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charlieoneill

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0611006

http://arxiv.org/pdf/cs/0611006v1

2006-11-02T00:47:57Z

2006-11-02T00:47:57Z

Evolving controllers for simulated car racing

This paper describes the evolution of controllers for racing a simulated radio-controlled car around a track, modelled on a real physical track. Five different controller architectures were compared, based on neural networks, force fields and action sequences. The controllers use either egocentric (first person), Newtonian (third person) or no information about the state of the car (open-loop controller). The only controller that was able to evolve good racing behaviour was based on a neural network acting on egocentric inputs.

0611011

http://arxiv.org/abs/cs/0611011v1

2006-11-02T18:44:49Z

2006-11-02T18:44:49Z

Hedging predictions in machine learning

Recent advances in machine learning make it possible to design efficient prediction algorithms for data sets with huge numbers of parameters. This paper describes a new technique for "hedging" the predictions output by many such algorithms, including support vector machines, kernel ridge regression, kernel nearest neighbours, and by many other state-of-the-art methods. The hedged predictions for the labels of new objects include quantitative measures of their own accuracy and reliability. These measures are provably valid under the assumption of randomness, traditional in machine learning: the objects and their labels are assumed to be generated independently from the same probability distribution. In particular, it becomes possible to control (up to statistical fluctuations) the number of erroneous predictions by selecting a suitable confidence level. Validity being achieved automatically, the remaining goal of hedged prediction is efficiency: taking full account of the new objects' features and other available information to produce as accurate predictions as possible. This can be done successfully using the powerful machinery of modern machine learning.

0611024

http://arxiv.org/pdf/cs/0611024v1

2006-11-06T08:43:02Z

2006-11-06T08:43:02Z

A Relational Approach to Functional Decomposition of Logic Circuits

Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is proposed. This approach is parallel to the normalization of relational databases, they are governed by the same concepts of functional dependency (FD) and multi-valued dependency (MVD). It is manifest that the functional decomposition of switching function actually exploits the same idea and serves a similar purpose as database normalization. Partitions play an important role in the decomposition. The interdependency of two partitions can be represented by a bipartite graph. We demonstrate that both FD and MVD can be represented by bipartite graphs with specific topological properties, which are delineated by partitions of minterms. It follows that our algorithms are procedures of constructing those specific bipartite graphs of interest to meet the information-lossless criteria of functional decomposition.

0611042

http://arxiv.org/pdf/cs/0611042v1

2006-11-09T21:10:32Z

2006-11-09T21:10:32Z

CSCR:Computer Supported Collaborative Research

It is suggested that a new area of CSCR (Computer Supported Collaborative Research) is distinguished from CSCW and CSCL and that the demarcation between the three areas could do with greater clarification and prescription.

0611054

http://arxiv.org/pdf/cs/0611054v1

2006-11-13T23:28:12Z

2006-11-13T23:28:12Z

How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a coarse-grained description of the behavior that accurately describes the invariant properties of an underlying chaotic attractor. In particular, measures of the rate of information production--the topological and metric entropy rates--can be estimated from the outputs of Markov or generating partitions. Here we develop Bayesian inference for k-th order Markov chains as a method to finding generating partitions and estimating entropy rates from finite samples of discretized data produced by coarse-grained dynamical systems.

0611114

http://arxiv.org/pdf/cs/0611114v2

2006-12-01T14:55:06Z

2006-11-22T11:38:25Z

Very Sparse Stable Random Projections, Estimators and Tail Bounds for Stable Random Projections

This paper will focus on three different aspects in improving the current practice of stable random projections. Firstly, we propose {em very sparse stable random projections} to significantly reduce the processing and storage cost, by replacing the $alpha$-stable distribution with a mixture of a symmetric $alpha$-Pareto distribution (with probability $beta$, $0<betaleq1$) and a point mass at the origin (with a probability $1-beta$). This leads to a significant $frac{1}{beta}$-fold speedup for small $beta$. Secondly, we provide an improved estimator for recovering the original $l_alpha$ norms from the projected data. The standard estimator is based on the (absolute) sample median, while we suggest using the geometric mean. The geometric mean estimator we propose is strictly unbiased and is easier to study. Moreover, the geometric mean estimator is more accurate, especially non-asymptotically. Thirdly, we provide an adequate answer to the basic question of how many projections (samples) are needed for achieving some pre-specified level of accuracy. cite{Proc:Indyk_FOCS00,Article:Indyk_TKDE03} did not provide a criterion that can be used in practice. The geometric mean estimator we propose allows us to derive sharp tail bounds which can be expressed in exponential forms with constants explicitly given.

0611123

http://arxiv.org/pdf/cs/0611123v1

2006-11-23T19:12:30Z

2006-11-23T19:12:30Z

Functional Bregman Divergence and Bayesian Estimation of Distributions

A class of distortions termed functional Bregman divergences is defined, which includes squared error and relative entropy. A functional Bregman divergence acts on functions or distributions, and generalizes the standard Bregman divergence for vectors and a previous pointwise Bregman divergence that was defined for functions. A recently published result showed that the mean minimizes the expected Bregman divergence. The new functional definition enables the extension of this result to the continuous case to show that the mean minimizes the expected functional Bregman divergence over a set of functions or distributions. It is shown how this theorem applies to the Bayesian estimation of distributions. Estimation of the uniform distribution from independent and identically drawn samples is used as a case study.

0611124

http://arxiv.org/pdf/cs/0611124v1

2006-11-24T08:49:30Z

2006-11-24T08:49:30Z

Low-rank matrix factorization with attributes

We develop a new collaborative filtering (CF) method that combines both previously known users' preferences, i.e. standard CF, as well as product/user attributes, i.e. classical function approximation, to predict a given user's interest in a particular product. Our method is a generalized low rank matrix completion problem, where we learn a function whose inputs are pairs of vectors -- the standard low rank matrix completion problem being a special case where the inputs to the function are the row and column indices of the matrix. We solve this generalized matrix completion problem using tensor product kernels for which we also formally generalize standard kernel properties. Benchmark experiments on movie ratings show the advantages of our generalized matrix completion method over the standard matrix completion one with no information about movies or people, as well as over standard multi-task or single task learning methods.

0611145

http://arxiv.org/pdf/cs/0611145v1

2006-11-29T00:00:57Z

2006-11-29T00:00:57Z

A Unified View of TD Algorithms; Introducing Full-Gradient TD and Equi-Gradient Descent TD

This paper addresses the issue of policy evaluation in Markov Decision Processes, using linear function approximation. It provides a unified view of algorithms such as TD(lambda), LSTD(lambda), iLSTD, residual-gradient TD. It is asserted that they all consist in minimizing a gradient function and differ by the form of this function and their means of minimizing it. Two new schemes are introduced in that framework: Full-gradient TD which uses a generalization of the principle introduced in iLSTD, and EGD TD, which reduces the gradient by successive equi-gradient descents. These three algorithms form a new intermediate family with the interesting property of making much better use of the samples than TD while keeping a gradient descent scheme, which is useful for complexity issues and optimistic policy iteration.

0611150

http://arxiv.org/pdf/cs/0611150v3

2006-12-05T15:04:52Z

2006-11-29T13:59:31Z

A Novel Bayesian Classifier using Copula Functions

A useful method for representing Bayesian classifiers is through emph{discriminant functions}. Here, using copula functions, we propose a new model for discriminants. This model provides a rich and generalized class of decision boundaries. These decision boundaries significantly boost the classification accuracy especially for high dimensional feature spaces. We strengthen our analysis through simulation results.

0611164

http://arxiv.org/pdf/cs/0611164v1

2006-11-30T15:36:27Z

2006-11-30T15:36:27Z

Player co-modelling in a strategy board game: discovering how to play fast

In this paper we experiment with a 2-player strategy board game where playing models are evolved using reinforcement learning and neural networks. The models are evolved to speed up automatic game development based on human involvement at varying levels of sophistication and density when compared to fully autonomous playing. The experimental results suggest a clear and measurable association between the ability to win games and the ability to do that fast, while at the same time demonstrating that there is a minimum level of human involvement beyond which no learning really occurs.

0612030

http://arxiv.org/pdf/cs/0612030v1

2006-12-05T15:57:44Z

2006-12-05T15:57:44Z

Loop corrections for approximate inference

We propose a method for improving approximate inference methods that corrects for the influence of loops in the graphical model. The method is applicable to arbitrary factor graphs, provided that the size of the Markov blankets is not too large. It is an alternative implementation of an idea introduced recently by Montanari and Rizzo (2005). In its simplest form, which amounts to the assumption that no loops are present, the method reduces to the minimal Cluster Variation Method approximation (which uses maximal factors as outer clusters). On the other hand, using estimates of the effect of loops (obtained by some approximate inference algorithm) and applying the Loop Correcting (LC) method usually gives significantly better results than applying the approximate inference algorithm directly without loop corrections. Indeed, we often observe that the loop corrected error is approximately the square of the error of the approximate inference method used to estimate the effect of loops. We compare different variants of the Loop Correcting method with other approximate inference methods on a variety of graphical models, including "real world" networks, and conclude that the LC approach generally obtains the most accurate results.

0612095

http://arxiv.org/pdf/cs/0612095v2

2008-09-15T15:51:15Z

2006-12-19T16:18:30Z

Approximation of the Two-Part MDL Code

Approximation of the optimal two-part MDL code for given data, through successive monotonically length-decreasing two-part MDL codes, has the following properties: (i) computation of each step may take arbitrarily long; (ii) we may not know when we reach the optimum, or whether we will reach the optimum at all; (iii) the sequence of models generated may not monotonically improve the goodness of fit; but (iv) the model associated with the optimum has (almost) the best goodness of fit. To express the practically interesting goodness of fit of individual models for individual data sets we have to rely on Kolmogorov complexity.

0612096

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

2006-12-19T22:32:18Z

2006-12-19T22:32:18Z

Using state space differential geometry for nonlinear blind source separation

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.

0612117

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

2006-12-22T00:25:04Z

2006-12-22T00:25:04Z

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

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.

