.005672612227499485, 0.06940282136201859, 0.0009443157468922436, 0.0873728021979332, 0.10008877515792847, 0.018407590687274933, -0.0025155229959636927, -0.0873529464006424, 0.005110127851366997, -0.044816646724939346, -0.02734885737299919, 0.03520425781607628, 0.006122329272329807, -0.02339201606810093, 0.006860645022243261, -0.053758859634399414, 0.053489282727241516, -0.06925613433122635, -0.05464118719100952, 0.005747145973145962, 0.016531024128198624, -0.018608009442687035, -0.037585318088531494, -0.010011651553213596, 0.023776642978191376, 0.02080395445227623, -0.027261095121502876, -0.00919113215059042, 0.026259522885084152, -0.010838793590664864, -0.022878123447299004, -0.005800164770334959, -0.004632378928363323, -0.03635150194168091, 0.012587349861860275, 0.04765024408698082, 0.045530226081609726, 0.03889760002493858, -0.026060333475470543, -0.010534236207604408, -0.02215486578643322, 0.034416183829307556, -0.0051443083211779594, 0.024058522656559944, -0.011328754015266895, 0.020717298611998558, 0.029437454417347908, 0.03150162845849991, -0.06509623676538467, -0.020079344511032104, 0.07921098172664642, 0.012885529547929764, -0.024544045329093933, 0.009109958074986935, -0.01152847707271576, 0.030942106619477272, -0.08702690154314041, -0.03392590582370758, -0.07219371199607849, 0.04055485501885414, 5.3904001106275246e-05, 0.06536884605884552, -0.04572997987270355, -0.003557737683877349, -0.03022610768675804, 0.08137115836143494, -0.034635886549949646, -0.05311880260705948, -0.034677498042583466, -0.03996993601322174, 0.008611368015408516, -0.0005265650688670576, -0.009487015195190907, 0.010883187875151634, -0.054888706654310226, -0.04943675920367241, -0.07317964732646942, 0.015527736395597458, 0.032493285834789276, -0.007014451082795858, 0.01781957410275936, 0.03721669316291809, -0.0005343508091755211, 0.005499118939042091, -0.009069062769412994, -0.022747134789824486, 0.0617595873773098, 0.002345115877687931, -0.025217976421117783, 0.03346085548400879, -0.046687833964824677, -0.030513759702444077, -0.04090522602200508, 0.015628106892108917, 0.006074074190109968, -0.018190918490290642, 0.008948507718741894, 0.04303761571645737, -0.0332941971719265, 0.05698445066809654, 0.024655742570757866, -0.002780704293400049, 0.012756790965795517, -0.008081835694611073, -0.013251383788883686, 0.008235440589487553, 0.022363629192113876, 0.019562892615795135, 0.10338801890611649, -0.028085099533200264, -0.05778731033205986, -0.0029097325168550014, -0.062204159796237946, 0.011499440297484398, 0.02887173555791378, -0.07085373252630234, 0.017700938507914543, -0.01721026562154293, 0.05782168731093407, -0.01659824699163437, -0.022741299122571945, 0.04471847787499428, -0.036417894065380096, 0.0746099054813385, -0.030682573094964027, 0.09266414493322372, -0.008062517270445824, 0.04041887819766998, -0.026618592441082, -0.07067399471998215, 0.047866202890872955, 0.0057685342617332935, -0.00902999471873045, 0.019331511110067368, 0.0008805267279967666, -0.05663907900452614, 0.00161838682834059, -0.07336928695440292, -0.09341023862361908, -0.02983199618756771, 0.05444145202636719, 0.007190947886556387, 0.025439554825425148, 0.002068190136924386, -0.0041627539321780205, -0.004322863183915615, -0.03203325718641281, 0.004565262235701084, -0.018248340114951134, 0.004077134188264608, 0.030084220692515373, 0.037040941417217255, -0.011363986879587173, 0.036696236580610275, -0.024585561826825142, 