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cs.LG

0904.4608

http://arxiv.org/pdf/0904.4608v2

2009-04-30T17:02:30Z

2009-04-29T13:17:31Z

Temporal data mining for root-cause analysis of machine faults in automotive assembly lines

Engine assembly is a complex and heavily automated distributed-control process, with large amounts of faults data logged everyday. We describe an application of temporal data mining for analyzing fault logs in an engine assembly plant. Frequent episode discovery framework is a model-free method that can be used to deduce (temporal) correlations among events from the logs in an efficient manner. In addition to being theoretically elegant and computationally efficient, frequent episodes are also easy to interpret in the form actionable recommendations. Incorporation of domain-specific information is critical to successful application of the method for analyzing fault logs in the manufacturing domain. We show how domain-specific knowledge can be incorporated using heuristic rules that act as pre-filters and post-filters to frequent episode discovery. The system described here is currently being used in one of the engine assembly plants of General Motors and is planned for adaptation in other plants. To the best of our knowledge, this paper presents the first real, large-scale application of temporal data mining in the manufacturing domain. We believe that the ideas presented in this paper can help practitioners engineer tools for analysis in other similar or related application domains as well.

cs.LG cs.AI cs.GT nlin.AO

10.1007/s10458-011-9181-6

0904.4717

http://arxiv.org/abs/0904.4717v2

2011-09-22T20:32:36Z

2009-04-29T23:00:03Z

Continuous Strategy Replicator Dynamics for Multi--Agent Learning

The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology. Most existing studies so far have been limited to discrete strategy spaces with a small number of available actions. In many cases, however, the choices available to agents are better characterized by continuous spectra. This paper suggests a generalization of the replicator framework that allows to study the adaptive dynamics of Q-learning agents with continuous strategy spaces. Instead of probability vectors, agents strategies are now characterized by probability measures over continuous variables. As a result, the ordinary differential equations for the discrete case are replaced by a system of coupled integral--differential replicator equations that describe the mutual evolution of individual agent strategies. We derive a set of functional equations describing the steady state of the replicator dynamics, examine their solutions for several two-player games, and confirm our analytical results using simulations.

cs.IT cs.LG math.IT

0904.4774

http://arxiv.org/pdf/0904.4774v2

2010-03-01T11:28:31Z

2009-04-30T10:04:09Z

Dictionary Identification - Sparse Matrix-Factorisation via $\ell_1$-Minimisation

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$-minimisation. The problem can also be seen as factorising a $\ddim \times \nsig$ matrix $Y=(y_1 >... y_\nsig), y_n\in \R^\ddim$ of training signals into a $\ddim \times \natoms$ dictionary matrix $\dico$ and a $\natoms \times \nsig$ coefficient matrix $\X=(x_1... x_\nsig), x_n \in \R^\natoms$, which is sparse. The exact question studied here is when a dictionary coefficient pair $(\dico,\X)$ can be recovered as local minimum of a (nonconvex) $\ell_1$-criterion with input $Y=\dico \X$. First, for general dictionaries and coefficient matrices, algebraic conditions ensuring local identifiability are derived, which are then specialised to the case when the dictionary is a basis. Finally, assuming a random Bernoulli-Gaussian sparse model on the coefficient matrix, it is shown that sufficiently incoherent bases are locally identifiable with high probability. The perhaps surprising result is that the typically sufficient number of training samples $\nsig$ grows up to a logarithmic factor only linearly with the signal dimension, i.e. $\nsig \approx C \natoms \log \natoms$, in contrast to previous approaches requiring combinatorially many samples.

cs.IT cs.LG math.IT

0905.1546

http://arxiv.org/pdf/0905.1546v2

2009-05-15T03:38:47Z

2009-05-11T06:13:49Z

Fast and Near-Optimal Matrix Completion via Randomized Basis Pursuit

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic variant of the well-studied matrix completion problem, and the main objective is to design an efficient algorithm that can reconstruct a matrix by inspecting only a small number of its entries. Although this is an impossible task in general, Cand\`es and co-authors have recently shown that under a so-called incoherence assumption, a rank $r$ $n\times n$ matrix can be reconstructed using semidefinite programming (SDP) after one inspects $O(nr\log^6n)$ of its entries. In this paper we propose an alternative approach that is much more efficient and can reconstruct a larger class of matrices by inspecting a significantly smaller number of the entries. Specifically, we first introduce a class of so-called stable matrices and show that it includes all those that satisfy the incoherence assumption. Then, we propose a randomized basis pursuit (RBP) algorithm and show that it can reconstruct a stable rank $r$ $n\times n$ matrix after inspecting $O(nr\log n)$ of its entries. Our sampling bound is only a logarithmic factor away from the information-theoretic limit and is essentially optimal. Moreover, the runtime of the RBP algorithm is bounded by $O(nr^2\log n+n^2r)$, which compares very favorably with the $\Omega(n^4r^2\log^{12}n)$ runtime of the SDP-based algorithm. Perhaps more importantly, our algorithm will provide an exact reconstruction of the input matrix in polynomial time. By contrast, the SDP-based algorithm can only provide an approximate one in polynomial time.

q-bio.NC cs.LG nlin.AO

10.3389/neuro.10.015.2009

0905.2125

http://arxiv.org/abs/0905.2125v3

2010-03-22T15:38:57Z

2009-05-13T14:23:36Z

Experience-driven formation of parts-based representations in a model of layered visual memory

Growing neuropsychological and neurophysiological evidence suggests that the visual cortex uses parts-based representations to encode, store and retrieve relevant objects. In such a scheme, objects are represented as a set of spatially distributed local features, or parts, arranged in stereotypical fashion. To encode the local appearance and to represent the relations between the constituent parts, there has to be an appropriate memory structure formed by previous experience with visual objects. Here, we propose a model how a hierarchical memory structure supporting efficient storage and rapid recall of parts-based representations can be established by an experience-driven process of self-organization. The process is based on the collaboration of slow bidirectional synaptic plasticity and homeostatic unit activity regulation, both running at the top of fast activity dynamics with winner-take-all character modulated by an oscillatory rhythm. These neural mechanisms lay down the basis for cooperation and competition between the distributed units and their synaptic connections. Choosing human face recognition as a test task, we show that, under the condition of open-ended, unsupervised incremental learning, the system is able to form memory traces for individual faces in a parts-based fashion. On a lower memory layer the synaptic structure is developed to represent local facial features and their interrelations, while the identities of different persons are captured explicitly on a higher layer. An additional property of the resulting representations is the sparseness of both the activity during the recall and the synaptic patterns comprising the memory traces.

cs.LG

0905.2347

http://arxiv.org/pdf/0905.2347v1

2009-05-14T14:59:15Z

2009-05-14T14:59:15Z

Combining Supervised and Unsupervised Learning for GIS Classification

This paper presents a new hybrid learning algorithm for unsupervised classification tasks. We combined Fuzzy c-means learning algorithm and a supervised version of Minimerror to develop a hybrid incremental strategy allowing unsupervised classifications. We applied this new approach to a real-world database in order to know if the information contained in unlabeled features of a Geographic Information System (GIS), allows to well classify it. Finally, we compared our results to a classical supervised classification obtained by a multilayer perceptron.

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

0905.2639

http://arxiv.org/pdf/0905.2639v1

2009-05-16T00:41:30Z

2009-05-16T00:41:30Z

Information-theoretic limits of selecting binary graphical models in high dimensions

The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph selection for binary Markov random fields under high-dimensional scaling, in which the graph size $p$ and the number of edges $k$, and/or the maximal node degree $d$ are allowed to increase to infinity as a function of the sample size $n$. For pairwise binary Markov random fields, we derive both necessary and sufficient conditions for correct graph selection over the class $\mathcal{G}_{p,k}$ of graphs on $p$ vertices with at most $k$ edges, and over the class $\mathcal{G}_{p,d}$ of graphs on $p$ vertices with maximum degree at most $d$. For the class $\mathcal{G}_{p, k}$, we establish the existence of constants $c$ and $c'$ such that if $\numobs < c k \log p$, any method has error probability at least 1/2 uniformly over the family, and we demonstrate a graph decoder that succeeds with high probability uniformly over the family for sample sizes $\numobs > c' k^2 \log p$. Similarly, for the class $\mathcal{G}_{p,d}$, we exhibit constants $c$ and $c'$ such that for $n < c d^2 \log p$, any method fails with probability at least 1/2, and we demonstrate a graph decoder that succeeds with high probability for $n > c' d^3 \log p$.

cs.LG

0905.2997

http://arxiv.org/pdf/0905.2997v1

2009-05-18T23:21:35Z

2009-05-18T23:21:35Z

Average-Case Active Learning with Costs

We analyze the expected cost of a greedy active learning algorithm. Our analysis extends previous work to a more general setting in which different queries have different costs. Moreover, queries may have more than two possible responses and the distribution over hypotheses may be non uniform. Specific applications include active learning with label costs, active learning for multiclass and partial label queries, and batch mode active learning. We also discuss an approximate version of interest when there are very many queries.

cs.CV cs.LG

0905.3347

http://arxiv.org/pdf/0905.3347v1

2009-05-20T16:37:16Z

2009-05-20T16:37:16Z

Information Distance in Multiples

Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples (finite lists). We study maximal overlap, metricity, universality, minimal overlap, additivity, and normalized information distance in multiples. We use the theoretical notion of Kolmogorov complexity which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program. {\em Index Terms}-- Information distance, multiples, pattern recognition, data mining, similarity, Kolmogorov complexity

cs.AI cs.LG

0905.3369

http://arxiv.org/pdf/0905.3369v2

2009-06-03T20:29:16Z

2009-05-20T18:08:18Z

Learning Nonlinear Dynamic Models

We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long range structure, and apply the approach to motion capture and high-dimensional video data, yielding results superior to standard alternatives.