0701052

http://arxiv.org/pdf/cs/0701052v1

2007-01-08T17:03:31Z

2007-01-08T17:03:31Z

Time Series Forecasting: Obtaining Long Term Trends with Self-Organizing Maps

Kohonen self-organisation maps are a well know classification tool, commonly used in a wide variety of problems, but with limited applications in time series forecasting context. In this paper, we propose a forecasting method specifically designed for multi-dimensional long-term trends prediction, with a double application of the Kohonen algorithm. Practical applications of the method are also presented.

0701105

http://arxiv.org/pdf/cs/0701105v1

2007-01-17T13:35:35Z

2007-01-17T13:35:35Z

A Delta Debugger for ILP Query Execution

Because query execution is the most crucial part of Inductive Logic Programming (ILP) algorithms, a lot of effort is invested in developing faster execution mechanisms. These execution mechanisms typically have a low-level implementation, making them hard to debug. Moreover, other factors such as the complexity of the problems handled by ILP algorithms and size of the code base of ILP data mining systems make debugging at this level a very difficult job. In this work, we present the trace-based debugging approach currently used in the development of new execution mechanisms in hipP, the engine underlying the ACE Data Mining system. This debugger uses the delta debugging algorithm to automatically reduce the total time needed to expose bugs in ILP execution, thus making manual debugging step much lighter.

0701120

http://arxiv.org/abs/cs/0701120v1

2007-01-19T07:36:40Z

2007-01-19T07:36:40Z

Algorithmic Complexity Bounds on Future Prediction Errors

We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor $M$ from the true distribution $mu$ by the algorithmic complexity of $mu$. Here we assume we are at a time $t>1$ and already observed $x=x_1...x_t$. We bound the future prediction performance on $x_{t+1}x_{t+2}...$ by a new variant of algorithmic complexity of $mu$ given $x$, plus the complexity of the randomness deficiency of $x$. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.

0701125

http://arxiv.org/pdf/cs/0701125v1

2007-01-20T00:18:06Z

2007-01-20T00:18:06Z

Universal Algorithmic Intelligence: A mathematical top->down approach

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t x 2^l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.

0701419

http://arxiv.org/pdf/math/0701419v4

2008-01-07T14:21:58Z

2007-01-15T16:45:38Z

Strategies for prediction under imperfect monitoring

We propose simple randomized strategies for sequential prediction under imperfect monitoring, that is, when the forecaster does not have access to the past outcomes but rather to a feedback signal. The proposed strategies are consistent in the sense that they achieve, asymptotically, the best possible average reward. It was Rustichini (1999) who first proved the existence of such consistent predictors. The forecasters presented here offer the first constructive proof of consistency. Moreover, the proposed algorithms are computationally efficient. We also establish upper bounds for the rates of convergence. In the case of deterministic feedback, these rates are optimal up to logarithmic terms.

0702804

http://arxiv.org/abs/math/0702804v1

2007-02-27T03:31:34Z

2007-02-27T03:31:34Z

The Loss Rank Principle for Model Selection

We introduce a new principle for model selection in regression and classification. Many regression models are controlled by some smoothness or flexibility or complexity parameter c, e.g. the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polynomials. Let f_D^c be the (best) regressor of complexity c on data D. A more flexible regressor can fit more data D' well than a more rigid one. If something (here small loss) is easy to achieve it's typically worth less. We define the loss rank of f_D^c as the number of other (fictitious) data D' that are fitted better by f_D'^c than D is fitted by f_D^c. We suggest selecting the model complexity c that has minimal loss rank (LoRP). Unlike most penalized maximum likelihood variants (AIC,BIC,MDL), LoRP only depends on the regression function and loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like kNN. In this paper we formalize, discuss, and motivate LoRP, study it for specific regression problems, in particular linear ones, and compare it to other model selection schemes.

0703055

http://arxiv.org/pdf/cs/0703055v1

2007-03-12T19:14:23Z

2007-03-12T19:14:23Z

Support and Quantile Tubes

This correspondence studies an estimator of the conditional support of a distribution underlying a set of i.i.d. observations. The relation with mutual information is shown via an extension of Fano's theorem in combination with a generalization bound based on a compression argument. Extensions to estimating the conditional quantile interval, and statistical guarantees on the minimal convex hull are given.

0703062

http://arxiv.org/pdf/cs/0703062v1

2007-03-13T08:53:41Z

2007-03-13T08:53:41Z

Bandit Algorithms for Tree Search

Bandit based methods for tree search have recently gained popularity when applied to huge trees, e.g. in the game of go (Gelly et al., 2006). The UCT algorithm (Kocsis and Szepesvari, 2006), a tree search method based on Upper Confidence Bounds (UCB) (Auer et al., 2002), is believed to adapt locally to the effective smoothness of the tree. However, we show that UCT is too ``optimistic'' in some cases, leading to a regret O(exp(exp(D))) where D is the depth of the tree. We propose alternative bandit algorithms for tree search. First, a modification of UCT using a confidence sequence that scales exponentially with the horizon depth is proven to have a regret O(2^D sqrt{n}), but does not adapt to possible smoothness in the tree. We then analyze Flat-UCB performed on the leaves and provide a finite regret bound with high probability. Then, we introduce a UCB-based Bandit Algorithm for Smooth Trees which takes into account actual smoothness of the rewards for performing efficient ``cuts'' of sub-optimal branches with high confidence. Finally, we present an incremental tree search version which applies when the full tree is too big (possibly infinite) to be entirely represented and show that with high probability, essentially only the optimal branches is indefinitely developed. We illustrate these methods on a global optimization problem of a Lipschitz function, given noisy data.

0703125

http://arxiv.org/abs/cs/0703125v1

2007-03-25T01:19:14Z

2007-03-25T01:19:14Z

Intrinsic dimension of a dataset: what properties does one expect?

We propose an axiomatic approach to the concept of an intrinsic dimension of a dataset, based on a viewpoint of geometry of high-dimensional structures. Our first axiom postulates that high values of dimension be indicative of the presence of the curse of dimensionality (in a certain precise mathematical sense). The second axiom requires the dimension to depend smoothly on a distance between datasets (so that the dimension of a dataset and that of an approximating principal manifold would be close to each other). The third axiom is a normalization condition: the dimension of the Euclidean $n$-sphere $s^n$ is $Theta(n)$. We give an example of a dimension function satisfying our axioms, even though it is in general computationally unfeasible, and discuss a computationally cheap function satisfying most but not all of our axioms (the ``intrinsic dimensionality'' of Ch'avez et al.)

0703132

http://arxiv.org/abs/cs/0703132v1

2007-03-27T05:46:31Z

2007-03-27T05:46:31Z

Structure induction by lossless graph compression

This work is motivated by the necessity to automate the discovery of structure in vast and evergrowing collection of relational data commonly represented as graphs, for example genomic networks. A novel algorithm, dubbed Graphitour, for structure induction by lossless graph compression is presented and illustrated by a clear and broadly known case of nested structure in a DNA molecule. This work extends to graphs some well established approaches to grammatical inference previously applied only to strings. The bottom-up graph compression problem is related to the maximum cardinality (non-bipartite) maximum cardinality matching problem. The algorithm accepts a variety of graph types including directed graphs and graphs with labeled nodes and arcs. The resulting structure could be used for representation and classification of graphs.

0703138

http://arxiv.org/pdf/cs/0703138v1

2007-03-28T04:41:54Z

2007-03-28T04:41:54Z

Reinforcement Learning for Adaptive Routing

Reinforcement learning means learning a policy--a mapping of observations into actions--based on feedback from the environment. The learning can be viewed as browsing a set of policies while evaluating them by trial through interaction with the environment. We present an application of gradient ascent algorithm for reinforcement learning to a complex domain of packet routing in network communication and compare the performance of this algorithm to other routing methods on a benchmark problem.

cs.IT cs.LG math.IT

10.1109/ITW.2007.4313111

0704.0671

http://arxiv.org/abs/0704.0671v1

2007-04-05T02:57:15Z

2007-04-05T02:57:15Z

Learning from compressed observations

The problem of statistical learning is to construct a predictor of a random variable $Y$ as a function of a related random variable $X$ on the basis of an i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable predictors are drawn from some specified class, and the goal is to approach asymptotically the performance (expected loss) of the best predictor in the class. We consider the setting in which one has perfect observation of the $X$-part of the sample, while the $Y$-part has to be communicated at some finite bit rate. The encoding of the $Y$-values is allowed to depend on the $X$-values. Under suitable regularity conditions on the admissible predictors, the underlying family of probability distributions and the loss function, we give an information-theoretic characterization of achievable predictor performance in terms of conditional distortion-rate functions. The ideas are illustrated on the example of nonparametric regression in Gaussian noise.

cs.IT cs.LG math.IT

10.1109/TSP.2008.920143

0704.0954

http://arxiv.org/abs/0704.0954v1

2007-04-06T21:58:52Z

2007-04-06T21:58:52Z

Sensor Networks with Random Links: Topology Design for Distributed Consensus

In a sensor network, in practice, the communication among sensors is subject to:(1) errors or failures at random times; (3) costs; and(2) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signal-to-noise ratio (SNR) is usually a main factor in determining the probability of error (or of communication failure) in a link. These probabilities are then a proxy for the SNR under which the links operate. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. To consider this problem, we address a number of preliminary issues: (1) model the network as a random topology; (2) establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail; and, in particular, (3) show that a necessary and sufficient condition for both mss and a.s. convergence is for the algebraic connectivity of the mean graph describing the network topology to be strictly positive. With these results, we formulate topology design, subject to random link failures and to a communication cost constraint, as a constrained convex optimization problem to which we apply semidefinite programming techniques. We show by an extensive numerical study that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the asymptotic performance of a non-random network at a fraction of the communication cost.