0.0007137847132980824, -0.008431673981249332, -0.011591261252760887, -0.01883597858250141, 0.08313503861427307, 0.020329643040895462, -0.057858411222696304, 0.014115087687969208, 0.024742191657423973, -0.0777847096323967, 0.01448163203895092, 0.024576110765337944, 0.023318253457546234, 0.0235862135887146, -0.0052039045840501785, 0.044530294835567474, 0.013189474120736122, 0.028722934424877167, 0.055504318326711655, -0.017135685309767723, 0.033812809735536575, -0.04657702520489693, 0.048114266246557236, 0.0010598573135212064, 0.01666393131017685, -0.01600341498851776, 0.006414041388779879, 0.026903053745627403, 0.005162016022950411, 0.06173364073038101, 0.04667699709534645, 0.050707947462797165, -0.029698390513658524, -0.007008351851254702, 0.0030838511884212494, 0.008908682502806187, 0.014070677570998669, -0.03081921860575676, 0.007274087984114885, -0.037597041577100754, 0.03149128705263138, 0.00428739795461297, 0.03815566003322601, 0.0441693440079689, -0.0045678396709263325, -0.012652990408241749, 0.03159024566411972, 0.041134368628263474, -0.005030476953834295, -0.10202734172344208, 0.013053416274487972, 0.04646144062280655, 0.02466869354248047, 0.005665678530931473, 0.05542942136526108, 0.015097211115062237, 0.07877557724714279, 0.012375466525554657, -0.06174776703119278, -0.017135469242930412, -0.031171973794698715, 0.052593715488910675, 0.04940895736217499, 0.049640703946352005, -0.032108407467603683, -0.00022535577591042966, 0.011926710605621338, 0.037820521742105484, -0.049102429300546646, -0.008614890277385712, 0.0028986772522330284, -0.025612378492951393, 0.05183659866452217, -0.0427163690328598, -0.03572019934654236, 0.06162618473172188, -0.03239955008029938, -0.03962762653827667, -0.006525042466819286, -0.025837384164333344, 0.007308919448405504, -6.213965093557979e-33, 0.007654283661395311, 0.004648317117244005, -0.011545470915734768, -0.050819918513298035, -0.04549868404865265, -0.03931179270148277, -0.004227703437209129, -0.010028949938714504, 0.018779244273900986, -0.05375591292977333, -0.010781722143292427, -0.010043423622846603, 0.04105272889137268, 0.00742478808388114, -0.0002854562771972269, 0.02337503246963024, 0.008987510576844215, 0.012044195085763931, -0.011682628653943539, -0.03459855914115906, -0.005542571656405926, 0.031269799917936325, -0.03050481155514717, 0.04690617322921753, -0.061334334313869476, 0.02914593555033207, -0.045834388583898544, -0.025763491168618202, -0.04518769308924675, 0.008832797408103943, -0.004362552426755428, 0.010720605030655861, -0.030909333378076553, -0.0376487635076046, 0.0200548954308033, -0.015051815658807755, 0.0005046939477324486, -0.013034899719059467, -0.06289418786764145, 0.025740347802639008, -0.033250778913497925, 0.04169502854347229, -0.011100193485617638, 0.020065367221832275, -0.07503275573253632, 0.04001699388027191, 0.05291898921132088, -0.0058456468395888805, -0.06888335943222046, -0.00013900210615247488, 0.03426298499107361, 0.006832384504377842, 0.024405594915151596, 0.014551500789821148, 0.012718121521174908, -0.0505530908703804, -0.062057219445705414, -0.045586273074150085, -0.04876643419265747, 0.046608004719018936, -0.028906449675559998, 0.07459590584039688, -0.03835666924715042, 0.029373381286859512, 0.033881571143865585, 0.055243413895368576, -0.049134522676467896, -0.014738555066287518, 0.023732461035251617, -0.005644046701490879, -0.03805868327617645, -0.053520265966653824, -0.06601864099502563, -0.01810353435575962, 