Online Learning via Sequential Complexities

We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our proposed sequential complexities can be seen as extensions of these measures to the sequential setting. The developed theory is shown to yield precise learning guarantees for the problem of sequential prediction. In particular, we show necessary and sufficient conditions for online learnability in the setting of supervised learning. Several examples show the utility of our framework: we can establish learnability without having to exhibit an explicit online learning algorithm.


Regression on fixed-rank positive semidefinite matrices: a Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks.


Uncovering the Riffled Independence Structure of Rankings

Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called \emph{riffled independence}, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the \emph{riffle shuffle}, common in card games, to combine the two permutations to form a single permutation. Within the context of ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. In this paper, we provide a formal introduction to riffled independence and present algorithms for using riffled independence within Fourier-theoretic frameworks which have been explored by a number of recent papers. Additionally, we propose an automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled independence.


Calibration and Internal no-Regret with Partial Monitoring

Calibrated strategies can be obtained by performing strategies that have no internal regret in some auxiliary game. Such strategies can be constructed explicitly with the use of Blackwell's approachability theorem, in an other auxiliary game. We establish the converse: a strategy that approaches a convex $B$-set can be derived from the construction of a calibrated strategy. We develop these tools in the framework of a game with partial monitoring, where players do not observe the actions of their opponents but receive random signals, to define a notion of internal regret and construct strategies that have no such regret.


Dyadic Prediction Using a Latent Feature Log-Linear Model

In dyadic prediction, labels must be predicted for pairs (dyads) whose members possess unique identifiers and, sometimes, additional features called side-information. Special cases of this problem include collaborative filtering and link prediction. We present the first model for dyadic prediction that satisfies several important desiderata: (i) labels may be ordinal or nominal, (ii) side-information can be easily exploited if present, (iii) with or without side-information, latent features are inferred for dyad members, (iv) it is resistant to sample-selection bias, (v) it can learn well-calibrated probabilities, and (vi) it can scale to very large datasets. To our knowledge, no existing method satisfies all the above criteria. In particular, many methods assume that the labels are ordinal and ignore side-information when it is present. Experimental results show that the new method is competitive with state-of-the-art methods for the special cases of collaborative filtering and link prediction, and that it makes accurate predictions on nominal data.


On the Achievability of Cram\'er-Rao Bound In Noisy Compressed Sensing

Recently, it has been proved in Babadi et al. that in noisy compressed sensing, a joint typical estimator can asymptotically achieve the Cramer-Rao lower bound of the problem.To prove this result, this paper used a lemma,which is provided in Akcakaya et al,that comprises the main building block of the proof. This lemma is based on the assumption of Gaussianity of the measurement matrix and its randomness in the domain of noise. In this correspondence, we generalize the results obtained in Babadi et al by dropping the Gaussianity assumption on the measurement matrix. In fact, by considering the measurement matrix as a deterministic matrix in our analysis, we find a theorem similar to the main theorem of Babadi et al for a family of randomly generated (but deterministic in the noise domain) measurement matrices that satisfy a generalized condition known as The Concentration of Measures Inequality. By this, we finally show that under our generalized assumptions, the Cramer-Rao bound of the estimation is achievable by using the typical estimator introduced in Babadi et al.


Agnostic Active Learning Without Constraints

We present and analyze an agnostic active learning algorithm that works without keeping a version space. This is unlike all previous approaches where a restricted set of candidate hypotheses is maintained throughout learning, and only hypotheses from this set are ever returned. By avoiding this version space approach, our algorithm sheds the computational burden and brittleness associated with maintaining version spaces, yet still allows for substantial improvements over supervised learning for classification.


Outlier Detection Using Nonconvex Penalized Regression

This paper studies the outlier detection problem from the point of view of penalized regressions. Our regression model adds one mean shift parameter for each of the $n$ data points. We then apply a regularization favoring a sparse vector of mean shift parameters. The usual $L_1$ penalty yields a convex criterion, but we find that it fails to deliver a robust estimator. The $L_1$ penalty corresponds to soft thresholding. We introduce a thresholding (denoted by $\Theta$) based iterative procedure for outlier detection ($\Theta$-IPOD). A version based on hard thresholding correctly identifies outliers on some hard test problems. We find that $\Theta$-IPOD is much faster than iteratively reweighted least squares for large data because each iteration costs at most $O(np)$ (and sometimes much less) avoiding an $O(np^2)$ least squares estimate. We describe the connection between $\Theta$-IPOD and $M$-estimators. Our proposed method has one tuning parameter with which to both identify outliers and estimate regression coefficients. A data-dependent choice can be made based on BIC. The tuned $\Theta$-IPOD shows outstanding performance in identifying outliers in various situations in comparison to other existing approaches. This methodology extends to high-dimensional modeling with $p\gg n$, if both the coefficient vector and the outlier pattern are sparse.