cs.LG cs.SC

0704.1020

http://arxiv.org/pdf/0704.1020v1

2007-04-08T10:15:54Z

2007-04-08T10:15:54Z

The on-line shortest path problem under partial monitoring

The on-line shortest path problem is considered under various models of partial monitoring. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way, a decision maker has to choose in each round of a game a path between two distinguished vertices such that the loss of the chosen path (defined as the sum of the weights of its composing edges) be as small as possible. In a setting generalizing the multi-armed bandit problem, after choosing a path, the decision maker learns only the weights of those edges that belong to the chosen path. For this problem, an algorithm is given whose average cumulative loss in n rounds exceeds that of the best path, matched off-line to the entire sequence of the edge weights, by a quantity that is proportional to 1/\sqrt{n} and depends only polynomially on the number of edges of the graph. The algorithm can be implemented with linear complexity in the number of rounds n and in the number of edges. An extension to the so-called label efficient setting is also given, in which the decision maker is informed about the weights of the edges corresponding to the chosen path at a total of m << n time instances. Another extension is shown where the decision maker competes against a time-varying path, a generalization of the problem of tracking the best expert. A version of the multi-armed bandit setting for shortest path is also discussed where the decision maker learns only the total weight of the chosen path but not the weights of the individual edges on the path. Applications to routing in packet switched networks along with simulation results are also presented.

cs.LG cs.AI cs.NE

0704.1028

http://arxiv.org/pdf/0704.1028v1

2007-04-08T17:36:00Z

2007-04-08T17:36:00Z

A neural network approach to ordinal regression

Ordinal regression is an important type of learning, which has properties of both classification and regression. Here we describe a simple and effective approach to adapt a traditional neural network to learn ordinal categories. Our approach is a generalization of the perceptron method for ordinal regression. On several benchmark datasets, our method (NNRank) outperforms a neural network classification method. Compared with the ordinal regression methods using Gaussian processes and support vector machines, NNRank achieves comparable performance. Moreover, NNRank has the advantages of traditional neural networks: learning in both online and batch modes, handling very large training datasets, and making rapid predictions. These features make NNRank a useful and complementary tool for large-scale data processing tasks such as information retrieval, web page ranking, collaborative filtering, and protein ranking in Bioinformatics.

cs.LG

0704.1274

http://arxiv.org/pdf/0704.1274v1

2007-04-10T17:01:07Z

2007-04-10T17:01:07Z

Parametric Learning and Monte Carlo Optimization

This paper uncovers and explores the close relationship between Monte Carlo Optimization of a parametrized integral (MCO), Parametric machine-Learning (PL), and `blackbox' or `oracle'-based optimization (BO). We make four contributions. First, we prove that MCO is mathematically identical to a broad class of PL problems. This identity potentially provides a new application domain for all broadly applicable PL techniques: MCO. Second, we introduce immediate sampling, a new version of the Probability Collectives (PC) algorithm for blackbox optimization. Immediate sampling transforms the original BO problem into an MCO problem. Accordingly, by combining these first two contributions, we can apply all PL techniques to BO. In our third contribution we validate this way of improving BO by demonstrating that cross-validation and bagging improve immediate sampling. Finally, conventional MC and MCO procedures ignore the relationship between the sample point locations and the associated values of the integrand; only the values of the integrand at those locations are considered. We demonstrate that one can exploit the sample location information using PL techniques, for example by forming a fit of the sample locations to the associated values of the integrand. This provides an additional way to apply PL techniques to improve MCO.

cs.LG cs.AI

0704.1409

http://arxiv.org/pdf/0704.1409v3

2012-06-08T14:08:19Z

2007-04-11T13:17:01Z

Preconditioned Temporal Difference Learning

This paper has been withdrawn by the author. This draft is withdrawn for its poor quality in english, unfortunately produced by the author when he was just starting his science route. Look at the ICML version instead: http://icml2008.cs.helsinki.fi/papers/111.pdf

cs.LG cs.DS

0704.2092

http://arxiv.org/pdf/0704.2092v2

2009-03-23T03:22:02Z

2007-04-17T03:52:41Z

A Note on the Inapproximability of Correlation Clustering

We consider inapproximability of the correlation clustering problem defined as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices into clusters so that the number of pairs correctly (resp. incorrectly) classified with respect to the labels is maximized (resp. minimized). The two complementary problems are called MaxAgree and MinDisagree, respectively, and have been studied on complete graphs, where every edge is labeled, and general graphs, where some edge might not have been labeled. Natural edge-weighted versions of both problems have been studied as well. Let S-MaxAgree denote the weighted problem where all weights are taken from set S, we show that S-MaxAgree with weights bounded by $O(|V|^{1/2-\delta})$ essentially belongs to the same hardness class in the following sense: if there is a polynomial time algorithm that approximates S-MaxAgree within a factor of $\lambda = O(\log{|V|})$ with high probability, then for any choice of S', S'-MaxAgree can be approximated in polynomial time within a factor of $(\lambda + \epsilon)$, where $\epsilon > 0$ can be arbitrarily small, with high probability. A similar statement also holds for $S-MinDisagree. This result implies it is hard (assuming $NP \neq RP$) to approximate unweighted MaxAgree within a factor of $80/79-\epsilon$, improving upon a previous known factor of $116/115-\epsilon$ by Charikar et. al. \cite{Chari05}.

cs.IT cs.LG math.IT

0704.2644

http://arxiv.org/pdf/0704.2644v1

2007-04-20T01:25:22Z

2007-04-20T01:25:22Z

Joint universal lossy coding and identification of stationary mixing sources

The problem of joint universal source coding and modeling, treated in the context of lossless codes by Rissanen, was recently generalized to fixed-rate lossy coding of finitely parametrized continuous-alphabet i.i.d. sources. We extend these results to variable-rate lossy block coding of stationary ergodic sources and show that, for bounded metric distortion measures, any finitely parametrized family of stationary sources satisfying suitable mixing, smoothness and Vapnik-Chervonenkis learnability conditions admits universal schemes for joint lossy source coding and identification. We also give several explicit examples of parametric sources satisfying the regularity conditions.

cs.LG

0704.2668

http://arxiv.org/pdf/0704.2668v1

2007-04-20T08:26:29Z

2007-04-20T08:26:29Z

Supervised Feature Selection via Dependence Estimation

We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between the features and the labels. The key idea is that good features should maximise such dependence. Feature selection for various supervised learning problems (including classification and regression) is unified under this framework, and the solutions can be approximated using a backward-elimination algorithm. We demonstrate the usefulness of our method on both artificial and real world datasets.

cs.IT cs.AI cs.LG cs.NI math.IT

0705.0760

http://arxiv.org/pdf/0705.0760v1

2007-05-05T18:57:47Z

2007-05-05T18:57:47Z

Equivalence of LP Relaxation and Max-Product for Weighted Matching in General Graphs

Max-product belief propagation is a local, iterative algorithm to find the mode/MAP estimate of a probability distribution. While it has been successfully employed in a wide variety of applications, there are relatively few theoretical guarantees of convergence and correctness for general loopy graphs that may have many short cycles. Of these, even fewer provide exact ``necessary and sufficient'' characterizations. In this paper we investigate the problem of using max-product to find the maximum weight matching in an arbitrary graph with edge weights. This is done by first constructing a probability distribution whose mode corresponds to the optimal matching, and then running max-product. Weighted matching can also be posed as an integer program, for which there is an LP relaxation. This relaxation is not always tight. In this paper we show that \begin{enumerate} \item If the LP relaxation is tight, then max-product always converges, and that too to the correct answer. \item If the LP relaxation is loose, then max-product does not converge. \end{enumerate} This provides an exact, data-dependent characterization of max-product performance, and a precise connection to LP relaxation, which is a well-studied optimization technique. Also, since LP relaxation is known to be tight for bipartite graphs, our results generalize other recent results on using max-product to find weighted matchings in bipartite graphs.

cs.LG

0705.1585

http://arxiv.org/pdf/0705.1585v1

2007-05-11T04:54:54Z

2007-05-11T04:54:54Z

HMM Speaker Identification Using Linear and Non-linear Merging Techniques

Speaker identification is a powerful, non-invasive and in-expensive biometric technique. The recognition accuracy, however, deteriorates when noise levels affect a specific band of frequency. In this paper, we present a sub-band based speaker identification that intends to improve the live testing performance. Each frequency sub-band is processed and classified independently. We also compare the linear and non-linear merging techniques for the sub-bands recognizer. Support vector machines and Gaussian Mixture models are the non-linear merging techniques that are investigated. Results showed that the sub-band based method used with linear merging techniques enormously improved the performance of the speaker identification over the performance of wide-band recognizers when tested live. A live testing improvement of 9.78% was achieved

cs.LG cond-mat.dis-nn

10.1143/JPSJ.76.114001

0705.2318

http://arxiv.org/abs/0705.2318v1

2007-05-16T09:58:39Z

2007-05-16T09:58:39Z

Statistical Mechanics of Nonlinear On-line Learning for Ensemble Teachers

We analyze the generalization performance of a student in a model composed of nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We calculate the generalization error of the student analytically or numerically using statistical mechanics in the framework of on-line learning. We treat two well-known learning rules: Hebbian learning and perceptron learning. As a result, it is proven that the nonlinear model shows qualitatively different behaviors from the linear model. Moreover, it is clarified that Hebbian learning and perceptron learning show qualitatively different behaviors from each other. In Hebbian learning, we can analytically obtain the solutions. In this case, the generalization error monotonically decreases. The steady value of the generalization error is independent of the learning rate. The larger the number of teachers is and the more variety the ensemble teachers have, the smaller the generalization error is. In perceptron learning, we have to numerically obtain the solutions. In this case, the dynamical behaviors of the generalization error are non-monotonic. The smaller the learning rate is, the larger the number of teachers is; and the more variety the ensemble teachers have, the smaller the minimum value of the generalization error is.

cs.LG cs.AI

0705.2765

http://arxiv.org/pdf/0705.2765v1

2007-05-18T19:44:19Z

2007-05-18T19:44:19Z

On the monotonization of the training set

We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is NP-hard in general and is equivalent to finding a maximal independent set in special orgraphs. Practically important cases of that problem considered in detail. These are the cases when a partial order given on the replies set is a total order or has a dimension 2. We show that the second case can be reduced to maximization of a quadratic convex function on a convex set. For this case we construct an approximate polynomial algorithm based on convex optimization.