cs.LG astro-ph.IM physics.data-an

10.1007/s10994-008-5093-3

0905.3428

http://arxiv.org/abs/0905.3428v1

2009-05-21T03:05:38Z

2009-05-21T03:05:38Z

Finding Anomalous Periodic Time Series: An Application to Catalogs of Periodic Variable Stars

Catalogs of periodic variable stars contain large numbers of periodic light-curves (photometric time series data from the astrophysics domain). Separating anomalous objects from well-known classes is an important step towards the discovery of new classes of astronomical objects. Most anomaly detection methods for time series data assume either a single continuous time series or a set of time series whose periods are aligned. Light-curve data precludes the use of these methods as the periods of any given pair of light-curves may be out of sync. One may use an existing anomaly detection method if, prior to similarity calculation, one performs the costly act of aligning two light-curves, an operation that scales poorly to massive data sets. This paper presents PCAD, an unsupervised anomaly detection method for large sets of unsynchronized periodic time-series data, that outputs a ranked list of both global and local anomalies. It calculates its anomaly score for each light-curve in relation to a set of centroids produced by a modified k-means clustering algorithm. Our method is able to scale to large data sets through the use of sampling. We validate our method on both light-curve data and other time series data sets. We demonstrate its effectiveness at finding known anomalies, and discuss the effect of sample size and number of centroids on our results. We compare our method to naive solutions and existing time series anomaly detection methods for unphased data, and show that PCAD's reported anomalies are comparable to or better than all other methods. Finally, astrophysicists on our team have verified that PCAD finds true anomalies that might be indicative of novel astrophysical phenomena.

cond-mat.dis-nn cond-mat.stat-mech cs.LG quant-ph

0905.3527

http://arxiv.org/pdf/0905.3527v2

2009-05-28T15:36:23Z

2009-05-21T17:01:12Z

Quantum Annealing for Clustering

This paper studies quantum annealing (QA) for clustering, which can be seen as an extension of simulated annealing (SA). We derive a QA algorithm for clustering and propose an annealing schedule, which is crucial in practice. Experiments show the proposed QA algorithm finds better clustering assignments than SA. Furthermore, QA is as easy as SA to implement.

cond-mat.dis-nn cond-mat.stat-mech cs.LG quant-ph

0905.3528

http://arxiv.org/pdf/0905.3528v3

2009-05-28T15:44:30Z

2009-05-21T17:01:28Z

Quantum Annealing for Variational Bayes Inference

This paper presents studies on a deterministic annealing algorithm based on quantum annealing for variational Bayes (QAVB) inference, which can be seen as an extension of the simulated annealing for variational Bayes (SAVB) inference. QAVB is as easy as SAVB to implement. Experiments revealed QAVB finds a better local optimum than SAVB in terms of the variational free energy in latent Dirichlet allocation (LDA).

cs.GT cs.LG

10.1155/2010/573107

0905.3640

http://arxiv.org/abs/0905.3640v1

2009-05-22T19:07:21Z

2009-05-22T19:07:21Z

Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games

We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The "social-learning" versions of the two co-evolutionary algorithms we introduce, establish Nash Equilibrium in those models, in contrast to the "individual learning" versions which, as we see here, do not imply the convergence of the players' strategies to the Nash outcome. When players use "canonical co-evolutionary genetic algorithms" as learning algorithms, the process of the game is an ergodic Markov Chain, and therefore we analyze simulation results using both the relevant methodology and more general statistical tests, to find that in the "social" case, states leading to NE play are highly frequent at the stationary distribution of the chain, in contrast to the "individual learning" case, when NE is not reached at all in our simulations; to find that the expected Hamming distance of the states at the limiting distribution from the "NE state" is significantly smaller in the "social" than in the "individual learning case"; to estimate the expected time that the "social" algorithms need to get to the "NE state" and verify their robustness and finally to show that a large fraction of the games played are indeed at the Nash Equilibrium.

cs.LG

0905.4022

http://arxiv.org/pdf/0905.4022v1

2009-05-25T14:29:59Z

2009-05-25T14:29:59Z

Transfer Learning Using Feature Selection

We present three related ways of using Transfer Learning to improve feature selection. The three methods address different problems, and hence share different kinds of information between tasks or feature classes, but all three are based on the information theoretic Minimum Description Length (MDL) principle and share the same underlying Bayesian interpretation. The first method, MIC, applies when predictive models are to be built simultaneously for multiple tasks (``simultaneous transfer'') that share the same set of features. MIC allows each feature to be added to none, some, or all of the task models and is most beneficial for selecting a small set of predictive features from a large pool of features, as is common in genomic and biological datasets. Our second method, TPC (Three Part Coding), uses a similar methodology for the case when the features can be divided into feature classes. Our third method, Transfer-TPC, addresses the ``sequential transfer'' problem in which the task to which we want to transfer knowledge may not be known in advance and may have different amounts of data than the other tasks. Transfer-TPC is most beneficial when we want to transfer knowledge between tasks which have unequal amounts of labeled data, for example the data for disambiguating the senses of different verbs. We demonstrate the effectiveness of these approaches with experimental results on real world data pertaining to genomics and to Word Sense Disambiguation (WSD).

cs.LG cs.AI

0906.0052

http://arxiv.org/pdf/0906.0052v1

2009-05-30T03:41:37Z

2009-05-30T03:41:37Z

A Minimum Description Length Approach to Multitask Feature Selection

Many regression problems involve not one but several response variables (y's). Often the responses are suspected to share a common underlying structure, in which case it may be advantageous to share information across them; this is known as multitask learning. As a special case, we can use multiple responses to better identify shared predictive features -- a project we might call multitask feature selection. This thesis is organized as follows. Section 1 introduces feature selection for regression, focusing on ell_0 regularization methods and their interpretation within a Minimum Description Length (MDL) framework. Section 2 proposes a novel extension of MDL feature selection to the multitask setting. The approach, called the "Multiple Inclusion Criterion" (MIC), is designed to borrow information across regression tasks by more easily selecting features that are associated with multiple responses. We show in experiments on synthetic and real biological data sets that MIC can reduce prediction error in settings where features are at least partially shared across responses. Section 3 surveys hypothesis testing by regression with a single response, focusing on the parallel between the standard Bonferroni correction and an MDL approach. Mirroring the ideas in Section 2, Section 4 proposes a novel MIC approach to hypothesis testing with multiple responses and shows that on synthetic data with significant sharing of features across responses, MIC sometimes outperforms standard FDR-controlling methods in terms of finding true positives for a given level of false positives. Section 5 concludes.

cs.LG

10.1587/transfun.E93.A.617

0906.0211

http://arxiv.org/abs/0906.0211v2

2009-06-03T03:25:56Z

2009-06-01T04:47:15Z

Equations of States in Statistical Learning for a Nonparametrizable and Regular Case

Many learning machines that have hierarchical structure or hidden variables are now being used in information science, artificial intelligence, and bioinformatics. However, several learning machines used in such fields are not regular but singular statistical models, hence their generalization performance is still left unknown. To overcome these problems, in the previous papers, we proved new equations in statistical learning, by which we can estimate the Bayes generalization loss from the Bayes training loss and the functional variance, on the condition that the true distribution is a singularity contained in a learning machine. In this paper, we prove that the same equations hold even if a true distribution is not contained in a parametric model. Also we prove that, the proposed equations in a regular case are asymptotically equivalent to the Takeuchi information criterion. Therefore, the proposed equations are always applicable without any condition on the unknown true distribution.

cs.LG

0906.0470

http://arxiv.org/pdf/0906.0470v1

2009-06-02T11:52:36Z

2009-06-02T11:52:36Z

An optimal linear separator for the Sonar Signals Classification task

The problem of classifying sonar signals from rocks and mines first studied by Gorman and Sejnowski has become a benchmark against which many learning algorithms have been tested. We show that both the training set and the test set of this benchmark are linearly separable, although with different hyperplanes. Moreover, the complete set of learning and test patterns together, is also linearly separable. We give the weights that separate these sets, which may be used to compare results found by other algorithms.

cs.LG cs.NE

0906.0861

http://arxiv.org/pdf/0906.0861v1

2009-06-04T09:41:47Z

2009-06-04T09:41:47Z

Using Genetic Algorithms for Texts Classification Problems

The avalanche quantity of the information developed by mankind has led to concept of automation of knowledge extraction - Data Mining ([1]). This direction is connected with a wide spectrum of problems - from recognition of the fuzzy set to creation of search machines. Important component of Data Mining is processing of the text information. Such problems lean on concept of classification and clustering ([2]). Classification consists in definition of an accessory of some element (text) to one of in advance created classes. Clustering means splitting a set of elements (texts) on clusters which quantity are defined by localization of elements of the given set in vicinities of these some natural centers of these clusters. Realization of a problem of classification initially should lean on the given postulates, basic of which - the aprioristic information on primary set of texts and a measure of affinity of elements and classes.

cs.LG cs.NE

0906.0872

http://arxiv.org/pdf/0906.0872v1

2009-06-04T10:25:08Z

2009-06-04T10:25:08Z

Fast Weak Learner Based on Genetic Algorithm

An approach to the acceleration of parametric weak classifier boosting is proposed. Weak classifier is called parametric if it has fixed number of parameters and, so, can be represented as a point into multidimensional space. Genetic algorithm is used instead of exhaustive search to learn parameters of such classifier. Proposed approach also takes cases when effective algorithm for learning some of the classifier parameters exists into account. Experiments confirm that such an approach can dramatically decrease classifier training time while keeping both training and test errors small.