Approximated Structured Prediction for Learning Large Scale Graphical Models

This manuscripts contains the proofs for "A Primal-Dual Message-Passing Algorithm for Approximated Large Scale Structured Prediction".


Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space. However, so far, the emphasis has been on batch techniques. It is only recently, that online techniques have been considered in the context of adaptive signal processing tasks. Moreover, these efforts have only been focussed on real valued data sequences. To the best of our knowledge, no adaptive kernel-based strategy has been developed, so far, for complex valued signals. Furthermore, although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications that deal with complex signals, with Communications being a typical example. In this paper, we present a general framework to attack the problem of adaptive filtering of complex signals, using either real reproducing kernels, taking advantage of a technique called \textit{complexification} of real RKHSs, or complex reproducing kernels, highlighting the use of the complex gaussian kernel. In order to derive gradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool of Wirtinger's Calculus, which has recently attracted attention in the signal processing community. To this end, in this paper, the notion of Wirtinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS offers significant performance improvements over several linear and nonlinear algorithms, when dealing with nonlinearities.


Fictitious Play with Time-Invariant Frequency Update for Network Security

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. The evolution of the game is based on a stochastic fictitious play process, where players do not have access to each other's payoff matrix. Each has to observe the other's actions up to present and plays the action generated based on the best response to these observations. In a regular fictitious play process, each player makes a maximum likelihood estimate of her opponent's mixed strategy, which results in a time-varying update based on the previous estimate and current action. In this paper, we explore an alternative scheme for frequency update, whose mean dynamic is instead time-invariant. We examine convergence properties of the mean dynamic of the fictitious play process with such an update scheme, and establish local stability of the equilibrium point when both players are restricted to two actions. We also propose an adaptive algorithm based on this time-invariant frequency update.


Segmentation of Natural Images by Texture and Boundary Compression

We present a novel algorithm for segmentation of natural images that harnesses the principle of minimum description length (MDL). Our method is based on observations that a homogeneously textured region of a natural image can be well modeled by a Gaussian distribution and the region boundary can be effectively coded by an adaptive chain code. The optimal segmentation of an image is the one that gives the shortest coding length for encoding all textures and boundaries in the image, and is obtained via an agglomerative clustering process applied to a hierarchy of decreasing window sizes as multi-scale texture features. The optimal segmentation also provides an accurate estimate of the overall coding length and hence the true entropy of the image. We test our algorithm on the publicly available Berkeley Segmentation Dataset. It achieves state-of-the-art segmentation results compared to other existing methods.


Least Squares Superposition Codes of Moderate Dictionary Size, Reliable at Rates up to Capacity

For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design, with the possible messages indexed by the choice of subset. Decoding is by least squares, tailored to the assumed form of linear combination. Communication is shown to be reliable with error probability exponentially small for all rates up to the Shannon capacity.


Toward Fast Reliable Communication at Rates Near Capacity with Gaussian Noise

For the additive Gaussian noise channel with average codeword power constraint, sparse superposition codes and adaptive successive decoding is developed. Codewords are linear combinations of subsets of vectors, with the message indexed by the choice of subset. A feasible decoding algorithm is presented. Communication is reliable with error probability exponentially small for all rates below the Shannon capacity.


Distributed Autonomous Online Learning: Regrets and Intrinsic Privacy-Preserving Properties

Online learning has become increasingly popular on handling massive data. The sequential nature of online learning, however, requires a centralized learner to store data and update parameters. In this paper, we consider online learning with {\em distributed} data sources. The autonomous learners update local parameters based on local data sources and periodically exchange information with a small subset of neighbors in a communication network. We derive the regret bound for strongly convex functions that generalizes the work by Ram et al. (2010) for convex functions. Most importantly, we show that our algorithm has \emph{intrinsic} privacy-preserving properties, and we prove the sufficient and necessary conditions for privacy preservation in the network. These conditions imply that for networks with greater-than-one connectivity, a malicious learner cannot reconstruct the subgradients (and sensitive raw data) of other learners, which makes our algorithm appealing in privacy sensitive applications.