stat.ME cs.LG math.ST physics.soc-ph stat.ML stat.TH

0705.4485

http://arxiv.org/pdf/0705.4485v1

2007-05-30T23:22:59Z

2007-05-30T23:22:59Z

Mixed membership stochastic blockmodels

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.

cs.AI cs.LG

0705.4566

http://arxiv.org/pdf/0705.4566v1

2007-05-31T10:35:07Z

2007-05-31T10:35:07Z

Loop corrections for message passing algorithms in continuous variable models

In this paper we derive the equations for Loop Corrected Belief Propagation on a continuous variable Gaussian model. Using the exactness of the averages for belief propagation for Gaussian models, a different way of obtaining the covariances is found, based on Belief Propagation on cavity graphs. We discuss the relation of this loop correction algorithm to Expectation Propagation algorithms for the case in which the model is no longer Gaussian, but slightly perturbed by nonlinear terms.

cs.LG cs.AI

10.1109/ICTAI.2007.99

0706.0585

http://arxiv.org/abs/0706.0585v1

2007-06-05T05:55:07Z

2007-06-05T05:55:07Z

A Novel Model of Working Set Selection for SMO Decomposition Methods

In the process of training Support Vector Machines (SVMs) by decomposition methods, working set selection is an important technique, and some exciting schemes were employed into this field. To improve working set selection, we propose a new model for working set selection in sequential minimal optimization (SMO) decomposition methods. In this model, it selects B as working set without reselection. Some properties are given by simple proof, and experiments demonstrate that the proposed method is in general faster than existing methods.

q-bio.QM cs.LG physics.soc-ph stat.ME stat.ML

10.1371/journal.pcbi.0030252

0706.2040

http://arxiv.org/abs/0706.2040v2

2007-11-10T19:25:59Z

2007-06-14T14:52:06Z

Getting started in probabilistic graphical models

Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are biologically relevant? And to what extent can PGMs help us formulate new hypotheses that are testable at the bench? This note sketches out some answers and illustrates the main ideas behind the statistical approach to biological pattern discovery.

cs.LG stat.ML

0706.3188

http://arxiv.org/pdf/0706.3188v1

2007-06-21T16:40:06Z

2007-06-21T16:40:06Z

A tutorial on conformal prediction

Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability $\epsilon$, together with a method that makes a prediction $\hat{y}$ of a label $y$, it produces a set of labels, typically containing $\hat{y}$, that also contains $y$ with probability $1-\epsilon$. Conformal prediction can be applied to any method for producing $\hat{y}$: a nearest-neighbor method, a support-vector machine, ridge regression, etc. Conformal prediction is designed for an on-line setting in which labels are predicted successively, each one being revealed before the next is predicted. The most novel and valuable feature of conformal prediction is that if the successive examples are sampled independently from the same distribution, then the successive predictions will be right $1-\epsilon$ of the time, even though they are based on an accumulating dataset rather than on independent datasets. In addition to the model under which successive examples are sampled independently, other on-line compression models can also use conformal prediction. The widely used Gaussian linear model is one of these. This tutorial presents a self-contained account of the theory of conformal prediction and works through several numerical examples. A more comprehensive treatment of the topic is provided in "Algorithmic Learning in a Random World", by Vladimir Vovk, Alex Gammerman, and Glenn Shafer (Springer, 2005).

0706.3679

http://arxiv.org/pdf/0706.3679v1

2007-06-25T17:28:57Z

2007-06-25T17:28:57Z

Scale-sensitive Psi-dimensions: the Capacity Measures for Classifiers Taking Values in R^Q

Bounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such "VC dimensions" exist for models taking values in {0, 1}, {1,..., Q} and R. We introduce the generalizations appropriate for the missing case, the one of models with values in R^Q. This provides us with a new guaranteed risk for M-SVMs which appears superior to the existing one.

cs.LG cs.AI cs.IT math.IT

0707.0498

http://arxiv.org/pdf/0707.0498v1

2007-07-03T20:43:43Z

2007-07-03T20:43:43Z

The Role of Time in the Creation of Knowledge

This paper I assume that in humans the creation of knowledge depends on a discrete time, or stage, sequential decision-making process subjected to a stochastic, information transmitting environment. For each time-stage, this environment randomly transmits Shannon type information-packets to the decision-maker, who examines each of them for relevancy and then determines his optimal choices. Using this set of relevant information-packets, the decision-maker adapts, over time, to the stochastic nature of his environment, and optimizes the subjective expected rate-of-growth of knowledge. The decision-maker's optimal actions, lead to a decision function that involves, over time, his view of the subjective entropy of the environmental process and other important parameters at each time-stage of the process. Using this model of human behavior, one could create psychometric experiments using computer simulation and real decision-makers, to play programmed games to measure the resulting human performance.

cs.AI cs.LG cs.MS

0707.0701

http://arxiv.org/pdf/0707.0701v2

2008-10-08T18:41:53Z

2007-07-04T21:53:11Z

Clustering and Feature Selection using Sparse Principal Component Analysis

In this paper, we study the application of sparse principal component analysis (PCA) to clustering and feature selection problems. Sparse PCA seeks sparse factors, or linear combinations of the data variables, explaining a maximum amount of variance in the data while having only a limited number of nonzero coefficients. PCA is often used as a simple clustering technique and sparse factors allow us here to interpret the clusters in terms of a reduced set of variables. We begin with a brief introduction and motivation on sparse PCA and detail our implementation of the algorithm in d'Aspremont et al. (2005). We then apply these results to some classic clustering and feature selection problems arising in biology.

cs.AI cs.LG

0707.0704

http://arxiv.org/pdf/0707.0704v1

2007-07-04T22:13:42Z

2007-07-04T22:13:42Z

Model Selection Through Sparse Maximum Likelihood Estimation

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm penalty term. The problem as formulated is convex but the memory requirements and complexity of existing interior point methods are prohibitive for problems with more than tens of nodes. We present two new algorithms for solving problems with at least a thousand nodes in the Gaussian case. Our first algorithm uses block coordinate descent, and can be interpreted as recursive l_1-norm penalized regression. Our second algorithm, based on Nesterov's first order method, yields a complexity estimate with a better dependence on problem size than existing interior point methods. Using a log determinant relaxation of the log partition function (Wainwright & Jordan (2006)), we show that these same algorithms can be used to solve an approximate sparse maximum likelihood problem for the binary case. We test our algorithms on synthetic data, as well as on gene expression and senate voting records data.

cs.AI cs.LG

0707.0705

http://arxiv.org/pdf/0707.0705v4

2007-11-09T17:27:11Z

2007-07-04T22:28:28Z

Optimal Solutions for Sparse Principal Component Analysis

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applications in machine learning and engineering. We formulate a new semidefinite relaxation to this problem and derive a greedy algorithm that computes a full set of good solutions for all target numbers of non zero coefficients, with total complexity O(n^3), where n is the number of variables. We then use the same relaxation to derive sufficient conditions for global optimality of a solution, which can be tested in O(n^3) per pattern. We discuss applications in subset selection and sparse recovery and show on artificial examples and biological data that our algorithm does provide globally optimal solutions in many cases.

math.ST cs.LG math.PR stat.AP stat.TH

0707.0805

http://arxiv.org/pdf/0707.0805v2

2011-06-24T15:08:17Z

2007-07-05T15:28:05Z

A New Generalization of Chebyshev Inequality for Random Vectors

In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization.

cs.AI cs.LG

0707.1452

http://arxiv.org/pdf/0707.1452v1

2007-07-10T13:47:32Z

2007-07-10T13:47:32Z

Clusters, Graphs, and Networks for Analysing Internet-Web-Supported Communication within a Virtual Community

The proposal is to use clusters, graphs and networks as models in order to analyse the Web structure. Clusters, graphs and networks provide knowledge representation and organization. Clusters were generated by co-site analysis. The sample is a set of academic Web sites from the countries belonging to the European Union. These clusters are here revisited from the point of view of graph theory and social network analysis. This is a quantitative and structural analysis. In fact, the Internet is a computer network that connects people and organizations. Thus we may consider it to be a social network. The set of Web academic sites represents an empirical social network, and is viewed as a virtual community. The network structural properties are here analysed applying together cluster analysis, graph theory and social network analysis.

cs.IT cs.LG math.IT

0707.3087

http://arxiv.org/pdf/0707.3087v3

2009-07-22T00:58:34Z

2007-07-20T14:51:39Z

Universal Reinforcement Learning

We consider an agent interacting with an unmodeled environment. At each time, the agent makes an observation, takes an action, and incurs a cost. Its actions can influence future observations and costs. The goal is to minimize the long-term average cost. We propose a novel algorithm, known as the active LZ algorithm, for optimal control based on ideas from the Lempel-Ziv scheme for universal data compression and prediction. We establish that, under the active LZ algorithm, if there exists an integer $K$ such that the future is conditionally independent of the past given a window of $K$ consecutive actions and observations, then the average cost converges to the optimum. Experimental results involving the game of Rock-Paper-Scissors illustrate merits of the algorithm.

cs.LG

0707.3390

http://arxiv.org/pdf/0707.3390v2

2008-01-28T10:10:31Z

2007-07-23T14:35:20Z

Consistency of the group Lasso and multiple kernel learning

We consider the least-square regression problem with regularization by a block 1-norm, i.e., a sum of Euclidean norms over spaces of dimensions larger than one. This problem, referred to as the group Lasso, extends the usual regularization by the 1-norm where all spaces have dimension one, where it is commonly referred to as the Lasso. In this paper, we study the asymptotic model consistency of the group Lasso. We derive necessary and sufficient conditions for the consistency of group Lasso under practical assumptions, such as model misspecification. When the linear predictors and Euclidean norms are replaced by functions and reproducing kernel Hilbert norms, the problem is usually referred to as multiple kernel learning and is commonly used for learning from heterogeneous data sources and for non linear variable selection. Using tools from functional analysis, and in particular covariance operators, we extend the consistency results to this infinite dimensional case and also propose an adaptive scheme to obtain a consistent model estimate, even when the necessary condition required for the non adaptive scheme is not satisfied.