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

0906.1713

http://arxiv.org/pdf/0906.1713v1

2009-06-09T12:50:29Z

2009-06-09T12:50:29Z

Feature Reinforcement Learning: Part I: Unstructured MDPs

General-purpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and non-Markovian. On the other hand, reinforcement learning is well-developed for small finite state Markov decision processes (MDPs). Up to now, extracting the right state representations out of bare observations, that is, reducing the general agent setup to the MDP framework, is an art that involves significant effort by designers. The primary goal of this work is to automate the reduction process and thereby significantly expand the scope of many existing reinforcement learning algorithms and the agents that employ them. Before we can think of mechanizing this search for suitable MDPs, we need a formal objective criterion. The main contribution of this article is to develop such a criterion. I also integrate the various parts into one learning algorithm. Extensions to more realistic dynamic Bayesian networks are developed in Part II. The role of POMDPs is also considered there.

cs.LG cs.AI

0906.1814

http://arxiv.org/pdf/0906.1814v1

2009-06-09T20:06:45Z

2009-06-09T20:06:45Z

Large-Margin kNN Classification Using a Deep Encoder Network

KNN is one of the most popular classification methods, but it often fails to work well with inappropriate choice of distance metric or due to the presence of numerous class-irrelevant features. Linear feature transformation methods have been widely applied to extract class-relevant information to improve kNN classification, which is very limited in many applications. Kernels have been used to learn powerful non-linear feature transformations, but these methods fail to scale to large datasets. In this paper, we present a scalable non-linear feature mapping method based on a deep neural network pretrained with restricted boltzmann machines for improving kNN classification in a large-margin framework, which we call DNet-kNN. DNet-kNN can be used for both classification and for supervised dimensionality reduction. The experimental results on two benchmark handwritten digit datasets show that DNet-kNN has much better performance than large-margin kNN using a linear mapping and kNN based on a deep autoencoder pretrained with retricted boltzmann machines.

cs.LG stat.ML

0906.2027

http://arxiv.org/pdf/0906.2027v2

2012-04-09T17:37:45Z

2009-06-11T00:22:58Z

Matrix Completion from Noisy Entries

Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the `Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm introduced by Keshavan et al.(2009), based on a combination of spectral techniques and manifold optimization, that we call here OptSpace. We prove performance guarantees that are order-optimal in a number of circumstances.

cs.LG

10.1007/978-3-642-04744-2_13

0906.2635

http://arxiv.org/abs/0906.2635v1

2009-06-15T08:43:51Z

2009-06-15T08:43:51Z

Bayesian History Reconstruction of Complex Human Gene Clusters on a Phylogeny

Clusters of genes that have evolved by repeated segmental duplication present difficult challenges throughout genomic analysis, from sequence assembly to functional analysis. Improved understanding of these clusters is of utmost importance, since they have been shown to be the source of evolutionary innovation, and have been linked to multiple diseases, including HIV and a variety of cancers. Previously, Zhang et al. (2008) developed an algorithm for reconstructing parsimonious evolutionary histories of such gene clusters, using only human genomic sequence data. In this paper, we propose a probabilistic model for the evolution of gene clusters on a phylogeny, and an MCMC algorithm for reconstruction of duplication histories from genomic sequences in multiple species. Several projects are underway to obtain high quality BAC-based assemblies of duplicated clusters in multiple species, and we anticipate that our method will be useful in analyzing these valuable new data sets.

cs.LG cs.IT math.IT

10.1109/TIT.2010.2090235

0906.2895

http://arxiv.org/abs/0906.2895v6

2010-11-08T01:37:37Z

2009-06-16T10:58:50Z

Entropy Message Passing

The paper proposes a new message passing algorithm for cycle-free factor graphs. The proposed "entropy message passing" (EMP) algorithm may be viewed as sum-product message passing over the entropy semiring, which has previously appeared in automata theory. The primary use of EMP is to compute the entropy of a model. However, EMP can also be used to compute expressions that appear in expectation maximization and in gradient descent algorithms.

cs.NI cs.LG

0906.3923

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

2009-12-03T02:15:11Z

2009-06-22T07:48:12Z

Bayesian Forecasting of WWW Traffic on the Time Varying Poisson Model

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

cs.LG

0906.4032

http://arxiv.org/pdf/0906.4032v1

2009-06-22T15:25:23Z

2009-06-22T15:25:23Z

Bayesian two-sample tests

In this paper, we present two classes of Bayesian approaches to the two-sample problem. Our first class of methods extends the Bayesian t-test to include all parametric models in the exponential family and their conjugate priors. Our second class of methods uses Dirichlet process mixtures (DPM) of such conjugate-exponential distributions as flexible nonparametric priors over the unknown distributions.

cs.DB cs.LG

0906.4172

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

2009-06-23T06:24:57Z

2009-06-23T06:24:57Z

Rough Set Model for Discovering Hybrid Association Rules

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

cs.LG cs.DS

0906.4539

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

2010-05-10T17:19:30Z

2009-06-24T18:38:31Z

Learning with Spectral Kernels and Heavy-Tailed Data

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

stat.ML cs.CV cs.LG

10.1098/rsta.2009.0161

0906.4582

http://arxiv.org/abs/0906.4582v1

2009-06-24T23:40:22Z

2009-06-24T23:40:22Z

On landmark selection and sampling in high-dimensional data analysis

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nystrom extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.

cs.LG

0906.4663

http://arxiv.org/pdf/0906.4663v1

2009-06-25T11:09:39Z

2009-06-25T11:09:39Z

Acquiring Knowledge for Evaluation of Teachers Performance in Higher Education using a Questionnaire

In this paper, we present the step by step knowledge acquisition process by choosing a structured method through using a questionnaire as a knowledge acquisition tool. Here we want to depict the problem domain as, how to evaluate teachers performance in higher education through the use of expert system technology. The problem is how to acquire the specific knowledge for a selected problem efficiently and effectively from human experts and encode it in the suitable computer format. Acquiring knowledge from human experts in the process of expert systems development is one of the most common problems cited till yet. This questionnaire was sent to 87 domain experts within all public and private universities in Pakistani. Among them 25 domain experts sent their valuable opinions. Most of the domain experts were highly qualified, well experienced and highly responsible persons. The whole questionnaire was divided into 15 main groups of factors, which were further divided into 99 individual questions. These facts were analyzed further to give a final shape to the questionnaire. This knowledge acquisition technique may be used as a learning tool for further research work.

cs.LG physics.data-an stat.ML

0906.4779

http://arxiv.org/pdf/0906.4779v4

2011-09-25T01:33:51Z

2009-06-25T19:15:44Z

Minimum Probability Flow Learning

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable normalization factor or sampling from the equilibrium distribution of the model. This is achieved by establishing dynamics that would transform the observed data distribution into the model distribution, and then setting as the objective the minimization of the KL divergence between the data distribution and the distribution produced by running the dynamics for an infinitesimal time. Score matching, minimum velocity learning, and certain forms of contrastive divergence are shown to be special cases of this learning technique. We demonstrate parameter estimation in Ising models, deep belief networks and an independent component analysis model of natural scenes. In the Ising model case, current state of the art techniques are outperformed by at least an order of magnitude in learning time, with lower error in recovered coupling parameters.

cs.CR cs.LG

0906.5110

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

2009-06-27T23:24:14Z

2009-06-27T23:24:14Z

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

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

cs.LG

0906.5151

http://arxiv.org/pdf/0906.5151v1

2009-06-28T17:47:22Z

2009-06-28T17:47:22Z

Unsupervised Search-based Structured Prediction

We describe an adaptation and application of a search-based structured prediction algorithm "Searn" to unsupervised learning problems. We show that it is possible to reduce unsupervised learning to supervised learning and demonstrate a high-quality unsupervised shift-reduce parsing model. We additionally show a close connection between unsupervised Searn and expectation maximization. Finally, we demonstrate the efficacy of a semi-supervised extension. The key idea that enables this is an application of the predict-self idea for unsupervised learning.

cs.LG cs.MM

10.1109/TIP.2009.2035228

0906.5325

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

2009-06-29T17:48:40Z

2009-06-29T17:48:40Z

Online Reinforcement Learning for Dynamic Multimedia Systems

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

cs.NE cs.LG

0907.0229

http://arxiv.org/pdf/0907.0229v1

2009-07-01T19:54:39Z

2009-07-01T19:54:39Z

A new model of artificial neuron: cyberneuron and its use

This article describes a new type of artificial neuron, called the authors "cyberneuron". Unlike classical models of artificial neurons, this type of neuron used table substitution instead of the operation of multiplication of input values for the weights. This allowed to significantly increase the information capacity of a single neuron, but also greatly simplify the process of learning. Considered an example of the use of "cyberneuron" with the task of detecting computer viruses.

cs.LG

0907.0453

http://arxiv.org/pdf/0907.0453v2

2009-07-20T08:59:45Z

2009-07-02T17:54:45Z

Random DFAs are Efficiently PAC Learnable

This paper has been withdrawn due to an error found by Dana Angluin and Lev Reyzin.