0.050076596438884735, -0.026080237701535225, 0.008556927554309368, 0.006874969694763422, 0.049203529953956604, -0.002365552820265293, -0.020212456583976746, 0.016756651923060417, 0.0063468087464571, 0.03200451657176018, -0.004654266405850649, -0.014803547412157059, 0.007439596112817526, -0.051285237073898315, -0.0036505653988569975, 0.04036594554781914, 0.02449542097747326, 0.0017620555590838194, -0.02458067797124386, -0.020946918055415154, -0.024255484342575073, -0.02832193300127983, 1.073043040378252e-05, 0.03840925544500351, -0.029503492638468742, -0.021527037024497986, -0.08691609650850296, -0.04790869727730751, 0.03315386921167374, -0.015360293909907341, 0.019321922212839127, -0.017134562134742737, -0.005937461741268635, 0.04652128368616104, -0.05705490708351135, 0.027712645009160042, 0.024342957884073257, 0.03879060968756676, 0.0754544734954834, 0.01426931656897068, 0.05960194766521454, -0.07654143124818802, -0.020882878452539444, 0.08826037496328354, -0.012207025662064552, -0.05248481035232544, -0.009084945544600487, -0.031399764120578766, 0.0034078997559845448, -0.02074027620255947, -0.03333568200469017, 0.07573340833187103, -0.07034299522638321, 0.03188031539320946, -0.024168312549591064, -0.04112541675567627, 0.001105699804611504, -0.010569090023636818, 2.6461594870852423e-07, -0.025100866332650185, 0.04031185433268547, -0.010375075973570347, -0.02609557844698429, -0.009456603787839413, 0.003947209566831589, -0.04336804151535034, -0.033140480518341064, -0.018476957455277443, 0.04936199262738228, 0.006520605180412531, -0.04286295920610428, 0.028740953654050827, 0.008221824653446674, -0.01709769107401371, -0.03041801042854786, 0.004871145356446505, 0.05880512669682503, -0.023364203050732613, -0.02319762110710144, 0.021116014569997787, 0.024930555373430252, 0.01603747345507145, -0.03494064509868622, 0.0792170986533165, 0.004270661622285843, 0.008449661545455456, 0.05491172894835472, -0.010137812234461308, -0.013904898427426815, 0.00010504410602152348, 0.022691434249281883, -0.05560283362865448, -0.023042673245072365, -0.03245100378990173, 0.02236378751695156, -0.03638846054673195, 0.021385710686445236, 0.021331068128347397, -0.039030663669109344, 0.013760456815361977, 0.045316584408283234, 0.03949977457523346, 0.0030129437800496817, 0.012630540877580643, -0.01737605780363083, -0.06146800518035889, -0.035048048943281174, 0.04698450118303299, -0.013495123013854027, -0.03529195114970207, -0.022790703922510147, -0.002903260989114642, -0.03596704453229904, -0.01758555881679058, 0.07680201530456543, 0.015075979754328728, -0.014546406455338001, 0.02912229672074318, 0.052651531994342804, 0.03548375517129898, -0.024517061188817024, -0.03848952800035477, 0.09619708359241486, 0.061416227370500565, -0.03446943312883377, 0.0327397845685482, 2.356367277065808e-34, 0.02719564363360405, 0.011148652993142605, -0.004662069957703352, 0.0077199130319058895, -0.045358896255493164, -0.008253568783402443, 0.05961313843727112, 0.003174894256517291, 0.03413507342338562, 0.0052919937297701836, 0.0008094916702248156]

['Andri Mirzal']

1010.5290v2

This paper proposes uni-orthogonal and bi-orthogonal nonnegative matrix factorization algorithms with robust convergence proofs. We design the algorithms based on the work of Lee and Seung [1], and derive the converged versions by utilizing ideas from the work of Lin [2]. The experimental results confirm the theoretical guarantees of the convergences.