quant-ph cs.LG

10.1007/s11128-007-0061-6

0707.3479

http://arxiv.org/abs/0707.3479v1

2007-07-24T13:17:55Z

2007-07-24T13:17:55Z

Quantum Algorithms for Learning and Testing Juntas

In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity has no dependence on n, the dimension of the domain the Boolean functions are defined over; - with no access to any classical or quantum membership ("black-box") queries. Instead, our algorithms use only classical examples generated uniformly at random and fixed quantum superpositions of such classical examples; - which require only a few quantum examples but possibly many classical random examples (which are considered quite "cheap" relative to quantum examples). Our quantum algorithms are based on a subroutine FS which enables sampling according to the Fourier spectrum of f; the FS subroutine was used in earlier work of Bshouty and Jackson on quantum learning. Our results are as follows: - We give an algorithm for testing k-juntas to accuracy $\epsilon$ that uses $O(k/\epsilon)$ quantum examples. This improves on the number of examples used by the best known classical algorithm. - We establish the following lower bound: any FS-based k-junta testing algorithm requires $\Omega(\sqrt{k})$ queries. - We give an algorithm for learning $k$-juntas to accuracy $\epsilon$ that uses $O(\epsilon^{-1} k\log k)$ quantum examples and $O(2^k \log(1/\epsilon))$ random examples. We show that this learning algorithms is close to optimal by giving a related lower bound.

q-bio.QM cs.LG

0708.0171

http://arxiv.org/pdf/0708.0171v1

2007-08-01T19:13:52Z

2007-08-01T19:13:52Z

Virtual screening with support vector machines and structure kernels

Support vector machines and kernel methods have recently gained considerable attention in chemoinformatics. They offer generally good performance for problems of supervised classification or regression, and provide a flexible and computationally efficient framework to include relevant information and prior knowledge about the data and problems to be handled. In particular, with kernel methods molecules do not need to be represented and stored explicitly as vectors or fingerprints, but only to be compared to each other through a comparison function technically called a kernel. While classical kernels can be used to compare vector or fingerprint representations of molecules, completely new kernels were developed in the recent years to directly compare the 2D or 3D structures of molecules, without the need for an explicit vectorization step through the extraction of molecular descriptors. While still in their infancy, these approaches have already demonstrated their relevance on several toxicity prediction and structure-activity relationship problems.

physics.data-an cond-mat.stat-mech cs.IT cs.LG math-ph math.IT math.MP math.ST nlin.CD stat.TH

0708.0654

http://arxiv.org/pdf/0708.0654v2

2008-06-29T23:52:26Z

2007-08-05T01:37:53Z

Structure or Noise?

We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render the future and past conditionally independent. From this, we construct an objective function for model making whose extrema embody the trade-off between a model's structural complexity and its predictive power. The solutions correspond to a hierarchy of models that, at each level of complexity, achieve optimal predictive power at minimal cost. In the limit of maximal prediction the resulting optimal model identifies a process's intrinsic organization by extracting the underlying causal states. In this limit, the model's complexity is given by the statistical complexity, which is known to be minimal for achieving maximum prediction. Examples show how theory building can profit from analyzing a process's causal compressibility, which is reflected in the optimal models' rate-distortion curve--the process's characteristic for optimally balancing structure and noise at different levels of representation.

cs.LG

0708.1242

http://arxiv.org/pdf/0708.1242v3

2007-11-15T16:37:51Z

2007-08-09T10:21:34Z

Cost-minimising strategies for data labelling : optimal stopping and active learning

Supervised learning deals with the inference of a distribution over an output or label space $\CY$ conditioned on points in an observation space $\CX$, given a training dataset $D$ of pairs in $\CX \times \CY$. However, in a lot of applications of interest, acquisition of large amounts of observations is easy, while the process of generating labels is time-consuming or costly. One way to deal with this problem is {\em active} learning, where points to be labelled are selected with the aim of creating a model with better performance than that of an model trained on an equal number of randomly sampled points. In this paper, we instead propose to deal with the labelling cost directly: The learning goal is defined as the minimisation of a cost which is a function of the expected model performance and the total cost of the labels used. This allows the development of general strategies and specific algorithms for (a) optimal stopping, where the expected cost dictates whether label acquisition should continue (b) empirical evaluation, where the cost is used as a performance metric for a given combination of inference, stopping and sampling methods. Though the main focus of the paper is optimal stopping, we also aim to provide the background for further developments and discussion in the related field of active learning.

cs.LG

0708.1503

http://arxiv.org/pdf/0708.1503v1

2007-08-10T19:19:54Z

2007-08-10T19:19:54Z

Defensive forecasting for optimal prediction with expert advice

The method of defensive forecasting is applied to the problem of prediction with expert advice for binary outcomes. It turns out that defensive forecasting is not only competitive with the Aggregating Algorithm but also handles the case of "second-guessing" experts, whose advice depends on the learner's prediction; this paper assumes that the dependence on the learner's prediction is continuous.

cs.IT cond-mat.stat-mech cs.LG math.IT math.ST stat.TH

0708.1580

http://arxiv.org/pdf/0708.1580v2

2010-08-19T23:46:24Z

2007-08-11T19:13:29Z

Optimal Causal Inference: Estimating Stored Information and Approximating Causal Architecture

We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that, in the limit in which a model complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of underlying causal states can be found by optimal causal estimation. A previously derived model complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid over-fitting.

cs.IT cs.LG math.IT math.PR

0708.2319

http://arxiv.org/pdf/0708.2319v1

2007-08-17T06:39:11Z

2007-08-17T06:39:11Z

On Semimeasures Predicting Martin-Loef Random Sequences

Solomonoff's central result on induction is that the posterior of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating posterior mu, if the latter is computable. Hence, M is eligible as a universal sequence predictor in case of unknown mu. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Loef) random sequences remained open. Such a convergence result would be particularly interesting and natural, since randomness can be defined in terms of M itself. We show that there are universal semimeasures M which do not converge for all random sequences, i.e. we give a partial negative answer to the open problem. We also provide a positive answer for some non-universal semimeasures. We define the incomputable measure D as a mixture over all computable measures and the enumerable semimeasure W as a mixture over all enumerable nearly-measures. We show that W converges to D and D to mu on all random sequences. The Hellinger distance measuring closeness of two distributions plays a central role.

cs.LG

0708.2353

http://arxiv.org/pdf/0708.2353v2

2007-08-23T12:44:34Z

2007-08-17T12:18:24Z

Continuous and randomized defensive forecasting: unified view

Defensive forecasting is a method of transforming laws of probability (stated in game-theoretic terms as strategies for Sceptic) into forecasting algorithms. There are two known varieties of defensive forecasting: "continuous", in which Sceptic's moves are assumed to depend on the forecasts in a (semi)continuous manner and which produces deterministic forecasts, and "randomized", in which the dependence of Sceptic's moves on the forecasts is arbitrary and Forecaster's moves are allowed to be randomized. This note shows that the randomized variety can be obtained from the continuous variety by smearing Sceptic's moves to make them continuous.

cs.LG cs.CC

0708.3226

http://arxiv.org/pdf/0708.3226v7

2010-04-04T20:39:03Z

2007-08-23T18:26:21Z

A Dichotomy Theorem for General Minimum Cost Homomorphism Problem

In the constraint satisfaction problem ($CSP$), the aim is to find an assignment of values to a set of variables subject to specified constraints. In the minimum cost homomorphism problem ($MinHom$), one is additionally given weights $c_{va}$ for every variable $v$ and value $a$, and the aim is to find an assignment $f$ to the variables that minimizes $\sum_{v} c_{vf(v)}$. Let $MinHom(\Gamma)$ denote the $MinHom$ problem parameterized by the set of predicates allowed for constraints. $MinHom(\Gamma)$ is related to many well-studied combinatorial optimization problems, and concrete applications can be found in, for instance, defence logistics and machine learning. We show that $MinHom(\Gamma)$ can be studied by using algebraic methods similar to those used for CSPs. With the aid of algebraic techniques, we classify the computational complexity of $MinHom(\Gamma)$ for all choices of $\Gamma$. Our result settles a general dichotomy conjecture previously resolved only for certain classes of directed graphs, [Gutin, Hell, Rafiey, Yeo, European J. of Combinatorics, 2008].

cs.LG

0709.0509

http://arxiv.org/pdf/0709.0509v1

2007-09-04T19:36:22Z

2007-09-04T19:36:22Z

Filtering Additive Measurement Noise with Maximum Entropy in the Mean

The purpose of this note is to show how the method of maximum entropy in the mean (MEM) may be used to improve parametric estimation when the measurements are corrupted by large level of noise. The method is developed in the context on a concrete example: that of estimation of the parameter in an exponential distribution. We compare the performance of our method with the bayesian and maximum likelihood approaches.

math.ST cs.IT cs.LG math.IT stat.ML stat.TH

0709.1516

http://arxiv.org/pdf/0709.1516v1

2007-09-11T01:39:20Z

2007-09-11T01:39:20Z

On Universal Prediction and Bayesian Confirmation

The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or fail, in particular in complex situations. Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. We show that Solomonoff's model possesses many desirable properties: Strong total and weak instantaneous bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well (actually better) in non-computable environments.

cs.LG cs.GT

0709.2446

http://arxiv.org/pdf/0709.2446v1

2007-09-15T20:48:57Z

2007-09-15T20:48:57Z

Learning for Dynamic Bidding in Cognitive Radio Resources

In this paper, we model the various wireless users in a cognitive radio network as a collection of selfish, autonomous agents that strategically interact in order to acquire the dynamically available spectrum opportunities. Our main focus is on developing solutions for wireless users to successfully compete with each other for the limited and time-varying spectrum opportunities, given the experienced dynamics in the wireless network. We categorize these dynamics into two types: one is the disturbance due to the environment (e.g. wireless channel conditions, source traffic characteristics, etc.) and the other is the impact caused by competing users. To analyze the interactions among users given the environment disturbance, we propose a general stochastic framework for modeling how the competition among users for spectrum opportunities evolves over time. At each stage of the dynamic resource allocation, a central spectrum moderator auctions the available resources and the users strategically bid for the required resources. The joint bid actions affect the resource allocation and hence, the rewards and future strategies of all users. Based on the observed resource allocation and corresponding rewards from previous allocations, we propose a best response learning algorithm that can be deployed by wireless users to improve their bidding policy at each stage. The simulation results show that by deploying the proposed best response learning algorithm, the wireless users can significantly improve their own performance in terms of both the packet loss rate and the incurred cost for the used resources.