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

0907.0746

http://arxiv.org/pdf/0907.0746v1

2009-07-04T08:45:22Z

2009-07-04T08:45:22Z

Open Problems in Universal Induction & Intelligence

Specialized intelligent systems can be found everywhere: finger print, handwriting, speech, and face recognition, spam filtering, chess and other game programs, robots, et al. This decade the first presumably complete mathematical theory of artificial intelligence based on universal induction-prediction-decision-action has been proposed. This information-theoretic approach solidifies the foundations of inductive inference and artificial intelligence. Getting the foundations right usually marks a significant progress and maturing of a field. The theory provides a gold standard and guidance for researchers working on intelligent algorithms. The roots of universal induction have been laid exactly half-a-century ago and the roots of universal intelligence exactly one decade ago. So it is timely to take stock of what has been achieved and what remains to be done. Since there are already good recent surveys, I describe the state-of-the-art only in passing and refer the reader to the literature. This article concentrates on the open problems in universal induction and its extension to universal intelligence.

cs.LG

0907.0783

http://arxiv.org/pdf/0907.0783v1

2009-07-04T18:35:52Z

2009-07-04T18:35:52Z

Bayesian Multitask Learning with Latent Hierarchies

We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share covariance structure. Our hierarchical model is seen to subsume several previously proposed multitask learning models and performs well on three distinct real-world data sets.

cs.LG cs.CL

0907.0784

http://arxiv.org/pdf/0907.0784v1

2009-07-04T18:42:01Z

2009-07-04T18:42:01Z

Cross-Task Knowledge-Constrained Self Training

We present an algorithmic framework for learning multiple related tasks. Our framework exploits a form of prior knowledge that relates the output spaces of these tasks. We present PAC learning results that analyze the conditions under which such learning is possible. We present results on learning a shallow parser and named-entity recognition system that exploits our framework, showing consistent improvements over baseline methods.

cs.LG cs.CL

0907.0786

http://arxiv.org/pdf/0907.0786v1

2009-07-04T18:48:34Z

2009-07-04T18:48:34Z

Search-based Structured Prediction

We present Searn, an algorithm for integrating search and learning to solve complex structured prediction problems such as those that occur in natural language, speech, computational biology, and vision. Searn is a meta-algorithm that transforms these complex problems into simple classification problems to which any binary classifier may be applied. Unlike current algorithms for structured learning that require decomposition of both the loss function and the feature functions over the predicted structure, Searn is able to learn prediction functions for any loss function and any class of features. Moreover, Searn comes with a strong, natural theoretical guarantee: good performance on the derived classification problems implies good performance on the structured prediction problem.

cs.LG

0907.0808

http://arxiv.org/pdf/0907.0808v1

2009-07-04T22:32:58Z

2009-07-04T22:32:58Z

A Bayesian Model for Supervised Clustering with the Dirichlet Process Prior

We develop a Bayesian framework for tackling the supervised clustering problem, the generic problem encountered in tasks such as reference matching, coreference resolution, identity uncertainty and record linkage. Our clustering model is based on the Dirichlet process prior, which enables us to define distributions over the countably infinite sets that naturally arise in this problem. We add supervision to our model by positing the existence of a set of unobserved random variables (we call these "reference types") that are generic across all clusters. Inference in our framework, which requires integrating over infinitely many parameters, is solved using Markov chain Monte Carlo techniques. We present algorithms for both conjugate and non-conjugate priors. We present a simple--but general--parameterization of our model based on a Gaussian assumption. We evaluate this model on one artificial task and three real-world tasks, comparing it against both unsupervised and state-of-the-art supervised algorithms. Our results show that our model is able to outperform other models across a variety of tasks and performance metrics.

cs.LG cs.CL

0907.0809

http://arxiv.org/pdf/0907.0809v1

2009-07-04T22:34:25Z

2009-07-04T22:34:25Z

Learning as Search Optimization: Approximate Large Margin Methods for Structured Prediction

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be performed exactly. Unfortunately, in many complex problems, it is rare that exact search or parameter estimation is tractable. Instead of learning exact models and searching via heuristic means, we embrace this difficulty and treat the structured output problem in terms of approximate search. We present a framework for learning as search optimization, and two parameter updates with convergence theorems and bounds. Empirical evidence shows that our integrated approach to learning and decoding can outperform exact models at smaller computational cost.

cs.LG cs.DS

0907.1054

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

2010-05-13T19:20:36Z

2009-07-06T17:41:57Z

Learning Gaussian Mixtures with Arbitrary Separation

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

0907.1413

http://arxiv.org/pdf/0907.1413v3

2011-06-21T17:05:53Z

2009-07-09T06:51:54Z

Privacy constraints in regularized convex optimization

This paper is withdrawn due to some errors, which are corrected in arXiv:0912.0071v4 [cs.LG].

cs.LG

0907.1812

http://arxiv.org/pdf/0907.1812v1

2009-07-10T13:23:37Z

2009-07-10T13:23:37Z

Fast search for Dirichlet process mixture models

Dirichlet process (DP) mixture models provide a flexible Bayesian framework for density estimation. Unfortunately, their flexibility comes at a cost: inference in DP mixture models is computationally expensive, even when conjugate distributions are used. In the common case when one seeks only a maximum a posteriori assignment of data points to clusters, we show that search algorithms provide a practical alternative to expensive MCMC and variational techniques. When a true posterior sample is desired, the solution found by search can serve as a good initializer for MCMC. Experimental results show that using these techniques is it possible to apply DP mixture models to very large data sets.

cs.CL cs.IR cs.LG

0907.1814

http://arxiv.org/pdf/0907.1814v1

2009-07-10T13:24:55Z

2009-07-10T13:24:55Z

Bayesian Query-Focused Summarization

We present BayeSum (for ``Bayesian summarization''), a model for sentence extraction in query-focused summarization. BayeSum leverages the common case in which multiple documents are relevant to a single query. Using these documents as reinforcement for query terms, BayeSum is not afflicted by the paucity of information in short queries. We show that approximate inference in BayeSum is possible on large data sets and results in a state-of-the-art summarization system. Furthermore, we show how BayeSum can be understood as a justified query expansion technique in the language modeling for IR framework.

cs.LG cs.CL

0907.1815

http://arxiv.org/pdf/0907.1815v1

2009-07-10T13:25:48Z

2009-07-10T13:25:48Z

Frustratingly Easy Domain Adaptation

We describe an approach to domain adaptation that is appropriate exactly in the case when one has enough ``target'' data to do slightly better than just using only ``source'' data. Our approach is incredibly simple, easy to implement as a preprocessing step (10 lines of Perl!) and outperforms state-of-the-art approaches on a range of datasets. Moreover, it is trivially extended to a multi-domain adaptation problem, where one has data from a variety of different domains.

cs.GT cs.LG

0907.1916

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

2009-07-10T21:26:54Z

2009-07-10T21:26:54Z

Learning Equilibria in Games by Stochastic Distributed Algorithms

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

math.OC cs.LG math.ST stat.AP stat.CO stat.ME stat.ML stat.TH

0907.2079

http://arxiv.org/pdf/0907.2079v1

2009-07-13T00:45:51Z

2009-07-13T00:45:51Z

An Augmented Lagrangian Approach for Sparse Principal Component Analysis

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components (PCs) are usually linear combinations of all the original variables, and it is thus often difficult to interpret the PCs. To alleviate this drawback, various sparse PCA approaches were proposed in literature [15, 6, 17, 28, 8, 25, 18, 7, 16]. Despite success in achieving sparsity, some important properties enjoyed by the standard PCA are lost in these methods such as uncorrelation of PCs and orthogonality of loading vectors. Also, the total explained variance that they attempt to maximize can be too optimistic. In this paper we propose a new formulation for sparse PCA, aiming at finding sparse and nearly uncorrelated PCs with orthogonal loading vectors while explaining as much of the total variance as possible. We also develop a novel augmented Lagrangian method for solving a class of nonsmooth constrained optimization problems, which is well suited for our formulation of sparse PCA. We show that it converges to a feasible point, and moreover under some regularity assumptions, it converges to a stationary point. Additionally, we propose two nonmonotone gradient methods for solving the augmented Lagrangian subproblems, and establish their global and local convergence. Finally, we compare our sparse PCA approach with several existing methods on synthetic, random, and real data, respectively. The computational results demonstrate that the sparse PCs produced by our approach substantially outperform those by other methods in terms of total explained variance, correlation of PCs, and orthogonality of loading vectors.

cs.NI cs.LG

10.1109/COMSWA.2008.4554505

0907.2222

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

2009-07-13T18:18:28Z

2009-07-13T18:18:28Z

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

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

cs.LG cs.NE

10.1007/s10846-005-3806-y

0907.3342

http://arxiv.org/abs/0907.3342v1

2009-07-20T05:58:24Z

2009-07-20T05:58:24Z

Neural Modeling and Control of Diesel Engine with Pollution Constraints

The paper describes a neural approach for modelling and control of a turbocharged Diesel engine. A neural model, whose structure is mainly based on some physical equations describing the engine behaviour, is built for the rotation speed and the exhaust gas opacity. The model is composed of three interconnected neural submodels, each of them constituting a nonlinear multi-input single-output error model. The structural identification and the parameter estimation from data gathered on a real engine are described. The neural direct model is then used to determine a neural controller of the engine, in a specialized training scheme minimising a multivariable criterion. Simulations show the effect of the pollution constraint weighting on a trajectory tracking of the engine speed. Neural networks, which are flexible and parsimonious nonlinear black-box models, with universal approximation capabilities, can accurately describe or control complex nonlinear systems, with little a priori theoretical knowledge. The presented work extends optimal neuro-control to the multivariable case and shows the flexibility of neural optimisers. Considering the preliminary results, it appears that neural networks can be used as embedded models for engine control, to satisfy the more and more restricting pollutant emission legislation. Particularly, they are able to model nonlinear dynamics and outperform during transients the control schemes based on static mappings.