Converged Algorithms for Orthogonal Nonnegative Matrix Factorizations

http://arxiv.org/pdf/1010.5290v2

Title Converged Algorithms Orthogonal Nonnegative Matrix Factorizations Summary paper proposes uniorthogonal biorthogonal nonnegative matrix factorization algorithm robust convergence proof design algorithm based work Lee Seung 1 derive converged version utilizing idea work Lin 2 experimental result confirm theoretical guarantee convergence Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.06270299851894379, 0.03785886615514755, 0.008544456213712692, -0.001085922122001648, -0.030617473646998405, 0.002046912210062146, -0.02097672037780285, 0.03817601129412651, -0.025350399315357208, -0.004732214380055666, -0.016083573922514915, -0.014950703829526901, 0.01829279027879238, 0.019912149757146835, -0.01736157014966011, 0.019481521099805832, -0.0139932194724679, -0.0262298546731472, -0.07930032163858414, -0.022626414895057678, -0.037084225565195084, -0.031248457729816437, -0.015892542898654938, -0.000575818819925189, 0.013056911528110504, -0.01025161612778902, -0.0209268257021904, 0.0009552125702612102, 0.011809339746832848, -0.00770254572853446, -0.07354439795017242, -0.0037865687627345324, -0.007390952203422785, 0.005409929435700178, 1.908656713567325e-06, -0.0386805459856987, 0.010050659999251366, -0.016822174191474915, 0.07954172044992447, 0.044654931873083115, 0.04820677265524864, 0.0023696906864643097, 0.03547509387135506, -0.011201155371963978, -0.05063086375594139, -0.046977363526821136, 0.009516799822449684, 0.05955149605870247, 0.03694739192724228, -0.017110077664256096, -0.010922428220510483, 0.010274047031998634, 0.01838611625134945, -0.014032987877726555, -0.009419186040759087, -0.02027994766831398, 0.03306465223431587, -0.05980859324336052, 0.03309066593647003, -0.009971821680665016, -0.008191566914319992, 0.056224286556243896, -0.0067439004778862, 0.005497067701071501, 0.042936716228723526, 0.0468541719019413, 9.61143960012123e-05, 0.019192548468708992, 0.00875951163470745, 0.09650859236717224, -0.009093145839869976, -0.026638606563210487, -0.017086252570152283, -0.00503819715231657, 0.001097489963285625, 0.021961718797683716, -0.02451458014547825, 0.0014106984017416835, -0.0016274439403787255, 0.037343114614486694, -0.06143658608198166, 0.015230259858071804, 0.02875601500272751, -0.026891157031059265, 0.008741521276533604, 0.12734299898147583, 0.045039933174848557, -0.03533165156841278, 0.04956427216529846, -0.022067513316869736, -0.03356055170297623, 0.03846496343612671, 0.048000894486904144, -0.0032672365196049213, -0.03652486950159073, -0.0033251710701733828, 0.03042837418615818, 0.013183079659938812, 0.01974944770336151, -0.0035084669943898916, 0.0083610899746418, -0.012017139233648777, 0.020535895600914955, 0.016644282266497612, 0.0067407856695353985, -0.03527646139264107, -0.06365305930376053, 0.0050404672510921955, -0.019955869764089584, 0.03232937678694725, -0.056813254952430725, 0.009879695251584053, 0.0445183664560318, 0.10119333863258362, 0.012249650433659554, 0.027274979278445244, -0.05993323773145676, -0.017737384885549545, -0.05496907979249954, -0.05003652721643448, 0.0279266107827425, 0.052845511585474014, 0.059000637382268906, -0.005676917731761932, -0.02530524879693985, 0.040308862924575806, 0.011061334982514381, 0.010232353582978249, -0.10757174342870712, 0.04385478049516678, 0.0009515011333860457, 0.035835180431604385, 0.01413219515234232, 0.01714874990284443, -0.03157956525683403, 