cs.LG cs.NE stat.AP

10.1016/j.chemolab.2005.06.010

0709.3427

http://arxiv.org/abs/0709.3427v1

2007-09-21T12:49:47Z

2007-09-21T12:49:47Z

Mutual information for the selection of relevant variables in spectrometric nonlinear modelling

Data from spectrophotometers form vectors of a large number of exploitable variables. Building quantitative models using these variables most often requires using a smaller set of variables than the initial one. Indeed, a too large number of input variables to a model results in a too large number of parameters, leading to overfitting and poor generalization abilities. In this paper, we suggest the use of the mutual information measure to select variables from the initial set. The mutual information measures the information content in input variables with respect to the model output, without making any assumption on the model that will be used; it is thus suitable for nonlinear modelling. In addition, it leads to the selection of variables among the initial set, and not to linear or nonlinear combinations of them. Without decreasing the model performances compared to other variable projection methods, it allows therefore a greater interpretability of the results.

cs.NE cs.LG

10.1016/j.neunet.2006.05.002

0709.3461

http://arxiv.org/abs/0709.3461v1

2007-09-21T15:20:07Z

2007-09-21T15:20:07Z

Fast Algorithm and Implementation of Dissimilarity Self-Organizing Maps

In many real world applications, data cannot be accurately represented by vectors. In those situations, one possible solution is to rely on dissimilarity measures that enable sensible comparison between observations. Kohonen's Self-Organizing Map (SOM) has been adapted to data described only through their dissimilarity matrix. This algorithm provides both non linear projection and clustering of non vector data. Unfortunately, the algorithm suffers from a high cost that makes it quite difficult to use with voluminous data sets. In this paper, we propose a new algorithm that provides an important reduction of the theoretical cost of the dissimilarity SOM without changing its outcome (the results are exactly the same as the ones obtained with the original algorithm). Moreover, we introduce implementation methods that result in very short running times. Improvements deduced from the theoretical cost model are validated on simulated and real world data (a word list clustering problem). We also demonstrate that the proposed implementation methods reduce by a factor up to 3 the running time of the fast algorithm over a standard implementation.

cs.NE cs.LG

0709.3586

http://arxiv.org/pdf/0709.3586v1

2007-09-22T15:53:54Z

2007-09-22T15:53:54Z

Une adaptation des cartes auto-organisatrices pour des donn\'ees d\'ecrites par un tableau de dissimilarit\'es

Many data analysis methods cannot be applied to data that are not represented by a fixed number of real values, whereas most of real world observations are not readily available in such a format. Vector based data analysis methods have therefore to be adapted in order to be used with non standard complex data. A flexible and general solution for this adaptation is to use a (dis)similarity measure. Indeed, thanks to expert knowledge on the studied data, it is generally possible to define a measure that can be used to make pairwise comparison between observations. General data analysis methods are then obtained by adapting existing methods to (dis)similarity matrices. In this article, we propose an adaptation of Kohonen's Self Organizing Map (SOM) to (dis)similarity data. The proposed algorithm is an adapted version of the vector based batch SOM. The method is validated on real world data: we provide an analysis of the usage patterns of the web site of the Institut National de Recherche en Informatique et Automatique, constructed thanks to web log mining method.

cs.NE cs.LG

0709.3587

http://arxiv.org/pdf/0709.3587v1

2007-09-22T15:54:37Z

2007-09-22T15:54:37Z

Self-organizing maps and symbolic data

In data analysis new forms of complex data have to be considered like for example (symbolic data, functional data, web data, trees, SQL query and multimedia data, ...). In this context classical data analysis for knowledge discovery based on calculating the center of gravity can not be used because input are not $\mathbb{R}^p$ vectors. In this paper, we present an application on real world symbolic data using the self-organizing map. To this end, we propose an extension of the self-organizing map that can handle symbolic data.

cs.LG stat.AP

10.1016/j.chemolab.2006.06.007

0709.3639

http://arxiv.org/abs/0709.3639v1

2007-09-23T14:08:51Z

2007-09-23T14:08:51Z

Fast Selection of Spectral Variables with B-Spline Compression

The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach of testing all possible subsets of variables with the prediction model is intractable, an incremental selection approach using a nonparametric statistics is a good option, as it avoids the computationally intensive use of the model itself. It has two drawbacks however: the number of groups of variables to test is still huge, and colinearities can make the results unstable. To overcome these limitations, this paper presents a method to select groups of spectral variables. It consists in a forward-backward procedure applied to the coefficients of a B-Spline representation of the spectra. The criterion used in the forward-backward procedure is the mutual information, allowing to find nonlinear dependencies between variables, on the contrary of the generally used correlation. The spline representation is used to get interpretability of the results, as groups of consecutive spectral variables will be selected. The experiments conducted on NIR spectra from fescue grass and diesel fuels show that the method provides clearly identified groups of selected variables, making interpretation easy, while keeping a low computational load. The prediction performances obtained using the selected coefficients are higher than those obtained by the same method applied directly to the original variables and similar to those obtained using traditional models, although using significantly less spectral variables.

cs.LG stat.AP

10.1016/j.neucom.2006.11.019

0709.3640

http://arxiv.org/abs/0709.3640v1

2007-09-23T14:09:28Z

2007-09-23T14:09:28Z

Resampling methods for parameter-free and robust feature selection with mutual information

Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual information estimator and to determine when to halt the forward procedure. These two choices are difficult to make because, as the dimensionality of the subset increases, the estimation of the mutual information becomes less and less reliable. This paper proposes to use resampling methods, a K-fold cross-validation and the permutation test, to address both issues. The resampling methods bring information about the variance of the estimator, information which can then be used to automatically set the parameter and to calculate a threshold to stop the forward procedure. The procedure is illustrated on a synthetic dataset as well as on real-world examples.

cs.LG cs.AI cs.NE

0709.3965

http://arxiv.org/pdf/0709.3965v2

2007-09-26T10:37:00Z

2007-09-25T14:28:32Z

Evolving Classifiers: Methods for Incremental Learning

The ability of a classifier to take on new information and classes by evolving the classifier without it having to be fully retrained is known as incremental learning. Incremental learning has been successfully applied to many classification problems, where the data is changing and is not all available at once. In this paper there is a comparison between Learn++, which is one of the most recent incremental learning algorithms, and the new proposed method of Incremental Learning Using Genetic Algorithm (ILUGA). Learn++ has shown good incremental learning capabilities on benchmark datasets on which the new ILUGA method has been tested. ILUGA has also shown good incremental learning ability using only a few classifiers and does not suffer from catastrophic forgetting. The results obtained for ILUGA on the Optical Character Recognition (OCR) and Wine datasets are good, with an overall accuracy of 93% and 94% respectively showing a 4% improvement over Learn++.MT for the difficult multi-class OCR dataset.

cs.LG cs.AI

0709.3967

http://arxiv.org/pdf/0709.3967v1

2007-09-25T14:37:40Z

2007-09-25T14:37:40Z

Classification of Images Using Support Vector Machines

Support Vector Machines (SVMs) are a relatively new supervised classification technique to the land cover mapping community. They have their roots in Statistical Learning Theory and have gained prominence because they are robust, accurate and are effective even when using a small training sample. By their nature SVMs are essentially binary classifiers, however, they can be adopted to handle the multiple classification tasks common in remote sensing studies. The two approaches commonly used are the One-Against-One (1A1) and One-Against-All (1AA) techniques. In this paper, these approaches are evaluated in as far as their impact and implication for land cover mapping. The main finding from this research is that whereas the 1AA technique is more predisposed to yielding unclassified and mixed pixels, the resulting classification accuracy is not significantly different from 1A1 approach. It is the authors conclusions that ultimately the choice of technique adopted boils down to personal preference and the uniqueness of the dataset at hand.

cs.LG

0710.0485

http://arxiv.org/pdf/0710.0485v2

2008-06-27T18:45:01Z

2007-10-02T10:08:41Z

Prediction with expert advice for the Brier game

We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical performance guarantee turns out to be rather tight on these data sets, especially in the case of the more extensive tennis data.

cs.DB cs.LG cs.LO

0710.2083

http://arxiv.org/pdf/0710.2083v1

2007-10-10T18:00:44Z

2007-10-10T18:00:44Z

Association Rules in the Relational Calculus

One of the most utilized data mining tasks is the search for association rules. Association rules represent significant relationships between items in transactions. We extend the concept of association rule to represent a much broader class of associations, which we refer to as \emph{entity-relationship rules.} Semantically, entity-relationship rules express associations between properties of related objects. Syntactically, these rules are based on a broad subclass of safe domain relational calculus queries. We propose a new definition of support and confidence for entity-relationship rules and for the frequency of entity-relationship queries. We prove that the definition of frequency satisfies standard probability axioms and the Apriori property.

cs.CL cs.AI cs.LG

0710.2446

http://arxiv.org/pdf/0710.2446v1

2007-10-12T12:44:11Z

2007-10-12T12:44:11Z

The structure of verbal sequences analyzed with unsupervised learning techniques

Data mining allows the exploration of sequences of phenomena, whereas one usually tends to focus on isolated phenomena or on the relation between two phenomena. It offers invaluable tools for theoretical analyses and exploration of the structure of sentences, texts, dialogues, and speech. We report here the results of an attempt at using it for inspecting sequences of verbs from French accounts of road accidents. This analysis comes from an original approach of unsupervised training allowing the discovery of the structure of sequential data. The entries of the analyzer were only made of the verbs appearing in the sentences. It provided a classification of the links between two successive verbs into four distinct clusters, allowing thus text segmentation. We give here an interpretation of these clusters by applying a statistical analysis to independent semantic annotations.