cs.DS cs.LG

0907.3986

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

2014-05-20T03:52:46Z

2009-07-23T06:41:33Z

Contextual Bandits with Similarity Information

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

stat.ML cs.LG math.OC

0908.0050

http://arxiv.org/pdf/0908.0050v2

2010-02-11T07:33:02Z

2009-08-01T06:09:18Z

Online Learning for Matrix Factorization and Sparse Coding

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. Variations of this problem include dictionary learning in signal processing, non-negative matrix factorization and sparse principal component analysis. In this paper, we propose to address these tasks with a new online optimization algorithm, based on stochastic approximations, which scales up gracefully to large datasets with millions of training samples, and extends naturally to various matrix factorization formulations, making it suitable for a wide range of learning problems. A proof of convergence is presented, along with experiments with natural images and genomic data demonstrating that it leads to state-of-the-art performance in terms of speed and optimization for both small and large datasets.

stat.ML cs.AI cs.LG cs.NI

0908.0319

http://arxiv.org/pdf/0908.0319v1

2009-08-03T19:25:58Z

2009-08-03T19:25:58Z

Regret Bounds for Opportunistic Channel Access

We consider the task of opportunistic channel access in a primary system composed of independent Gilbert-Elliot channels where the secondary (or opportunistic) user does not dispose of a priori information regarding the statistical characteristics of the system. It is shown that this problem may be cast into the framework of model-based learning in a specific class of Partially Observed Markov Decision Processes (POMDPs) for which we introduce an algorithm aimed at striking an optimal tradeoff between the exploration (or estimation) and exploitation requirements. We provide finite horizon regret bounds for this algorithm as well as a numerical evaluation of its performance in the single channel model as well as in the case of stochastically identical channels.

cs.LG stat.ML

0908.0570

http://arxiv.org/pdf/0908.0570v1

2009-08-05T01:10:09Z

2009-08-05T01:10:09Z

The Infinite Hierarchical Factor Regression Model

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.

cs.LG stat.ML

0908.0572

http://arxiv.org/pdf/0908.0572v1

2009-08-05T00:40:23Z

2009-08-05T00:40:23Z

Streamed Learning: One-Pass SVMs

We present a streaming model for large-scale classification (in the context of $\ell_2$-SVM) by leveraging connections between learning and computational geometry. The streaming model imposes the constraint that only a single pass over the data is allowed. The $\ell_2$-SVM is known to have an equivalent formulation in terms of the minimum enclosing ball (MEB) problem, and an efficient algorithm based on the idea of \emph{core sets} exists (Core Vector Machine, CVM). CVM learns a $(1+\varepsilon)$-approximate MEB for a set of points and yields an approximate solution to corresponding SVM instance. However CVM works in batch mode requiring multiple passes over the data. This paper presents a single-pass SVM which is based on the minimum enclosing ball of streaming data. We show that the MEB updates for the streaming case can be easily adapted to learn the SVM weight vector in a way similar to using online stochastic gradient updates. Our algorithm performs polylogarithmic computation at each example, and requires very small and constant storage. Experimental results show that, even in such restrictive settings, we can learn efficiently in just one pass and get accuracies comparable to other state-of-the-art SVM solvers (batch and online). We also give an analysis of the algorithm, and discuss some open issues and possible extensions.

cs.LG cs.DS

0908.0772

http://arxiv.org/pdf/0908.0772v1

2009-08-05T23:56:22Z

2009-08-05T23:56:22Z

Online Learning of Assignments that Maximize Submodular Functions

Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize value of information? These applications exhibit strong diminishing returns: Selection of redundant ads and information sources decreases their marginal utility. We show that these and other problems can be formalized as repeatedly selecting an assignment of items to positions to maximize a sequence of monotone submodular functions that arrive one by one. We present an efficient algorithm for this general problem and analyze it in the no-regret model. Our algorithm possesses strong theoretical guarantees, such as a performance ratio that converges to the optimal constant of 1-1/e. We empirically evaluate our algorithm on two real-world online optimization problems on the web: ad allocation with submodular utilities, and dynamically ranking blogs to detect information cascades.

cs.LG

0908.0939

http://arxiv.org/pdf/0908.0939v1

2009-08-06T19:48:20Z

2009-08-06T19:48:20Z

Clustering for Improved Learning in Maze Traversal Problem

The maze traversal problem (finding the shortest distance to the goal from any position in a maze) has been an interesting challenge in computational intelligence. Recent work has shown that the cellular simultaneous recurrent neural network (CSRN) can solve this problem for simple mazes. This thesis focuses on exploiting relevant information about the maze to improve learning and decrease the training time for the CSRN to solve mazes. Appropriate variables are identified to create useful clusters using relevant information. The CSRN was next modified to allow for an additional external input. With this additional input, several methods were tested and results show that clustering the mazes improves the overall learning of the traversal problem for the CSRN.

cs.DB cs.LG

0908.0984

http://arxiv.org/pdf/0908.0984v1

2009-08-07T05:36:51Z

2009-08-07T05:36:51Z

An Application of Bayesian classification to Interval Encoded Temporal mining with prioritized items

In real life, media information has time attributes either implicitly or explicitly known as temporal data. This paper investigates the usefulness of applying Bayesian classification to an interval encoded temporal database with prioritized items. The proposed method performs temporal mining by encoding the database with weighted items which prioritizes the items according to their importance from the user perspective. Naive Bayesian classification helps in making the resulting temporal rules more effective. The proposed priority based temporal mining (PBTM) method added with classification aids in solving problems in a well informed and systematic manner. The experimental results are obtained from the complaints database of the telecommunications system, which shows the feasibility of this method of classification based temporal mining.

cs.LG cs.IT math.IT

0908.1769

http://arxiv.org/pdf/0908.1769v1

2009-08-12T18:27:54Z

2009-08-12T18:27:54Z

Approximating the Permanent with Belief Propagation

This work describes a method of approximating matrix permanents efficiently using belief propagation. We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this partition function. After deriving some speedups to standard belief propagation, the resulting algorithm requires $(n^2)$ time per iteration. Finally, we demonstrate the advantages of using this approximation.

cs.GT cs.LG cs.NI

0908.3265

http://arxiv.org/pdf/0908.3265v1

2009-08-22T16:45:32Z

2009-08-22T16:45:32Z

Rate Constrained Random Access over a Fading Channel

In this paper, we consider uplink transmissions involving multiple users communicating with a base station over a fading channel. We assume that the base station does not coordinate the transmissions of the users and hence the users employ random access communication. The situation is modeled as a non-cooperative repeated game with incomplete information. Each user attempts to minimize its long term power consumption subject to a minimum rate requirement. We propose a two timescale stochastic gradient algorithm (TTSGA) for tuning the users' transmission probabilities. The algorithm includes a 'waterfilling threshold update mechanism' that ensures that the rate constraints are satisfied. We prove that under the algorithm, the users' transmission probabilities converge to a Nash equilibrium. Moreover, we also prove that the rate constraints are satisfied; this is also demonstrated using simulation studies.

astro-ph.CO astro-ph.IM cs.LG cs.NE

0908.3706

http://arxiv.org/pdf/0908.3706v1

2009-08-25T23:21:39Z

2009-08-25T23:21:39Z

Uncovering delayed patterns in noisy and irregularly sampled time series: an astronomy application

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.

cs.LG cs.AI

0908.4144

http://arxiv.org/pdf/0908.4144v1

2009-08-28T07:09:19Z

2009-08-28T07:09:19Z

ABC-LogitBoost for Multi-class Classification

We develop abc-logitboost, based on the prior work on abc-boost and robust logitboost. Our extensive experiments on a variety of datasets demonstrate the considerable improvement of abc-logitboost over logitboost and abc-mart.

q-bio.GN cs.IT cs.LG math.IT q-bio.QM stat.AP stat.ML

0909.0400

http://arxiv.org/pdf/0909.0400v1

2009-09-02T13:25:48Z

2009-09-02T13:25:48Z

Rare-Allele Detection Using Compressed Se(que)nsing

Detection of rare variants by resequencing is important for the identification of individuals carrying disease variants. Rapid sequencing by new technologies enables low-cost resequencing of target regions, although it is still prohibitive to test more than a few individuals. In order to improve cost trade-offs, it has recently been suggested to apply pooling designs which enable the detection of carriers of rare alleles in groups of individuals. However, this was shown to hold only for a relatively low number of individuals in a pool, and requires the design of pooling schemes for particular cases. We propose a novel pooling design, based on a compressed sensing approach, which is both general, simple and efficient. We model the experimental procedure and show via computer simulations that it enables the recovery of rare allele carriers out of larger groups than were possible before, especially in situations where high coverage is obtained for each individual. Our approach can also be combined with barcoding techniques to enhance performance and provide a feasible solution based on current resequencing costs. For example, when targeting a small enough genomic region (~100 base-pairs) and using only ~10 sequencing lanes and ~10 distinct barcodes, one can recover the identity of 4 rare allele carriers out of a population of over 4000 individuals.

cs.LG cs.IT math.IT

10.1007/978-3-642-01805-3_4

0909.0635

http://arxiv.org/abs/0909.0635v1

2009-09-03T12:04:57Z

2009-09-03T12:04:57Z

Advances in Feature Selection with Mutual Information

The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the performances of prediction or classification methods, and interpreting the application. In a nonlinear context, the mutual information is widely used as relevance criterion for features and sets of features. Nevertheless, it suffers from at least three major limitations: mutual information estimators depend on smoothing parameters, there is no theoretically justified stopping criterion in the feature selection greedy procedure, and the estimation itself suffers from the curse of dimensionality. This chapter shows how to deal with these problems. The two first ones are addressed by using resampling techniques that provide a statistical basis to select the estimator parameters and to stop the search procedure. The third one is addressed by modifying the mutual information criterion into a measure of how features are complementary (and not only informative) for the problem at hand.

