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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


Random DFAs are Efficiently PAC Learnable

This paper has been withdrawn due to an error found by Dana Angluin and Lev Reyzin.


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.


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.


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.


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.


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.


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.


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 $n$.


Privacy constraints in regularized convex optimization

This paper is withdrawn due to some errors, which are corrected in arXiv:0912.0071v4 [cs.LG].


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


Local and global approaches of affinity propagation clustering for large scale data

Recently a new clustering algorithm called 'affinity propagation' (AP) has been proposed, which efficiently clustered sparsely related data by passing messages between data points. However, we want to cluster large scale data where the similarities are not sparse in many cases. This paper presents two variants of AP for grouping large scale data with a dense similarity matrix. The local approach is partition affinity propagation (PAP) and the global method is landmark affinity propagation (LAP). PAP passes messages in the subsets of data first and then merges them as the number of initial step of iterations; it can effectively reduce the number of iterations of clustering. LAP passes messages between the landmark data points first and then clusters non-landmark data points; it is a large global approximation method to speed up clustering. Experiments are conducted on many datasets, such as random data points, manifold subspaces, images of faces and Chinese calligraphy, and the results demonstrate that the two approaches are feasible and practicable.


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

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


Distributed Learning in Multi-Armed Bandit with Multiple Players

We formulate and study a decentralized multi-armed bandit (MAB) problem. There are M distributed players competing for N independent arms. Each arm, when played, offers i.i.d. reward according to a distribution with an unknown parameter. At each time, each player chooses one arm to play without exchanging observations or any information with other players. Players choosing the same arm collide, and, depending on the collision model, either no one receives reward or the colliding players share the reward in an arbitrary way. We show that the minimum system regret of the decentralized MAB grows with time at the same logarithmic order as in the centralized counterpart where players act collectively as a single entity by exchanging observations and making decisions jointly. A decentralized policy is constructed to achieve this optimal order while ensuring fairness among players and without assuming any pre-agreement or information exchange among players. Based on a Time Division Fair Sharing (TDFS) of the M best arms, the proposed policy is constructed and its order optimality is proven under a general reward model. Furthermore, the basic structure of the TDFS policy can be used with any order-optimal single-player policy to achieve order optimality in the decentralized setting. We also establish a lower bound on the system regret growth rate for a general class of decentralized polices, to which the proposed policy belongs. This problem finds potential applications in cognitive radio networks, multi-channel communication systems, multi-agent systems, web search and advertising, and social networks.


Repeated Auctions with Learning for Spectrum Access in Cognitive Radio Networks

In this paper, spectrum access in cognitive radio networks is modeled as a repeated auction game subject to monitoring and entry costs. For secondary users, sensing costs are incurred as the result of primary users' activity. Furthermore, each secondary user pays the cost of transmissions upon successful bidding for a channel. Knowledge regarding other secondary users' activity is limited due to the distributed nature of the network. The resulting formulation is thus a dynamic game with incomplete information. In this paper, an efficient bidding learning algorithm is proposed based on the outcome of past transactions. As demonstrated through extensive simulations, the proposed distributed scheme outperforms a myopic one-stage algorithm, and can achieve a good balance between efficiency and fairness.


Positive Semidefinite Metric Learning with Boosting

The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. \BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. \BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.


Effectiveness and Limitations of Statistical Spam Filters

In this paper we discuss the techniques involved in the design of the famous statistical spam filters that include Naive Bayes, Term Frequency-Inverse Document Frequency, K-Nearest Neighbor, Support Vector Machine, and Bayes Additive Regression Tree. We compare these techniques with each other in terms of accuracy, recall, precision, etc. Further, we discuss the effectiveness and limitations of statistical filters in filtering out various types of spam from legitimate e-mails.


On Learning Finite-State Quantum Sources

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


Self-concordant analysis for logistic regression

Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature, namely self-concordant functions, to provide simple extensions of theoretical results for the square loss to the logistic loss. We apply the extension techniques to logistic regression with regularization by the $\ell_2$-norm and regularization by the $\ell_1$-norm, showing that new results for binary classification through logistic regression can be easily derived from corresponding results for least-squares regression.


Competing with Gaussian linear experts

We study the problem of online regression. We prove a theoretical bound on the square loss of Ridge Regression. We do not make any assumptions about input vectors or outcomes. We also show that Bayesian Ridge Regression can be thought of as an online algorithm competing with all the Gaussian linear experts.