On the Implementation of the Probabilistic Logic Programming Language ProbLog

The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networks. In ProbLog, facts can be labeled with probabilities. These facts are treated as mutually independent random variables that indicate whether these facts belong to a randomly sampled program. Different kinds of queries can be posed to ProbLog programs. We introduce algorithms that allow the efficient execution of these queries, discuss their implementation on top of the YAP-Prolog system, and evaluate their performance in the context of large networks of biological entities.


A Novel Rough Set Reduct Algorithm for Medical Domain Based on Bee Colony Optimization

Feature selection refers to the problem of selecting relevant features which produce the most predictive outcome. In particular, feature selection task is involved in datasets containing huge number of features. Rough set theory has been one of the most successful methods used for feature selection. However, this method is still not able to find optimal subsets. This paper proposes a new feature selection method based on Rough set theory hybrid with Bee Colony Optimization (BCO) in an attempt to combat this. This proposed work is applied in the medical domain to find the minimal reducts and experimentally compared with the Quick Reduct, Entropy Based Reduct, and other hybrid Rough Set methods such as Genetic Algorithm (GA), Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO).


MINLIP for the Identification of Monotone Wiener Systems

This paper studies the MINLIP estimator for the identification of Wiener systems consisting of a sequence of a linear FIR dynamical model, and a monotonically increasing (or decreasing) static function. Given $T$ observations, this algorithm boils down to solving a convex quadratic program with $O(T)$ variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control. The resulting estimates of the linear submodel are found to be almost consistent when no noise is present in the data, under a condition of smoothness of the true nonlinearity and local Persistency of Excitation (local PE) of the data. This result is novel as it does not rely on classical tools as a 'linearization' using a Taylor decomposition, nor exploits stochastic properties of the data. It is indicated how to extend the method to cope with noisy data, and empirical evidence contrasts performance of the estimator against other recently proposed techniques.


GraphLab: A New Framework for Parallel Machine Learning

Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and Pthreads leave ML experts repeatedly solving the same design challenges. By targeting common patterns in ML, we developed GraphLab, which improves upon abstractions like MapReduce by compactly expressing asynchronous iterative algorithms with sparse computational dependencies while ensuring data consistency and achieving a high degree of parallel performance. We demonstrate the expressiveness of the GraphLab framework by designing and implementing parallel versions of belief propagation, Gibbs sampling, Co-EM, Lasso and Compressed Sensing. We show that using GraphLab we can achieve excellent parallel performance on large scale real-world problems.


Fast ABC-Boost for Multi-Class Classification

Abc-boost is a new line of boosting algorithms for multi-class classification, by utilizing the commonly used sum-to-zero constraint. To implement abc-boost, a base class must be identified at each boosting step. Prior studies used a very expensive procedure based on exhaustive search for determining the base class at each boosting step. Good testing performances of abc-boost (implemented as abc-mart and abc-logitboost) on a variety of datasets were reported. For large datasets, however, the exhaustive search strategy adopted in prior abc-boost algorithms can be too prohibitive. To overcome this serious limitation, this paper suggests a heuristic by introducing Gaps when computing the base class during training. That is, we update the choice of the base class only for every $G$ boosting steps (i.e., G=1 in prior studies). We test this idea on large datasets (Covertype and Poker) as well as datasets of moderate sizes. Our preliminary results are very encouraging. On the large datasets, even with G=100 (or larger), there is essentially no loss of test accuracy. On the moderate datasets, no obvious loss of test accuracy is observed when G<= 20~50. Therefore, aided by this heuristic, it is promising that abc-boost will be a practical tool for accurate multi-class classification.


Learning sparse gradients for variable selection and dimension reduction

Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning (SGL), for variable selection and dimension reduction via learning the gradients of the prediction function directly from samples. By imposing a sparsity constraint on the gradients, variable selection is achieved by selecting variables corresponding to non-zero partial derivatives, and effective dimensions are extracted based on the eigenvectors of the derived sparse empirical gradient covariance matrix. An error analysis is given for the convergence of the estimated gradients to the true ones in both the Euclidean and the manifold setting. We also develop an efficient forward-backward splitting algorithm to solve the SGL problem, making the framework practically scalable for medium or large datasets. The utility of SGL for variable selection and feature extraction is explicitly given and illustrated on artificial data as well as real-world examples. The main advantages of our method include variable selection for both linear and nonlinear predictions, effective dimension reduction with sparse loadings, and an efficient algorithm for large p, small n problems.