cs.LG q-bio.QM

10.1007/978-3-642-01805-3_6

0909.0638

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

2009-09-03T12:09:08Z

2009-09-03T12:09:08Z

Median topographic maps for biomedical data sets

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

q-bio.QM cs.LG q-bio.GN

0909.0737

http://arxiv.org/pdf/0909.0737v2

2012-10-16T21:57:24Z

2009-09-03T19:29:56Z

Efficient algorithms for training the parameters of hidden Markov models using stochastic expectation maximization EM training and Viterbi training

Background: Hidden Markov models are widely employed by numerous bioinformatics programs used today. Applications range widely from comparative gene prediction to time-series analyses of micro-array data. The parameters of the underlying models need to be adjusted for specific data sets, for example the genome of a particular species, in order to maximize the prediction accuracy. Computationally efficient algorithms for parameter training are thus key to maximizing the usability of a wide range of bioinformatics applications. Results: We introduce two computationally efficient training algorithms, one for Viterbi training and one for stochastic expectation maximization (EM) training, which render the memory requirements independent of the sequence length. Unlike the existing algorithms for Viterbi and stochastic EM training which require a two-step procedure, our two new algorithms require only one step and scan the input sequence in only one direction. We also implement these two new algorithms and the already published linear-memory algorithm for EM training into the hidden Markov model compiler HMM-Converter and examine their respective practical merits for three small example models. Conclusions: Bioinformatics applications employing hidden Markov models can use the two algorithms in order to make Viterbi training and stochastic EM training more computationally efficient. Using these algorithms, parameter training can thus be attempted for more complex models and longer training sequences. The two new algorithms have the added advantage of being easier to implement than the corresponding default algorithms for Viterbi training and stochastic EM training.

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

0909.0801

http://arxiv.org/pdf/0909.0801v2

2010-12-26T11:01:10Z

2009-09-04T03:13:58Z

A Monte Carlo AIXI Approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. Our approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a new Monte-Carlo Tree Search algorithm along with an agent-specific extension to the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a variety of stochastic and partially observable domains. We conclude by proposing a number of directions for future research.

cs.LG math.ST stat.TH

0909.0844

http://arxiv.org/pdf/0909.0844v1

2009-09-04T09:43:38Z

2009-09-04T09:43:38Z

High-Dimensional Non-Linear Variable Selection through Hierarchical Kernel Learning

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that characterize non-linear interactions between the original variables. To select efficiently from these many kernels, we use the natural hierarchical structure of the problem to extend the multiple kernel learning framework to kernels that can be embedded in a directed acyclic graph; we show that it is then possible to perform kernel selection through a graph-adapted sparsity-inducing norm, in polynomial time in the number of selected kernels. Moreover, we study the consistency of variable selection in high-dimensional settings, showing that under certain assumptions, our regularization framework allows a number of irrelevant variables which is exponential in the number of observations. Our simulations on synthetic datasets and datasets from the UCI repository show state-of-the-art predictive performance for non-linear regression problems.

cs.CG cs.DS cs.LG

0909.1062

http://arxiv.org/pdf/0909.1062v4

2010-09-15T00:54:09Z

2009-09-05T23:24:32Z

New Approximation Algorithms for Minimum Enclosing Convex Shapes

Given $n$ points in a $d$ dimensional Euclidean space, the Minimum Enclosing Ball (MEB) problem is to find the ball with the smallest radius which contains all $n$ points. We give a $O(nd\Qcal/\sqrt{\epsilon})$ approximation algorithm for producing an enclosing ball whose radius is at most $\epsilon$ away from the optimum (where $\Qcal$ is an upper bound on the norm of the points). This improves existing results using \emph{coresets}, which yield a $O(nd/\epsilon)$ greedy algorithm. Finding the Minimum Enclosing Convex Polytope (MECP) is a related problem wherein a convex polytope of a fixed shape is given and the aim is to find the smallest magnification of the polytope which encloses the given points. For this problem we present a $O(mnd\Qcal/\epsilon)$ approximation algorithm, where $m$ is the number of faces of the polytope. Our algorithms borrow heavily from convex duality and recently developed techniques in non-smooth optimization, and are in contrast with existing methods which rely on geometric arguments. In particular, we specialize the excessive gap framework of \citet{Nesterov05a} to obtain our results.

cs.LG cs.CL

10.1109/JSTSP.2010.2076150

0909.1308

http://arxiv.org/abs/0909.1308v2

2010-01-03T16:48:14Z

2009-09-07T18:48:42Z

Efficient Learning of Sparse Conditional Random Fields for Supervised Sequence Labelling

Conditional Random Fields (CRFs) constitute a popular and efficient approach for supervised sequence labelling. CRFs can cope with large description spaces and can integrate some form of structural dependency between labels. In this contribution, we address the issue of efficient feature selection for CRFs based on imposing sparsity through an L1 penalty. We first show how sparsity of the parameter set can be exploited to significantly speed up training and labelling. We then introduce coordinate descent parameter update schemes for CRFs with L1 regularization. We finally provide some empirical comparisons of the proposed approach with state-of-the-art CRF training strategies. In particular, it is shown that the proposed approach is able to take profit of the sparsity to speed up processing and hence potentially handle larger dimensional models.

cs.LG cs.AI cs.DS

0909.1334

http://arxiv.org/pdf/0909.1334v2

2009-09-08T22:00:12Z

2009-09-07T20:58:47Z

Lower Bounds for BMRM and Faster Rates for Training SVMs

Regularized risk minimization with the binary hinge loss and its variants lies at the heart of many machine learning problems. Bundle methods for regularized risk minimization (BMRM) and the closely related SVMStruct are considered the best general purpose solvers to tackle this problem. It was recently shown that BMRM requires $O(1/\epsilon)$ iterations to converge to an $\epsilon$ accurate solution. In the first part of the paper we use the Hadamard matrix to construct a regularized risk minimization problem and show that these rates cannot be improved. We then show how one can exploit the structure of the objective function to devise an algorithm for the binary hinge loss which converges to an $\epsilon$ accurate solution in $O(1/\sqrt{\epsilon})$ iterations.

cs.DB cs.LG

0909.1776

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

2009-09-09T18:10:07Z

2009-09-09T18:10:07Z

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

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

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

0909.1933

http://arxiv.org/pdf/0909.1933v2

2010-06-04T08:43:38Z

2009-09-10T11:51:10Z

Chromatic PAC-Bayes Bounds for Non-IID Data: Applications to Ranking and Stationary $\beta$-Mixing Processes

Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned from independently and identically distributed (IID) data, and it is particularly so for margin classifiers: there have been recent contributions showing how practical these bounds can be either to perform model selection (Ambroladze et al., 2007) or even to directly guide the learning of linear classifiers (Germain et al., 2009). However, there are many practical situations where the training data show some dependencies and where the traditional IID assumption does not hold. Stating generalization bounds for such frameworks is therefore of the utmost interest, both from theoretical and practical standpoints. In this work, we propose the first - to the best of our knowledge - Pac-Bayes generalization bounds for classifiers trained on data exhibiting interdependencies. The approach undertaken to establish our results is based on the decomposition of a so-called dependency graph that encodes the dependencies within the data, in sets of independent data, thanks to graph fractional covers. Our bounds are very general, since being able to find an upper bound on the fractional chromatic number of the dependency graph is sufficient to get new Pac-Bayes bounds for specific settings. We show how our results can be used to derive bounds for ranking statistics (such as Auc) and classifiers trained on data distributed according to a stationary {\ss}-mixing process. In the way, we show how our approach seemlessly allows us to deal with U-processes. As a side note, we also provide a Pac-Bayes generalization bound for classifiers learned on data from stationary $\varphi$-mixing distributions.

cs.DS cs.DB cs.LG

0909.2194

http://arxiv.org/pdf/0909.2194v1

2009-09-11T15:32:03Z

2009-09-11T15:32:03Z

Approximate Nearest Neighbor Search through Comparisons

This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object q in a database of n objects. In contrast with most existing approaches, we can only access the ``hidden'' space in which the objects live through a similarity oracle. The oracle, given two reference objects and a query object, returns the reference object closest to the query object. The oracle attempts to model the behavior of human users, capable of making statements about similarity, but not of assigning meaningful numerical values to distances between objects.