cs.LG

0710.2848

http://arxiv.org/pdf/0710.2848v1

2007-10-15T15:38:33Z

2007-10-15T15:38:33Z

Consistency of trace norm minimization

Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide necessary and sufficient conditions for rank consistency of trace norm minimization with the square loss. We also provide an adaptive version that is rank consistent even when the necessary condition for the non adaptive version is not fulfilled.

cs.LG cs.IR

0710.2889

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

2007-12-07T00:02:44Z

2007-10-15T18:25:15Z

An efficient reduction of ranking to classification

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.

cs.LG cs.CE q-bio.QM

0710.5116

http://arxiv.org/pdf/0710.5116v1

2007-10-26T15:13:21Z

2007-10-26T15:13:21Z

Combining haplotypers

Statistically resolving the underlying haplotype pair for a genotype measurement is an important intermediate step in gene mapping studies, and has received much attention recently. Consequently, a variety of methods for this problem have been developed. Different methods employ different statistical models, and thus implicitly encode different assumptions about the nature of the underlying haplotype structure. Depending on the population sample in question, their relative performance can vary greatly, and it is unclear which method to choose for a particular sample. Instead of choosing a single method, we explore combining predictions returned by different methods in a principled way, and thereby circumvent the problem of method selection. We propose several techniques for combining haplotype reconstructions and analyze their computational properties. In an experimental study on real-world haplotype data we show that such techniques can provide more accurate and robust reconstructions, and are useful for outlier detection. Typically, the combined prediction is at least as accurate as or even more accurate than the best individual method, effectively circumventing the method selection problem.

cs.DS cs.LG

0711.0189

http://arxiv.org/pdf/0711.0189v1

2007-11-01T19:04:43Z

2007-11-01T19:04:43Z

A Tutorial on Spectral Clustering

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

cs.AI cs.LG

0711.1814

http://arxiv.org/pdf/0711.1814v1

2007-11-12T17:15:34Z

2007-11-12T17:15:34Z

Building Rules on Top of Ontologies for the Semantic Web with Inductive Logic Programming

Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems such as $\mathcal{AL}$-log that integrates the description logic $\mathcal{ALC}$ and the function-free Horn clausal language \textsc{Datalog}. In this paper we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of $\mathcal{AL}$-log. The framework is valid whatever the scope of induction (description vs. prediction) is. Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement. Keywords: Inductive Logic Programming, Hybrid Knowledge Representation and Reasoning Systems, Ontologies, Semantic Web. Note: To appear in Theory and Practice of Logic Programming (TPLP)

cs.LG cs.CL cs.IR

0711.2023

http://arxiv.org/pdf/0711.2023v1

2007-11-13T16:28:47Z

2007-11-13T16:28:47Z

Empirical Evaluation of Four Tensor Decomposition Algorithms

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in information retrieval, collaborative filtering, computational linguistics, computational vision, and other fields. However, SVD is limited to two-dimensional arrays of data (two modes), and many potential applications have three or more modes, which require higher-order tensor decompositions. This paper evaluates four algorithms for higher-order tensor decomposition: Higher-Order Singular Value Decomposition (HO-SVD), Higher-Order Orthogonal Iteration (HOOI), Slice Projection (SP), and Multislice Projection (MP). We measure the time (elapsed run time), space (RAM and disk space requirements), and fit (tensor reconstruction accuracy) of the four algorithms, under a variety of conditions. We find that standard implementations of HO-SVD and HOOI do not scale up to larger tensors, due to increasing RAM requirements. We recommend HOOI for tensors that are small enough for the available RAM and MP for larger tensors.

math.ST cs.LG math.PR stat.TH

0711.2801

http://arxiv.org/pdf/0711.2801v2

2007-12-02T21:59:44Z

2007-11-18T17:28:23Z

Inverse Sampling for Nonasymptotic Sequential Estimation of Bounded Variable Means

In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level, it suffices to continue sampling until the sample sum is no less than a certain bound and then take the average of samples as an estimate for the mean of the bounded random variable. We have developed an explicit formula and a bisection search method for the determination of such bound of sample sum, without any knowledge of the bounded variable. Moreover, we have derived bounds for the distribution of sample size. In the special case of Bernoulli random variables, we have established analytical and numerical methods to further reduce the bound of sample sum and thus improve the efficiency of sampling. Furthermore, the fallacy of existing results are detected and analyzed.

cs.LG cs.AI cs.CV

0711.2914

http://arxiv.org/pdf/0711.2914v1

2007-11-19T12:25:00Z

2007-11-19T12:25:00Z

Image Classification Using SVMs: One-against-One Vs One-against-All

Support Vector Machines (SVMs) are a relatively new supervised classification technique to the land cover mapping community. They have their roots in Statistical Learning Theory and have gained prominence because they are robust, accurate and are effective even when using a small training sample. By their nature SVMs are essentially binary classifiers, however, they can be adopted to handle the multiple classification tasks common in remote sensing studies. The two approaches commonly used are the One-Against-One (1A1) and One-Against-All (1AA) techniques. In this paper, these approaches are evaluated in as far as their impact and implication for land cover mapping. The main finding from this research is that whereas the 1AA technique is more predisposed to yielding unclassified and mixed pixels, the resulting classification accuracy is not significantly different from 1A1 approach. It is the authors conclusion therefore that ultimately the choice of technique adopted boils down to personal preference and the uniqueness of the dataset at hand.

cs.LG

0711.3594

http://arxiv.org/pdf/0711.3594v1

2007-11-22T15:05:35Z

2007-11-22T15:05:35Z

Clustering with Transitive Distance and K-Means Duality

Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a non-eigenproblem based clustering method is proposed to deal with the clustering problem. Its performance is comparable to the spectral clustering algorithms but it is more efficient with computational complexity $O(n^2)$. We show that with a transitive distance and an observed property, called K-means duality, our algorithm can be used to handle data sets with complex cluster shapes, multi-scale clusters, and noise. Moreover, no parameters except the number of clusters need to be set in our algorithm.

cs.LG cs.IT math.IT

0711.3675

http://arxiv.org/pdf/0711.3675v1

2007-11-23T07:45:52Z

2007-11-23T07:45:52Z

Derivations of Normalized Mutual Information in Binary Classifications

This correspondence studies the basic problem of classifications - how to evaluate different classifiers. Although the conventional performance indexes, such as accuracy, are commonly used in classifier selection or evaluation, information-based criteria, such as mutual information, are becoming popular in feature/model selections. In this work, we propose to assess classifiers in terms of normalized mutual information (NI), which is novel and well defined in a compact range for classifier evaluation. We derive close-form relations of normalized mutual information with respect to accuracy, precision, and recall in binary classifications. By exploring the relations among them, we reveal that NI is actually a set of nonlinear functions, with a concordant power-exponent form, to each performance index. The relations can also be expressed with respect to precision and recall, or to false alarm and hitting rate (recall).

cs.LG

0711.4452

http://arxiv.org/pdf/0711.4452v1

2007-11-28T12:05:47Z

2007-11-28T12:05:47Z

Covariance and PCA for Categorical Variables

Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated results give reasonable values for test data. A method of principal component analysis (RS-PCA) is also proposed using regular simplex expressions, which allows easy interpretation of the principal components. The proposed methods apply to variable selection problem of categorical data USCensus1990 data. The proposed methods give appropriate criterion for the variable selection problem of categorical

cs.LG

0712.0130

http://arxiv.org/pdf/0712.0130v1

2007-12-02T09:38:26Z

2007-12-02T09:38:26Z

On the Relationship between the Posterior and Optimal Similarity

For a classification problem described by the joint density $P(\omega,x)$, models of $P(\omega\eq\omega'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification. This paper analyzes demonstrates several additional properties of that conditional distribution. The paper first shows that we can reconstruct, up to class labels, the class posterior distribution $P(\omega|x)$ given $P(\omega\eq\omega'|x,x')$, gives a procedure for recovering the class labels, and gives an asymptotically Bayes-optimal classification procedure. It also shows, given such an optimal similarity measure, how to construct a classifier that outperforms the nearest neighbor classifier and achieves Bayes-optimal classification rates. The paper then analyzes Bayesian similarity in a framework where a classifier faces a number of related classification tasks (multitask learning) and illustrates that reconstruction of the class posterior distribution is not possible in general. Finally, the paper identifies a distinct class of classification problems using $P(\omega\eq\omega'|x,x')$ and shows that using $P(\omega\eq\omega'|x,x')$ to solve those problems is the Bayes optimal solution.

cs.AI cs.CC cs.DM cs.LG

0712.0451

http://arxiv.org/pdf/0712.0451v1

2007-12-04T08:52:46Z

2007-12-04T08:52:46Z

A Reactive Tabu Search Algorithm for Stimuli Generation in Psycholinguistics

The generation of meaningless "words" matching certain statistical and/or linguistic criteria is frequently needed for experimental purposes in Psycholinguistics. Such stimuli receive the name of pseudowords or nonwords in the Cognitive Neuroscience literatue. The process for building nonwords sometimes has to be based on linguistic units such as syllables or morphemes, resulting in a numerical explosion of combinations when the size of the nonwords is increased. In this paper, a reactive tabu search scheme is proposed to generate nonwords of variables size. The approach builds pseudowords by using a modified Metaheuristic algorithm based on a local search procedure enhanced by a feedback-based scheme. Experimental results show that the new algorithm is a practical and effective tool for nonword generation.

cs.LG

0712.0653

http://arxiv.org/pdf/0712.0653v2

2009-05-11T05:49:09Z

2007-12-05T05:39:07Z

Equations of States in Singular Statistical Estimation

Learning machines which have hierarchical structures or hidden variables are singular statistical models because they are nonidentifiable and their Fisher information matrices are singular. In singular statistical models, neither the Bayes a posteriori distribution converges to the normal distribution nor the maximum likelihood estimator satisfies asymptotic normality. This is the main reason why it has been difficult to predict their generalization performances from trained states. In this paper, we study four errors, (1) Bayes generalization error, (2) Bayes training error, (3) Gibbs generalization error, and (4) Gibbs training error, and prove that there are mathematical relations among these errors. The formulas proved in this paper are equations of states in statistical estimation because they hold for any true distribution, any parametric model, and any a priori distribution. Also we show that Bayes and Gibbs generalization errors are estimated by Bayes and Gibbs training errors, and propose widely applicable information criteria which can be applied to both regular and singular statistical models.