Split Bregman method for large scale fused Lasso

rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\ell_1$ norm regularizer. However, due to nonseparability and nonsmoothness of the regularization term, solving the fused Lasso problem is computationally demanding. Existing solvers can only deal with problems of small or medium size, or a special case of the fused Lasso problem in which the predictor matrix is identity matrix. In this paper, we propose an iterative algorithm based on split Bregman method to solve a class of large-scale fused Lasso problems, including a generalized fused Lasso and a fused Lasso support vector classifier. We derive our algorithm using augmented Lagrangian method and prove its convergence properties. The performance of our method is tested on both artificial data and real-world applications including proteomic data from mass spectrometry and genomic data from array CGH. We demonstrate that our method is many times faster than the existing solvers, and show that it is especially efficient for large p, small n problems.


PAC learnability of a concept class under non-atomic measures: a problem by Vidyasagar

In response to a 1997 problem of M. Vidyasagar, we state a necessary and sufficient condition for distribution-free PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain $\Omega$. Clearly, finiteness of the classical Vapnik-Chervonenkis dimension of $\mathscr C$ is a sufficient, but no longer necessary, condition. Besides, learnability of $\mathscr C$ under non-atomic measures does not imply the uniform Glivenko-Cantelli property with regard to non-atomic measures. Our learnability criterion is stated in terms of a combinatorial parameter $\VC({\mathscr C}\,{\mathrm{mod}}\,\omega_1)$ which we call the VC dimension of $\mathscr C$ modulo countable sets. The new parameter is obtained by ``thickening up'' single points in the definition of VC dimension to uncountable ``clusters''. Equivalently, $\VC(\mathscr C\modd\omega_1)\leq d$ if and only if every countable subclass of $\mathscr C$ has VC dimension $\leq d$ outside a countable subset of $\Omega$. The new parameter can be also expressed as the classical VC dimension of $\mathscr C$ calculated on a suitable subset of a compactification of $\Omega$. We do not make any measurability assumptions on $\mathscr C$, assuming instead the validity of Martin's Axiom (MA).


Feature Construction for Relational Sequence Learning

We tackle the problem of multi-class relational sequence learning using relevant patterns discovered from a set of labelled sequences. To deal with this problem, firstly each relational sequence is mapped into a feature vector using the result of a feature construction method. Since, the efficacy of sequence learning algorithms strongly depends on the features used to represent the sequences, the second step is to find an optimal subset of the constructed features leading to high classification accuracy. This feature selection task has been solved adopting a wrapper approach that uses a stochastic local search algorithm embedding a naive Bayes classifier. The performance of the proposed method applied to a real-world dataset shows an improvement when compared to other established methods, such as hidden Markov models, Fisher kernels and conditional random fields for relational sequences.


Data Stream Clustering: Challenges and Issues

Very large databases are required to store massive amounts of data that are continuously inserted and queried. Analyzing huge data sets and extracting valuable pattern in many applications are interesting for researchers. We can identify two main groups of techniques for huge data bases mining. One group refers to streaming data and applies mining techniques whereas second group attempts to solve this problem directly with efficient algorithms. Recently many researchers have focused on data stream as an efficient strategy against huge data base mining instead of mining on entire data base. The main problem in data stream mining means evolving data is more difficult to detect in this techniques therefore unsupervised methods should be applied. However, clustering techniques can lead us to discover hidden information. In this survey, we try to clarify: first, the different problem definitions related to data stream clustering in general; second, the specific difficulties encountered in this field of research; third, the varying assumptions, heuristics, and intuitions forming the basis of different approaches; and how several prominent solutions tackle different problems. Index Terms- Data Stream, Clustering, K-Means, Concept drift


A Survey Paper on Recommender Systems

Recommender systems apply data mining techniques and prediction algorithms to predict users' interest on information, products and services among the tremendous amount of available items. The vast growth of information on the Internet as well as number of visitors to websites add some key challenges to recommender systems. These are: producing accurate recommendation, handling many recommendations efficiently and coping with the vast growth of number of participants in the system. Therefore, new recommender system technologies are needed that can quickly produce high quality recommendations even for huge data sets. To address these issues we have explored several collaborative filtering techniques such as the item based approach, which identify relationship between items and indirectly compute recommendations for users based on these relationships. The user based approach was also studied, it identifies relationships between users of similar tastes and computes recommendations based on these relationships. In this paper, we introduce the topic of recommender system. It provides ways to evaluate efficiency, scalability and accuracy of recommender system. The paper also analyzes different algorithms of user based and item based techniques for recommendation generation. Moreover, a simple experiment was conducted using a data mining application -Weka- to apply data mining algorithms to recommender system. We conclude by proposing our approach that might enhance the quality of recommender systems.