A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion

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


The Cyborg Astrobiologist: Testing a Novelty-Detection Algorithm on Two Mobile Exploration Systems at Rivas Vaciamadrid in Spain and at the Mars Desert Research Station in Utah

(ABRIDGED) In previous work, two platforms have been developed for testing computer-vision algorithms for robotic planetary exploration (McGuire et al. 2004b,2005; Bartolo et al. 2007). The wearable-computer platform has been tested at geological and astrobiological field sites in Spain (Rivas Vaciamadrid and Riba de Santiuste), and the phone-camera has been tested at a geological field site in Malta. In this work, we (i) apply a Hopfield neural-network algorithm for novelty detection based upon color, (ii) integrate a field-capable digital microscope on the wearable computer platform, (iii) test this novelty detection with the digital microscope at Rivas Vaciamadrid, (iv) develop a Bluetooth communication mode for the phone-camera platform, in order to allow access to a mobile processing computer at the field sites, and (v) test the novelty detection on the Bluetooth-enabled phone-camera connected to a netbook computer at the Mars Desert Research Station in Utah. This systems engineering and field testing have together allowed us to develop a real-time computer-vision system that is capable, for example, of identifying lichens as novel within a series of images acquired in semi-arid desert environments. We acquired sequences of images of geologic outcrops in Utah and Spain consisting of various rock types and colors to test this algorithm. The algorithm robustly recognized previously-observed units by their color, while requiring only a single image or a few images to learn colors as familiar, demonstrating its fast learning capability.


Anomaly Detection with Score functions based on Nearest Neighbor Graphs

We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on $n$-point nominal data. Anomalies are declared whenever the score of a test sample falls below $\alpha$, which is supposed to be the desired false alarm level. The resulting anomaly detector is shown to be asymptotically optimal in that it is uniformly most powerful for the specified false alarm level, $\alpha$, for the case when the anomaly density is a mixture of the nominal and a known density. Our algorithm is computationally efficient, being linear in dimension and quadratic in data size. It does not require choosing complicated tuning parameters or function approximation classes and it can adapt to local structure such as local change in dimensionality. We demonstrate the algorithm on both artificial and real data sets in high dimensional feature spaces.


Which graphical models are difficult to learn?

We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-complexity algorithms systematically fail when the Markov random field develops long-range correlations. More precisely, this phenomenon appears to be related to the Ising model phase transition (although it does not coincide with it).


Metric and Kernel Learning using a Linear Transformation

Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are often limited to the transductive setting and do not generalize to new data points. In this paper, we study metric learning as a problem of learning a linear transformation of the input data. We show that for high-dimensional data, a particular framework for learning a linear transformation of the data based on the LogDet divergence can be efficiently kernelized to learn a metric (or equivalently, a kernel function) over an arbitrarily high dimensional space. We further demonstrate that a wide class of convex loss functions for learning linear transformations can similarly be kernelized, thereby considerably expanding the potential applications of metric learning. We demonstrate our learning approach by applying it to large-scale real world problems in computer vision and text mining.


Learning Exponential Families in High-Dimensions: Strong Convexity and Sparsity

The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity pattern of the optimal parameter. This work characterizes a certain strong convexity property of general exponential families, which allow their generalization ability to be quantified. In particular, we show how this property can be used to analyze generic exponential families under L_1 regularization.


A Mirroring Theorem and its Application to a New Method of Unsupervised Hierarchical Pattern Classification

In this paper, we prove a crucial theorem called Mirroring Theorem which affirms that given a collection of samples with enough information in it such that it can be classified into classes and subclasses then (i) There exists a mapping which classifies and subclassifies these samples (ii) There exists a hierarchical classifier which can be constructed by using Mirroring Neural Networks (MNNs) in combination with a clustering algorithm that can approximate this mapping. Thus, the proof of the Mirroring theorem provides a theoretical basis for the existence and a practical feasibility of constructing hierarchical classifiers, given the maps. Our proposed Mirroring Theorem can also be considered as an extension to Kolmogrovs theorem in providing a realistic solution for unsupervised classification. The techniques we develop, are general in nature and have led to the construction of learning machines which are (i) tree like in structure, (ii) modular (iii) with each module running on a common algorithm (tandem algorithm) and (iv) selfsupervised. We have actually built the architecture, developed the tandem algorithm of such a hierarchical classifier and demonstrated it on an example problem.


Feature-Weighted Linear Stacking

Ensemble methods, such as stacking, are designed to boost predictive accuracy by blending the predictions of multiple machine learning models. Recent work has shown that the use of meta-features, additional inputs describing each example in a dataset, can boost the performance of ensemble methods, but the greatest reported gains have come from nonlinear procedures requiring significant tuning and training time. Here, we present a linear technique, Feature-Weighted Linear Stacking (FWLS), that incorporates meta-features for improved accuracy while retaining the well-known virtues of linear regression regarding speed, stability, and interpretability. FWLS combines model predictions linearly using coefficients that are themselves linear functions of meta-features. This technique was a key facet of the solution of the second place team in the recently concluded Netflix Prize competition. Significant increases in accuracy over standard linear stacking are demonstrated on the Netflix Prize collaborative filtering dataset.


Strange Bedfellows: Quantum Mechanics and Data Mining

Last year, in 2008, I gave a talk titled {\it Quantum Calisthenics}. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.