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

10.1109/TIT.2011.2104670

0909.2234

http://arxiv.org/abs/0909.2234v3

2010-09-09T06:56:44Z

2009-09-11T18:35:52Z

Universal and Composite Hypothesis Testing via Mismatched Divergence

For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal test statistic can be written in terms of Kullback-Leibler (K-L) divergence between the empirical distribution of the observations and the null hypothesis distribution. In this paper a modification of Hoeffding's test is considered based on a relaxation of the K-L divergence test statistic, referred to as the mismatched divergence. The resulting mismatched test is shown to be a generalized likelihood-ratio test (GLRT) for the case where the alternate distribution lies in a parametric family of the distributions characterized by a finite dimensional parameter, i.e., it is a solution to the corresponding composite hypothesis testing problem. For certain choices of the alternate distribution, it is shown that both the Hoeffding test and the mismatched test have the same asymptotic performance in terms of error exponents. A consequence of this result is that the GLRT is optimal in differentiating a particular distribution from others in an exponential family. It is also shown that the mismatched test has a significant advantage over the Hoeffding test in terms of finite sample size performance. This advantage is due to the difference in the asymptotic variances of the two test statistics under the null hypothesis. In particular, the variance of the K-L divergence grows linearly with the alphabet size, making the test impractical for applications involving large alphabet distributions. The variance of the mismatched divergence on the other hand grows linearly with the dimension of the parameter space, and can hence be controlled through a prudent choice of the function class defining the mismatched divergence.

cs.LG cs.CC

0909.2927

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

2009-09-16T06:19:12Z

2009-09-16T06:19:12Z

Distribution-Specific Agnostic Boosting

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

cs.LG cs.AI

0909.2934

http://arxiv.org/pdf/0909.2934v1

2009-09-16T07:08:44Z

2009-09-16T07:08:44Z

A Convergent Online Single Time Scale Actor Critic Algorithm

Actor-Critic based approaches were among the first to address reinforcement learning in a general setting. Recently, these algorithms have gained renewed interest due to their generality, good convergence properties, and possible biological relevance. In this paper, we introduce an online temporal difference based actor-critic algorithm which is proved to converge to a neighborhood of a local maximum of the average reward. Linear function approximation is used by the critic in order estimate the value function, and the temporal difference signal, which is passed from the critic to the actor. The main distinguishing feature of the present convergence proof is that both the actor and the critic operate on a similar time scale, while in most current convergence proofs they are required to have very different time scales in order to converge. Moreover, the same temporal difference signal is used to update the parameters of both the actor and the critic. A limitation of the proposed approach, compared to results available for two time scale convergence, is that convergence is guaranteed only to a neighborhood of an optimal value, rather to an optimal value itself. The single time scale and identical temporal difference signal used by the actor and the critic, may provide a step towards constructing more biologically realistic models of reinforcement learning in the brain.

cs.CV cs.LG

10.1109/ICCVW.2009.5457695

0909.3123

http://arxiv.org/abs/0909.3123v1

2009-09-16T23:09:16Z

2009-09-16T23:09:16Z

Median K-flats for hybrid linear modeling with many outliers

We describe the Median K-Flats (MKF) algorithm, a simple online method for hybrid linear modeling, i.e., for approximating data by a mixture of flats. This algorithm simultaneously partitions the data into clusters while finding their corresponding best approximating l1 d-flats, so that the cumulative l1 error is minimized. The current implementation restricts d-flats to be d-dimensional linear subspaces. It requires a negligible amount of storage, and its complexity, when modeling data consisting of N points in D-dimensional Euclidean space with K d-dimensional linear subspaces, is of order O(n K d D+n d^2 D), where n is the number of iterations required for convergence (empirically on the order of 10^4). Since it is an online algorithm, data can be supplied to it incrementally and it can incrementally produce the corresponding output. The performance of the algorithm is carefully evaluated using synthetic and real data.

cs.LG cs.AI

0909.3593

http://arxiv.org/pdf/0909.3593v2

2010-09-25T02:27:46Z

2009-09-19T16:10:19Z

Exploiting Unlabeled Data to Enhance Ensemble Diversity

Ensemble learning aims to improve generalization ability by using multiple base learners. It is well-known that to construct a good ensemble, the base learners should be accurate as well as diverse. In this paper, unlabeled data is exploited to facilitate ensemble learning by helping augment the diversity among the base learners. Specifically, a semi-supervised ensemble method named UDEED is proposed. Unlike existing semi-supervised ensemble methods where error-prone pseudo-labels are estimated for unlabeled data to enlarge the labeled data to improve accuracy, UDEED works by maximizing accuracies of base learners on labeled data while maximizing diversity among them on unlabeled data. Experiments show that UDEED can effectively utilize unlabeled data for ensemble learning and is highly competitive to well-established semi-supervised ensemble methods.

cs.LG cs.CV

0909.3606

http://arxiv.org/pdf/0909.3606v1

2009-09-19T23:46:21Z

2009-09-19T23:46:21Z

Extension of Path Probability Method to Approximate Inference over Time

There has been a tremendous growth in publicly available digital video footage over the past decade. This has necessitated the development of new techniques in computer vision geared towards efficient analysis, storage and retrieval of such data. Many mid-level computer vision tasks such as segmentation, object detection, tracking, etc. involve an inference problem based on the video data available. Video data has a high degree of spatial and temporal coherence. The property must be intelligently leveraged in order to obtain better results. Graphical models, such as Markov Random Fields, have emerged as a powerful tool for such inference problems. They are naturally suited for expressing the spatial dependencies present in video data, It is however, not clear, how to extend the existing techniques for the problem of inference over time. This thesis explores the Path Probability Method, a variational technique in statistical mechanics, in the context of graphical models and approximate inference problems. It extends the method to a general framework for problems involving inference in time, resulting in an algorithm, \emph{DynBP}. We explore the relation of the algorithm with existing techniques, and find the algorithm competitive with existing approaches. The main contribution of this thesis are the extended GBP algorithm, the extension of Path Probability Methods to the DynBP algorithm and the relationship between them. We have also explored some applications in computer vision involving temporal evolution with promising results.

cs.LG

0909.3609

http://arxiv.org/pdf/0909.3609v1

2009-09-19T23:40:10Z

2009-09-19T23:40:10Z

Randomized Algorithms for Large scale SVMs

We propose a randomized algorithm for training Support vector machines(SVMs) on large datasets. By using ideas from Random projections we show that the combinatorial dimension of SVMs is $O({log} n)$ with high probability. This estimate of combinatorial dimension is used to derive an iterative algorithm, called RandSVM, which at each step calls an existing solver to train SVMs on a randomly chosen subset of size $O({log} n)$. The algorithm has probabilistic guarantees and is capable of training SVMs with Kernels for both classification and regression problems. Experiments done on synthetic and real life data sets demonstrate that the algorithm scales up existing SVM learners, without loss of accuracy.

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

0909.4588

http://arxiv.org/pdf/0909.4588v1

2009-09-25T02:57:17Z

2009-09-25T02:57:17Z

Discrete MDL Predicts in Total Variation

The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result is completely general. No independence, ergodicity, stationarity, identifiability, or other assumption on the model class need to be made. More formally, we show that for any countable class of models, the distributions selected by MDL (or MAP) asymptotically predict (merge with) the true measure in the class in total variation distance. Implications for non-i.i.d. domains like time-series forecasting, discriminative learning, and reinforcement learning are discussed.

cs.LG

0909.4603

http://arxiv.org/pdf/0909.4603v1

2009-09-25T05:23:33Z

2009-09-25T05:23:33Z

Scalable Inference for Latent Dirichlet Allocation

We investigate the problem of learning a topic model - the well-known Latent Dirichlet Allocation - in a distributed manner, using a cluster of C processors and dividing the corpus to be learned equally among them. We propose a simple approximated method that can be tuned, trading speed for accuracy according to the task at hand. Our approach is asynchronous, and therefore suitable for clusters of heterogenous machines.

cs.LG cs.NA cs.NE

0909.5000

http://arxiv.org/pdf/0909.5000v1

2009-09-28T04:25:03Z

2009-09-28T04:25:03Z

Eignets for function approximation on manifolds

Let $\XX$ be a compact, smooth, connected, Riemannian manifold without boundary, $G:\XX\times\XX\to \RR$ be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form $\sum_{j=1}^M a_jG(\circ,y_j)$, where $a_j\in\RR$, $y_j\in\XX$, $1\le j\le M$. We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in $L^p(\mu;\XX)$ for a general class of measures $\mu$ and kernels $G$. Our algorithm yields linear operators. Using the minimal separation amongst the centers $y_j$ as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every \emph{individual function}. We also give estimates on the coefficients $a_j$ in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in terms of the minimal separation, then the derivatives of the eignets also approximate the corresponding derivatives of the target function in an optimal manner.

cs.CC cs.LG

10.4086/toc.2014.v010a001

0909.5175

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

2009-11-09T23:23:19Z

2009-09-28T19:55:46Z

Bounding the Sensitivity of Polynomial Threshold Functions

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

cs.LG cs.IT math.IT

0909.5457

http://arxiv.org/pdf/0909.5457v3

2009-10-19T21:21:57Z

2009-09-30T14:44:54Z

Guaranteed Rank Minimization via Singular Value Projection

Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with many important applications in machine learning and statistics. In this paper we propose a simple and fast algorithm SVP (Singular Value Projection) for rank minimization with affine constraints (ARMP) and show that SVP recovers the minimum rank solution for affine constraints that satisfy the "restricted isometry property" and show robustness of our method to noise. Our results improve upon a recent breakthrough by Recht, Fazel and Parillo (RFP07) and Lee and Bresler (LB09) in three significant ways: 1) our method (SVP) is significantly simpler to analyze and easier to implement, 2) we give recovery guarantees under strictly weaker isometry assumptions 3) we give geometric convergence guarantees for SVP even in presense of noise and, as demonstrated empirically, SVP is significantly faster on real-world and synthetic problems. In addition, we address the practically important problem of low-rank matrix completion (MCP), which can be seen as a special case of ARMP. We empirically demonstrate that our algorithm recovers low-rank incoherent matrices from an almost optimal number of uniformly sampled entries. We make partial progress towards proving exact recovery and provide some intuition for the strong performance of SVP applied to matrix completion by showing a more restricted isometry property. Our algorithm outperforms existing methods, such as those of \cite{RFP07,CR08,CT09,CCS08,KOM09,LB09}, for ARMP and the matrix-completion problem by an order of magnitude and is also significantly more robust to noise.