0.04564519599080086, -0.011220503598451614, 0.023660635575652122, -0.011750392615795135, -0.010199782438576221, -0.007254182361066341, -0.0190830547362566, -0.03154725581407547, -0.03306638076901436, -0.021108729764819145, -0.02674558386206627, -0.018918680027127266, -0.021408844739198685, 0.01377131137996912, 0.0010208095191046596, -0.037981294095516205, 0.057212091982364655, 0.001974420854821801, 0.0027228686958551407, 0.025434622541069984, 0.007123617921024561, 0.041486918926239014, 0.006473949179053307, -0.009916475974023342, -0.06330078095197678, 0.031103216111660004, 0.008865993469953537, -0.008878039196133614, 0.0041456762701272964, -0.0038962808903306723, -0.004628518130630255, -0.010944758541882038, -0.044757526367902756, 0.00647443113848567, -0.012982058338820934, -0.019058002158999443, 0.03538868948817253, 0.010092491284012794, -0.026636343449354172, 0.012412238866090775, 0.04043681174516678, -0.027927318587899208, 0.054168928414583206, -0.015749486163258553, 0.0014704684726893902, -0.03731600195169449, 0.020351333543658257, 0.015150303021073341, 0.030044851824641228, -0.051026348024606705, -0.0380919948220253, -0.031208356842398643, -0.009610469453036785, -0.05385931581258774, 0.010602489113807678, 0.038214463740587234, -0.06529808789491653, -0.03258288651704788, -0.03859155997633934, 0.05081774294376373, -0.06320934742689133, -0.05102279409766197, -0.081312395632267, 0.031478676944971085, -0.06826359033584595, 0.01788073591887951, -0.003466293914243579, 0.016904739663004875, -0.05317164957523346, 0.0021263097878545523, -0.06044702231884003, -0.021854950115084648, -0.03965243324637413, -0.03094564750790596, -0.04732726886868477, -0.07207679003477097, 0.00024139000743161887, 0.01894085295498371, -0.004497419111430645, -0.00506361061707139, 0.08711688965559006, 0.01007060520350933, -0.030850850045681, -0.07018209248781204, 0.04954201355576515, 0.008198500610888004, 0.013782004825770855, -0.003881810000166297, -0.014012819156050682, -0.007308180443942547, 0.016609545797109604, 0.11833541840314865, 0.024315932765603065, 0.03630803897976875, 0.0826159343123436, 0.045333124697208405, -0.04088883846998215, 0.05493989586830139, -0.05436400696635246, -0.05201014131307602, -0.04005524888634682, -0.008754272013902664, 0.005027927923947573, 0.03746561333537102, -0.03642868995666504, 0.00690615875646472, 0.07637542486190796, 0.024817971512675285, -0.04060254245996475, 0.07758069038391113, 0.015379492193460464, -0.06724348664283752, -0.006068879272788763, 0.03382522985339165, -0.034694477915763855, -1.6830501408549026e-05, 0.014824019744992256, 0.009629367850720882, -0.025230862200260162, 0.06506018340587616, 0.024292754009366035, -0.055863071233034134, 0.05770917981863022, -0.014071800746023655, 0.0027213627472519875, -0.01966840960085392, -0.023027049377560616, -0.0067341523244977, 0.005171255208551884, -0.013727733865380287, 0.062242623418569565, 0.04152711108326912, -0.011803681030869484, -0.01475499477237463, 0.006383491680026054, -0.005790443159639835, 0.022701643407344818, -0.038607314229011536, 0.06259752810001373, -0.00047959788935258985, -0.014856635592877865, 0.0418081060051918, 0.0012931441888213158, -0.05016619339585304, 0.014111110009253025, -0.048751767724752426, -0.008002616465091705, 0.00235409801825881, -0.03428126126527786, -0.03831760585308075, 0.0448281466960907, -0.019512727856636047, -0.020320216193795204, -0.022628052160143852, 0.032342929393053055, -0.03734731301665306, 0.0021902178414165974, 0.0023568812757730484, 