Novel Intrusion Detection using Probabilistic Neural Network and Adaptive Boosting

This article applies Machine Learning techniques to solve Intrusion Detection problems within computer networks. Due to complex and dynamic nature of computer networks and hacking techniques, detecting malicious activities remains a challenging task for security experts, that is, currently available defense systems suffer from low detection capability and high number of false alarms. To overcome such performance limitations, we propose a novel Machine Learning algorithm, namely Boosted Subspace Probabilistic Neural Network (BSPNN), which integrates an adaptive boosting technique and a semi parametric neural network to obtain good tradeoff between accuracy and generality. As the result, learning bias and generalization variance can be significantly minimized. Substantial experiments on KDD 99 intrusion benchmark indicate that our model outperforms other state of the art learning algorithms, with significantly improved detection accuracy, minimal false alarms and relatively small computational complexity.


Bayes estimators for phylogenetic reconstruction

Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree. Yet most reconstruction methods like ML do not explicitly maximize this accuracy. To address this problem, we propose a Bayesian solution. Given tree samples, we propose finding the tree estimate which is closest on average to the samples. This ``median'' tree is known as the Bayes estimator (BE). The BE literally maximizes posterior expected accuracy, measured in terms of closeness (distance) to the true tree. We discuss a unified framework of BE trees, focusing especially on tree distances which are expressible as squared euclidean distances. Notable examples include Robinson--Foulds distance, quartet distance, and squared path difference. Using simulated data, we show Bayes estimators can be efficiently computed in practice by hill climbing. We also show that Bayes estimators achieve higher accuracy, compared to maximum likelihood and neighbor joining.


Sharp Dichotomies for Regret Minimization in Metric Spaces

The Lipschitz multi-armed bandit (MAB) problem generalizes the classical multi-armed bandit problem by assuming one is given side information consisting of a priori upper bounds on the difference in expected payoff between certain pairs of strategies. Classical results of (Lai and Robbins 1985) and (Auer et al. 2002) imply a logarithmic regret bound for the Lipschitz MAB problem on finite metric spaces. Recent results on continuum-armed bandit problems and their generalizations imply lower bounds of $\sqrt{t}$, or stronger, for many infinite metric spaces such as the unit interval. Is this dichotomy universal? We prove that the answer is yes: for every metric space, the optimal regret of a Lipschitz MAB algorithm is either bounded above by any $f\in \omega(\log t)$, or bounded below by any $g\in o(\sqrt{t})$. Perhaps surprisingly, this dichotomy does not coincide with the distinction between finite and infinite metric spaces; instead it depends on whether the completion of the metric space is compact and countable. Our proof connects upper and lower bound techniques in online learning with classical topological notions such as perfect sets and the Cantor-Bendixson theorem. Among many other results, we show a similar dichotomy for the "full-feedback" (a.k.a., "best-expert") version.


Machine Learning: When and Where the Horses Went Astray?

Machine Learning is usually defined as a subfield of AI, which is busy with information extraction from raw data sets. Despite of its common acceptance and widespread recognition, this definition is wrong and groundless. Meaningful information does not belong to the data that bear it. It belongs to the observers of the data and it is a shared agreement and a convention among them. Therefore, this private information cannot be extracted from the data by any means. Therefore, all further attempts of Machine Learning apologists to justify their funny business are inappropriate.


Belief Propagation and Loop Calculus for the Permanent of a Non-Negative Matrix

We consider computation of permanent of a positive $(N\times N)$ non-negative matrix, $P=(P_i^j|i,j=1,\cdots,N)$, or equivalently the problem of weighted counting of the perfect matchings over the complete bipartite graph $K_{N,N}$. The problem is known to be of likely exponential complexity. Stated as the partition function $Z$ of a graphical model, the problem allows exact Loop Calculus representation [Chertkov, Chernyak '06] in terms of an interior minimum of the Bethe Free Energy functional over non-integer doubly stochastic matrix of marginal beliefs, $\beta=(\beta_i^j|i,j=1,\cdots,N)$, also correspondent to a fixed point of the iterative message-passing algorithm of the Belief Propagation (BP) type. Our main result is an explicit expression of the exact partition function (permanent) in terms of the matrix of BP marginals, $\beta$, as $Z=\mbox{Perm}(P)=Z_{BP} \mbox{Perm}(\beta_i^j(1-\beta_i^j))/\prod_{i,j}(1-\beta_i^j)$, where $Z_{BP}$ is the BP expression for the permanent stated explicitly in terms if $\beta$. We give two derivations of the formula, a direct one based on the Bethe Free Energy and an alternative one combining the Ihara graph-$\zeta$ function and the Loop Calculus approaches. Assuming that the matrix $\beta$ of the Belief Propagation marginals is calculated, we provide two lower bounds and one upper-bound to estimate the multiplicative term. Two complementary lower bounds are based on the Gurvits-van der Waerden theorem and on a relation between the modified permanent and determinant respectively.