cs.DS cs.DB cs.LG

0910.0112

http://arxiv.org/pdf/0910.0112v2

2010-02-17T09:32:14Z

2009-10-01T09:02:54Z

Finding Associations and Computing Similarity via Biased Pair Sampling

This version is ***superseded*** by a full version that can be found at http://www.itu.dk/people/pagh/papers/mining-jour.pdf, which contains stronger theoretical results and fixes a mistake in the reporting of experiments. Abstract: Sampling-based methods have previously been proposed for the problem of finding interesting associations in data, even for low-support items. While these methods do not guarantee precise results, they can be vastly more efficient than approaches that rely on exact counting. However, for many similarity measures no such methods have been known. In this paper we show how a wide variety of measures can be supported by a simple biased sampling method. The method also extends to find high-confidence association rules. We demonstrate theoretically that our method is superior to exact methods when the threshold for "interesting similarity/confidence" is above the average pairwise similarity/confidence, and the average support is not too low. Our method is particularly good when transactions contain many items. We confirm in experiments on standard association mining benchmarks that this gives a significant speedup on real data sets (sometimes much larger than the theoretical guarantees). Reductions in computation time of over an order of magnitude, and significant savings in space, are observed.

cs.IT cs.LG math.IT

0910.0239

http://arxiv.org/pdf/0910.0239v2

2010-01-25T15:40:48Z

2009-10-01T19:49:36Z

Compressed Blind De-convolution

Suppose the signal x is realized by driving a k-sparse signal u through an arbitrary unknown stable discrete-linear time invariant system H. These types of processes arise naturally in Reflection Seismology. In this paper we are interested in several problems: (a) Blind-Deconvolution: Can we recover both the filter $H$ and the sparse signal $u$ from noisy measurements? (b) Compressive Sensing: Is x compressible in the conventional sense of compressed sensing? Namely, can x, u and H be reconstructed from a sparse set of measurements. We develop novel L1 minimization methods to solve both cases and establish sufficient conditions for exact recovery for the case when the unknown system H is auto-regressive (i.e. all pole) of a known order. In the compressed sensing/sampling setting it turns out that both H and x can be reconstructed from O(k log(n)) measurements under certain technical conditions on the support structure of u. Our main idea is to pass x through a linear time invariant system G and collect O(k log(n)) sequential measurements. The filter G is chosen suitably, namely, its associated Toeplitz matrix satisfies the RIP property. We develop a novel LP optimization algorithm and show that both the unknown filter H and the sparse input u can be reliably estimated.

cs.LG

10.1109/ICDMW.2008.87

0910.0349

http://arxiv.org/abs/0910.0349v1

2009-10-02T08:40:01Z

2009-10-02T08:40:01Z

Post-Processing of Discovered Association Rules Using Ontologies

In Data Mining, the usefulness of association rules is strongly limited by the huge amount of delivered rules. In this paper we propose a new approach to prune and filter discovered rules. Using Domain Ontologies, we strengthen the integration of user knowledge in the post-processing task. Furthermore, an interactive and iterative framework is designed to assist the user along the analyzing task. On the one hand, we represent user domain knowledge using a Domain Ontology over database. On the other hand, a novel technique is suggested to prune and to filter discovered rules. The proposed framework was applied successfully over the client database provided by Nantes Habitat.

stat.ML cs.LG stat.AP

0910.0483

http://arxiv.org/pdf/0910.0483v1

2009-10-05T19:43:40Z

2009-10-05T19:43:40Z

Statistical Decision Making for Authentication and Intrusion Detection

User authentication and intrusion detection differ from standard classification problems in that while we have data generated from legitimate users, impostor or intrusion data is scarce or non-existent. We review existing techniques for dealing with this problem and propose a novel alternative based on a principled statistical decision-making view point. We examine the technique on a toy problem and validate it on complex real-world data from an RFID based access control system. The results indicate that it can significantly outperform the classical world model approach. The method could be more generally useful in other decision-making scenarios where there is a lack of adversary data.

cs.LG stat.ML

0910.0610

http://arxiv.org/pdf/0910.0610v2

2010-10-17T21:34:13Z

2009-10-04T14:48:46Z

Regularization Techniques for Learning with Matrices

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge). This work describes and analyzes a systematic method for constructing such matrix-based, regularization methods. In particular, we focus on how the underlying statistical properties of a given problem can help us decide which regularization function is appropriate. Our methodology is based on the known duality fact: that a function is strongly convex with respect to some norm if and only if its conjugate function is strongly smooth with respect to the dual norm. This result has already been found to be a key component in deriving and analyzing several learning algorithms. We demonstrate the potential of this framework by deriving novel generalization and regret bounds for multi-task learning, multi-class learning, and kernel learning.

cs.LG

0910.0668

http://arxiv.org/pdf/0910.0668v2

2009-10-07T21:52:48Z

2009-10-05T03:30:13Z

Variable sigma Gaussian processes: An expectation propagation perspective

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate GP methods have been proposed that essentially map the large dataset into a small set of basis points. The most advanced of these, the variable-sigma GP (VSGP) (Walder et al., 2008), allows each basis point to have its own length scale. However, VSGP was only derived for regression. We describe how VSGP can be applied to classification and other problems, by deriving it as an expectation propagation algorithm. In this view, sparse GP approximations correspond to a KL-projection of the true posterior onto a compact exponential family of GPs. VSGP constitutes one such family, and we show how to enlarge this family to get additional accuracy. In particular, we show that endowing each basis point with its own full covariance matrix provides a significant increase in approximation power.

cs.LG q-bio.QM

0910.0820

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

2009-10-08T11:05:26Z

2009-10-05T18:36:11Z

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

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

cs.LG cs.AI

0910.0902

http://arxiv.org/pdf/0910.0902v3

2009-12-22T23:31:57Z

2009-10-06T06:00:47Z

Reduced-Rank Hidden Markov Models

We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in continuous-observation HMMs. RR-HMMs assume an m-dimensional latent state and n discrete observations, with a transition matrix of rank k <= m. This implies the dynamics evolve in a k-dimensional subspace, while the shape of the set of predictive distributions is determined by m. Latent state belief is represented with a k-dimensional state vector and inference is carried out entirely in R^k, making RR-HMMs as computationally efficient as k-state HMMs yet more expressive. To learn RR-HMMs, we relax the assumptions of a recently proposed spectral learning algorithm for HMMs (Hsu, Kakade and Zhang 2009) and apply it to learn k-dimensional observable representations of rank-k RR-HMMs. The algorithm is consistent and free of local optima, and we extend its performance guarantees to cover the RR-HMM case. We show how this algorithm can be used in conjunction with a kernel density estimator to efficiently model high-dimensional multivariate continuous data. We also relax the assumption that single observations are sufficient to disambiguate state, and extend the algorithm accordingly. Experiments on synthetic data and a toy video, as well as on a difficult robot vision modeling problem, yield accurate models that compare favorably with standard alternatives in simulation quality and prediction capability.

cs.LG cs.NA

0910.0921

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

2009-11-03T23:56:31Z

2009-10-06T04:41:05Z

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

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

cs.CV cs.LG

0910.1273

http://arxiv.org/pdf/0910.1273v1

2009-10-07T14:26:01Z

2009-10-07T14:26:01Z

Adaboost with "Keypoint Presence Features" for Real-Time Vehicle Visual Detection

We present promising results for real-time vehicle visual detection, obtained with adaBoost using new original ?keypoints presence features?. These weak-classifiers produce a boolean response based on presence or absence in the tested image of a ?keypoint? (~ a SURF interest point) with a descriptor sufficiently similar (i.e. within a given distance) to a reference descriptor characterizing the feature. A first experiment was conducted on a public image dataset containing lateral-viewed cars, yielding 95% recall with 95% precision on test set. Moreover, analysis of the positions of adaBoost-selected keypoints show that they correspond to a specific part of the object category (such as ?wheel? or ?side skirt?) and thus have a ?semantic? meaning.

cs.CV cs.LG

0910.1293

http://arxiv.org/pdf/0910.1293v1

2009-10-07T15:42:03Z

2009-10-07T15:42:03Z

Introducing New AdaBoost Features for Real-Time Vehicle Detection

This paper shows how to improve the real-time object detection in complex robotics applications, by exploring new visual features as AdaBoost weak classifiers. These new features are symmetric Haar filters (enforcing global horizontal and vertical symmetry) and N-connexity control points. Experimental evaluation on a car database show that the latter appear to provide the best results for the vehicle-detection problem.

cs.CV cs.LG

0910.1294

http://arxiv.org/pdf/0910.1294v1

2009-10-07T15:42:30Z

2009-10-07T15:42:30Z

Visual object categorization with new keypoint-based adaBoost features

We present promising results for visual object categorization, obtained with adaBoost using new original ?keypoints-based features?. These weak-classifiers produce a boolean response based on presence or absence in the tested image of a ?keypoint? (a kind of SURF interest point) with a descriptor sufficiently similar (i.e. within a given distance) to a reference descriptor characterizing the feature. A first experiment was conducted on a public image dataset containing lateral-viewed cars, yielding 95% recall with 95% precision on test set. Preliminary tests on a small subset of a pedestrians database also gives promising 97% recall with 92 % precision, which shows the generality of our new family of features. Moreover, analysis of the positions of adaBoost-selected keypoints show that they correspond to a specific part of the object category (such as ?wheel? or ?side skirt? in the case of lateral-cars) and thus have a ?semantic? meaning. We also made a first test on video for detecting vehicles from adaBoostselected keypoints filtered in real-time from all detected keypoints.