0.015441527590155602, -0.02575046382844448, 0.00036815597559325397, 0.02028968557715416, 0.05612611770629883, -0.0012473880778998137, -0.06261487305164337, 0.027415171265602112, 0.07726185023784637, 0.04031559079885483, -0.011121885851025581, 0.0016193946357816458, 0.03596554696559906, 0.050996556878089905, -0.033177219331264496, 0.056546520441770554, -0.020166071131825447, 0.022338734939694405, -0.018418913707137108, 0.005577089264988899, 0.009299514815211296, -0.06295870989561081, -0.03828621655702591, -0.055722955614328384, -0.009732725098729134, -0.043961696326732635, 0.0035739452578127384, 0.006299913860857487, 0.016997020691633224, 0.06301099807024002, 0.02810923382639885, -0.02611171267926693, -0.008636491373181343, -0.02281836047768593, 0.017487136647105217, -0.06267420202493668, -0.05102868750691414, -0.004741159733384848, -0.044632188975811005, 0.013564374297857285, 0.028229637071490288, -0.05949660390615463, 0.024789446964859962, -0.023530062288045883, 0.0332481786608696, 0.04146610572934151, -0.03135550394654274, 0.013678488321602345, -0.013441113755106926, 0.007321859244257212, -0.03270220756530762, 0.044684167951345444, 0.013182365335524082, -0.016411690041422844, 0.017060808837413788, -0.02059405855834484, 0.03235191851854324, 0.010762440040707588, -0.017070911824703217, -0.06352214515209198, 0.003406239440664649, 0.020223911851644516, 0.055650822818279266, 0.010249965824186802, -0.022977666929364204, -0.014721926301717758, 0.008465299382805824, 0.091802679002285, 0.008225368335843086, -0.01824072375893593, -0.05060999467968941, 0.0017480840906500816, 0.03402094542980194, 0.011159510351717472, 0.000801767804659903, -0.045421499758958817, 0.0016052721766754985, -0.007044229656457901, 0.07840093225240707, 0.010228685103356838, 0.0454128198325634, 0.055080730468034744, -0.09599270671606064, 0.021223803982138634, -0.015059313736855984, 0.023285051807761192, 0.05840727314352989, -0.008045957423746586, 0.011798041872680187, -0.0034011241514235735, -0.038163281977176666, 0.049750205129384995, 0.04727138951420784, -0.06552932411432266, 0.0025979625061154366, -0.03375433385372162, 0.054374970495700836, 0.02503836899995804, -0.007732591591775417, -0.05291059985756874, -0.047556355595588684, 0.001897568698041141, -0.06944158673286438, -0.0620199516415596, 0.043690506368875504, -0.020143887028098106, -0.000477680005133152, -0.02310323715209961, -0.02544649876654148, 0.004140697419643402, -0.052866846323013306, -0.05887020751833916, 0.014238468371331692, -0.04324134811758995, 0.0008715068106539547, -0.028219664469361305, -0.08439567685127258, 0.038163281977176666, -0.04265065863728523, -0.030707919970154762, -0.07316965609788895, 0.04121601581573486, 0.043033696711063385, -0.008253092877566814, -0.08476047217845917, 0.09405043721199036, -0.06892210990190506, 0.04045255854725838, 0.011810225434601307, 0.09444717317819595, 0.04141451045870781, -0.01103106141090393, 0.025465507060289383, 0.01091246958822012, 0.02909846603870392, 0.04952339828014374, -0.042039141058921814, -0.038615502417087555, -0.03437761962413788, 0.056924235075712204, 0.0510321743786335, 0.04620448499917984, -0.025033852085471153, -0.02656801976263523, 0.0015267659910023212, -0.02435545064508915, -0.04858247935771942, 0.028557227924466133, -0.006213644985109568, 0.07361617684364319, 0.02191677875816822, 0.02071712538599968, 0.03139398247003555, -0.01767093688249588, 0.01813887245953083, -0.053629472851753235, 0.03179827332496643, 0.004885051399469376, -0.01138059888035059, 