cs.LG cs.DM

0712.0840

http://arxiv.org/pdf/0712.0840v1

2007-12-05T22:25:03Z

2007-12-05T22:25:03Z

A Universal Kernel for Learning Regular Languages

We give a universal kernel that renders all the regular languages linearly separable. We are not able to compute this kernel efficiently and conjecture that it is intractable, but we do have an efficient $\eps$-approximation.

cs.LG cs.AI cs.NE

0712.0938

http://arxiv.org/pdf/0712.0938v1

2007-12-06T13:52:04Z

2007-12-06T13:52:04Z

Automatic Pattern Classification by Unsupervised Learning Using Dimensionality Reduction of Data with Mirroring Neural Networks

This paper proposes an unsupervised learning technique by using Multi-layer Mirroring Neural Network and Forgy's clustering algorithm. Multi-layer Mirroring Neural Network is a neural network that can be trained with generalized data inputs (different categories of image patterns) to perform non-linear dimensionality reduction and the resultant low-dimensional code is used for unsupervised pattern classification using Forgy's algorithm. By adapting the non-linear activation function (modified sigmoidal function) and initializing the weights and bias terms to small random values, mirroring of the input pattern is initiated. In training, the weights and bias terms are changed in such a way that the input presented is reproduced at the output by back propagating the error. The mirroring neural network is capable of reducing the input vector to a great degree (approximately 1/30th the original size) and also able to reconstruct the input pattern at the output layer from this reduced code units. The feature set (output of central hidden layer) extracted from this network is fed to Forgy's algorithm, which classify input data patterns into distinguishable classes. In the implementation of Forgy's algorithm, initial seed points are selected in such a way that they are distant enough to be perfectly grouped into different categories. Thus a new method of unsupervised learning is formulated and demonstrated in this paper. This method gave impressive results when applied to classification of different image patterns.

cs.CC cs.LG

0712.1402

http://arxiv.org/pdf/0712.1402v2

2010-03-08T19:30:26Z

2007-12-10T06:50:36Z

Reconstruction of Markov Random Fields from Samples: Some Easy Observations and Algorithms

Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random fields. We analyze a simple algorithm for reconstructing the underlying graph defining a Markov random field on $n$ nodes and maximum degree $d$ given observations. We show that under mild non-degeneracy conditions it reconstructs the generating graph with high probability using $\Theta(d \epsilon^{-2}\delta^{-4} \log n)$ samples where $\epsilon,\delta$ depend on the local interactions. For most local interaction $\eps,\delta$ are of order $\exp(-O(d))$. Our results are optimal as a function of $n$ up to a multiplicative constant depending on $d$ and the strength of the local interactions. Our results seem to be the first results for general models that guarantee that {\em the} generating model is reconstructed. Furthermore, we provide explicit $O(n^{d+2} \epsilon^{-2}\delta^{-4} \log n)$ running time bound. In cases where the measure on the graph has correlation decay, the running time is $O(n^2 \log n)$ for all fixed $d$. We also discuss the effect of observing noisy samples and show that as long as the noise level is low, our algorithm is effective. On the other hand, we construct an example where large noise implies non-identifiability even for generic noise and interactions. Finally, we briefly show that in some simple cases, models with hidden nodes can also be recovered.

cs.NI cs.LG

0712.2497

http://arxiv.org/pdf/0712.2497v1

2007-12-15T06:50:43Z

2007-12-15T06:50:43Z

A New Theoretic Foundation for Cross-Layer Optimization

Cross-layer optimization solutions have been proposed in recent years to improve the performance of network users operating in a time-varying, error-prone wireless environment. However, these solutions often rely on ad-hoc optimization approaches, which ignore the different environmental dynamics experienced at various layers by a user and violate the layered network architecture of the protocol stack by requiring layers to provide access to their internal protocol parameters to other layers. This paper presents a new theoretic foundation for cross-layer optimization, which allows each layer to make autonomous decisions individually, while maximizing the utility of the wireless user by optimally determining what information needs to be exchanged among layers. Hence, this cross-layer framework does not change the current layered architecture. Specifically, because the wireless user interacts with the environment at various layers of the protocol stack, the cross-layer optimization problem is formulated as a layered Markov decision process (MDP) in which each layer adapts its own protocol parameters and exchanges information (messages) with other layers in order to cooperatively maximize the performance of the wireless user. The message exchange mechanism for determining the optimal cross-layer transmission strategies has been designed for both off-line optimization and on-line dynamic adaptation. We also show that many existing cross-layer optimization algorithms can be formulated as simplified, sub-optimal, versions of our layered MDP framework.

cs.LG

0712.2869

http://arxiv.org/pdf/0712.2869v1

2007-12-18T03:30:05Z

2007-12-18T03:30:05Z

Density estimation in linear time

We consider the problem of choosing a density estimate from a set of distributions F, minimizing the L1-distance to an unknown distribution (Devroye, Lugosi 2001). Devroye and Lugosi analyze two algorithms for the problem: Scheffe tournament winner and minimum distance estimate. The Scheffe tournament estimate requires fewer computations than the minimum distance estimate, but has strictly weaker guarantees than the latter. We focus on the computational aspect of density estimation. We present two algorithms, both with the same guarantee as the minimum distance estimate. The first one, a modification of the minimum distance estimate, uses the same number (quadratic in |F|) of computations as the Scheffe tournament. The second one, called ``efficient minimum loss-weight estimate,'' uses only a linear number of computations, assuming that F is preprocessed. We also give examples showing that the guarantees of the algorithms cannot be improved and explore randomized algorithms for density estimation.

cs.LG

0712.3402

http://arxiv.org/pdf/0712.3402v1

2007-12-20T13:06:50Z

2007-12-20T13:06:50Z

Graph kernels between point clouds

Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. In this paper, we present extensions of graph kernels for point clouds, which allow to use kernel methods for such ob jects as shapes, line drawings, or any three-dimensional point clouds. In order to design rich and numerically efficient kernels with as few free parameters as possible, we use kernels between covariance matrices and their factorizations on graphical models. We derive polynomial time dynamic programming recursions and present applications to recognition of handwritten digits and Chinese characters from few training examples.

cs.NE cs.AI cs.LG

0712.3654

http://arxiv.org/pdf/0712.3654v1

2007-12-21T10:05:52Z

2007-12-21T10:05:52Z

Improving the Performance of PieceWise Linear Separation Incremental Algorithms for Practical Hardware Implementations

In this paper we shall review the common problems associated with Piecewise Linear Separation incremental algorithms. This kind of neural models yield poor performances when dealing with some classification problems, due to the evolving schemes used to construct the resulting networks. So as to avoid this undesirable behavior we shall propose a modification criterion. It is based upon the definition of a function which will provide information about the quality of the network growth process during the learning phase. This function is evaluated periodically as the network structure evolves, and will permit, as we shall show through exhaustive benchmarks, to considerably improve the performance(measured in terms of network complexity and generalization capabilities) offered by the networks generated by these incremental models.

cs.LG cs.CY

10.1142/S0129183109013613

0712.3807

http://arxiv.org/abs/0712.3807v3

2009-10-14T15:30:56Z

2007-12-26T14:25:18Z

Improved Collaborative Filtering Algorithm via Information Transformation

In this paper, we propose a spreading activation approach for collaborative filtering (SA-CF). By using the opinion spreading process, the similarity between any users can be obtained. The algorithm has remarkably higher accuracy than the standard collaborative filtering (CF) using Pearson correlation. Furthermore, we introduce a free parameter $\beta$ to regulate the contributions of objects to user-user correlations. The numerical results indicate that decreasing the influence of popular objects can further improve the algorithmic accuracy and personality. We argue that a better algorithm should simultaneously require less computation and generate higher accuracy. Accordingly, we further propose an algorithm involving only the top-$N$ similar neighbors for each target user, which has both less computational complexity and higher algorithmic accuracy.

stat.CO cs.LG

10.1111/j.1467-9868.2009.00698.x

0712.4273

http://arxiv.org/abs/0712.4273v4

2017-03-01T13:40:32Z

2007-12-27T19:44:34Z

Online EM Algorithm for Latent Data Models

In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e., that of the maximum likelihood estimator. In addition, the proposed approach is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.

cs.IT cs.LG math.IT math.OC

0801.0390

http://arxiv.org/pdf/0801.0390v1

2008-01-02T13:23:04Z

2008-01-02T13:23:04Z

Staring at Economic Aggregators through Information Lenses

It is hard to exaggerate the role of economic aggregators -- functions that summarize numerous and / or heterogeneous data -- in economic models since the early XX$^{th}$ century. In many cases, as witnessed by the pioneering works of Cobb and Douglas, these functions were information quantities tailored to economic theories, i.e. they were built to fit economic phenomena. In this paper, we look at these functions from the complementary side: information. We use a recent toolbox built on top of a vast class of distortions coined by Bregman, whose application field rivals metrics' in various subfields of mathematics. This toolbox makes it possible to find the quality of an aggregator (for consumptions, prices, labor, capital, wages, etc.), from the standpoint of the information it carries. We prove a rather striking result. From the informational standpoint, well-known economic aggregators do belong to the \textit{optimal} set. As common economic assumptions enter the analysis, this large set shrinks, and it essentially ends up \textit{exactly fitting} either CES, or Cobb-Douglas, or both. To summarize, in the relevant economic contexts, one could not have crafted better some aggregator from the information standpoint. We also discuss global economic behaviors of optimal information aggregators in general, and present a brief panorama of the links between economic and information aggregators. Keywords: Economic Aggregators, CES, Cobb-Douglas, Bregman divergences