0.04609552398324013, 0.06761150062084198, -0.01219228096306324, 0.020496893674135208, -0.044706836342811584, -0.009557449258863926, 0.021822132170200348, -0.049875207245349884, 0.011019189842045307, 0.0006961567560210824, -0.04372699186205864, -0.015137400478124619, -0.053952883929014206, -0.0025390645023435354, 0.009992614388465881, -0.001826917752623558, 0.06591327488422394, 0.005162608344107866, -0.0015787435695528984, 0.008815501816570759, 0.05467195808887482, 0.010165143758058548, 0.01470794714987278, -0.0009324699058197439, 0.015616693533957005, -0.03485330939292908, 0.004976482130587101, 0.009158979170024395, 0.012461879290640354, 0.05394938588142395, 0.01361970417201519, 0.014373104088008404, -0.028254322707653046, 0.0006852103397250175, -0.01828952133655548, 0.024339187890291214, -0.012614327482879162, 0.037746135145425797, 0.06690389662981033, 0.024951592087745667, -0.029377726837992668, 0.009636233560740948, -0.014509701170027256, 0.003242109902203083, 0.02302684262394905, 0.008120646700263023, 0.021658897399902344, -0.010909488424658775, -0.03913547843694687, 0.03282755985856056, 0.010666243731975555, -0.007020740304142237, 0.01309786457568407, 0.020761752501130104, -0.02701897919178009, 0.025058573111891747, -0.059597767889499664, 0.057588256895542145, -0.059890687465667725, -0.03155206888914108, -0.026982830837368965, 0.07404886931180954, 0.0317537747323513, 0.028947364538908005, 0.048115748912096024, 0.024953076615929604, 0.05017705634236336, 0.03643723577260971, -0.003072716761380434, -0.04836082085967064, 0.0385688878595829, -0.06527558714151382, 0.06106116995215416, 0.008031921461224556, -0.025543730705976486, -0.02751021645963192, 0.034659404307603836, 0.060384295880794525, -0.05049743503332138, -0.0704830065369606, -0.009554415009915829, -0.009174590930342674, -0.05059310793876648, 0.05322609841823578, 0.05791646987199783, 0.08850407600402832, -0.0516568161547184, 0.035075750201940536, -0.01408880203962326, -0.009037242271006107, 0.007294792681932449, -0.02965390868484974, 0.03710091859102249, 0.008880634792149067, -0.0019055265001952648, -0.024781517684459686, -0.0013002199120819569, 0.009853514842689037, 0.001498368219472468, -0.01196974515914917, -0.039981815963983536, -0.05015024542808533, -0.049728427082300186, -5.578199708599714e-33, 0.03557067736983299, -0.018561135977506638, -0.07628566026687622, 0.08573787659406662, 0.013848407194018364, -0.00679577374830842, 0.03874747082591057, 0.07574876397848129, 0.014929873868823051, -0.03901763632893562, 0.0013908061664551497, -0.006301775109022856, -0.014197027310729027, 0.009525771252810955, 0.02175944671034813, 0.02503051795065403, 0.029937906190752983, -0.014400140382349491, -0.0011385023826733232, 0.018505312502384186, 0.01680181547999382, 0.019477682188153267, -0.02153661847114563, -0.09823117405176163, -0.07989362627267838, -0.0008657720172777772, -0.00970300193876028, 0.036420129239559174, -0.002631548559293151, -0.0379716195166111, -0.0055583505891263485, 0.027735885232686996, 0.025161951780319214, -0.00984233245253563, 0.02781183458864689, -0.08368394523859024, -0.015532732009887695, -0.009503454901278019, 0.0027595055289566517, -0.0034339663106948137, -0.031904760748147964, 0.0093773752450943, 0.02348370850086212, 0.030529579147696495, -0.08686303347349167, 0.018820106983184814, 0.04991622269153595, 0.015587354078888893, -0.043750662356615067, 0.0019773845560848713, 0.013643484562635422, 0.017362114042043686, -0.05052849277853966, -0.004690367728471756, 0.04030771553516388, -0.0031672099139541388, -0.06563802063465118, -0.03098180703818798, -0.022973626852035522, 0.021675528958439827, 0.010746575891971588, 0.015785854309797287, 0.02918759547173977, -0.0006884835311211646, -0.0030642638448625803, 0.003990804776549339, 0.04404250532388687, 0.01339032594114542, -0.008783978410065174, -0.0692104697227478, -0.03629409894347191, 0.0069597926922142506, 0.018352441489696503, 0.035576146095991135, 0.02516952157020569, -0.01105139497667551, -0.028793977573513985, 0.05622490867972374, -0.007673928514122963, -0.01648355834186077, 0.005957710091024637, 0.009863092564046383, 0.04004572331905365, 0.00476829195395112, -0.004704271908849478, -0.01823730580508709, -0.05497157573699951, 0.01275594998151064, -0.004636789672076702, -0.010699989274144173, -0.06710980832576752, 0.009582106955349445, -0.02527792379260063, -0.05904928967356682, 0.01371641643345356, 0.003609919687733054, -0.016456814482808113, 0.025986673310399055, 0.02670898102223873, -0.08559207618236542, -0.05464527755975723, 0.012690245173871517, 0.017602719366550446, -0.012798641808331013, -0.004576690029352903, -0.044968172907829285, -0.00585599709302187, 0.028466975316405296, -0.045986685901880264, -0.034850578755140305, 0.04053333401679993, -0.0055993059650063515, 0.03647855669260025, -0.005134611390531063, 0.0262308306992054, -0.057628437876701355, -0.0005120699643157423, 0.0608091801404953, 0.03903907909989357, 0.05091826617717743, -0.03703578934073448, -0.027735497802495956, 0.022866053506731987, 0.01140637882053852, -0.021389581263065338, 0.009237249381840229, 0.009933206252753735, 0.017368335276842117, -0.01572670228779316, -0.030755240470170975, -0.016044175252318382, -0.04183769226074219, 2.533676592975098e-07, -0.028477169573307037, 0.04589053988456726, -0.04314381629228592, -0.050347261130809784, 0.02779235877096653, -0.0001492764422437176, -0.03950825706124306, -0.021883580833673477, -0.02916347235441208, -0.013229677453637123, 0.0516623817384243, -0.02061096392571926, -0.039748042821884155, 0.01693473570048809, -0.005601476412266493, -0.004525892902165651, 0.007407575845718384, 0.04614429920911789, -0.02480291947722435, -0.025357795879244804, 0.08283721655607224, 0.024482978507876396, 0.008452123962342739, -0.04588891565799713, 0.00818229466676712, 0.003949920181185007, 0.05043401941657066, 0.022770334035158157, 0.035761769860982895, -0.046586960554122925, 0.022436626255512238, -0.06204228848218918, 0.01029348187148571, 0.00036786473356187344, 0.02830929309129715, 0.018404122442007065, 0.008376977406442165, 0.023840995505452156, -0.017768679186701775, -0.01653873734176159, 0.029176337644457817, 0.05671573057770729, 0.06734942644834518, -0.018445489928126335, 0.05240090563893318, 0.04311911016702652, -0.07107292115688324, -0.013890455476939678, -0.01569540426135063, 0.051606275141239166, 0.037189170718193054, -0.004751925822347403, 0.0212739035487175, 0.00119326775893569, -0.024822503328323364, 0.005971222650259733, -0.0008210710948333144, 0.03312411531805992, 0.045481812208890915, 0.022630007937550545, -0.020094385370612144, -0.040504585951566696, 0.013380019925534725, 0.03848261013627052, 0.04725935682654381, 0.009020553901791573, -0.005844126455485821, 2.19811175831155e-34, -0.0030151791870594025, 0.012201250530779362, 0.018762419000267982, -0.017422718927264214, -0.06311046332120895, -0.06868427246809006, -0.04568818211555481, -0.01574595458805561, 0.0022854420822113752, -0.02361813746392727, 0.015130114741623402]