The Link Prediction Problem in Bipartite Networks

We define and study the link prediction problem in bipartite networks, specializing general link prediction algorithms to the bipartite case. In a graph, a link prediction function of two vertices denotes the similarity or proximity of the vertices. Common link prediction functions for general graphs are defined using paths of length two between two nodes. Since in a bipartite graph adjacency vertices can only be connected by paths of odd lengths, these functions do not apply to bipartite graphs. Instead, a certain class of graph kernels (spectral transformation kernels) can be generalized to bipartite graphs when the positive-semidefinite kernel constraint is relaxed. This generalization is realized by the odd component of the underlying spectral transformation. This construction leads to several new link prediction pseudokernels such as the matrix hyperbolic sine, which we examine for rating graphs, authorship graphs, folksonomies, document--feature networks and other types of bipartite networks.


A Bayesian View of the Poisson-Dirichlet Process

The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the Dirichlet Process, is increasingly being used for probabilistic modelling in discrete areas such as language technology, bioinformatics, and image analysis. There is a rich literature about the PDP and its derivative distributions such as the Chinese Restaurant Process (CRP). This article reviews some of the basic theory and then the major results needed for Bayesian modelling of discrete problems including details of priors, posteriors and computation. The PDP allows one to build distributions over countable partitions. The PDP has two other remarkable properties: first it is partially conjugate to itself, which allows one to build hierarchies of PDPs, and second using a marginalised relative the CRP, one gets fragmentation and clustering properties that lets one layer partitions to build trees. This article presents the basic theory for understanding the notion of partitions and distributions over them, the PDP and the CRP, and the important properties of conjugacy, fragmentation and clustering, as well as some key related properties such as consistency and convergence. This article also presents a Bayesian interpretation of the Poisson-Dirichlet process based on an improper and infinite dimensional Dirichlet distribution. This means we can understand the process as just another Dirichlet and thus all its sampling properties emerge naturally. The theory of PDPs is usually presented for continuous distributions (more generally referred to as non-atomic distributions), however, when applied to discrete distributions its remarkable conjugacy property emerges. This context and basic results are also presented, as well as techniques for computing the second order Stirling numbers that occur in the posteriors for discrete distributions.


Additive Non-negative Matrix Factorization for Missing Data

Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. We interpret the factorization in a new way and use it to generate missing attributes from test data. We provide a joint optimization scheme for the missing attributes as well as the NMF factors. We prove the monotonic convergence of our algorithms. We present classification results for cases with missing attributes.


IMP: A Message-Passing Algorithmfor Matrix Completion

A new message-passing (MP) method is considered for the matrix completion problem associated with recommender systems. We attack the problem using a (generative) factor graph model that is related to a probabilistic low-rank matrix factorization. Based on the model, we propose a new algorithm, termed IMP, for the recovery of a data matrix from incomplete observations. The algorithm is based on a clustering followed by inference via MP (IMP). The algorithm is compared with a number of other matrix completion algorithms on real collaborative filtering (e.g., Netflix) data matrices. Our results show that, while many methods perform similarly with a large number of revealed entries, the IMP algorithm outperforms all others when the fraction of observed entries is small. This is helpful because it reduces the well-known cold-start problem associated with collaborative filtering (CF) systems in practice.


Query Strategies for Evading Convex-Inducing Classifiers

Classifiers are often used to detect miscreant activities. We study how an adversary can systematically query a classifier to elicit information that allows the adversary to evade detection while incurring a near-minimal cost of modifying their intended malfeasance. We generalize the theory of Lowd and Meek (2005) to the family of convex-inducing classifiers that partition input space into two sets one of which is convex. We present query algorithms for this family that construct undetected instances of approximately minimal cost using only polynomially-many queries in the dimension of the space and in the level of approximation. Our results demonstrate that near-optimal evasion can be accomplished without reverse-engineering the classifier's decision boundary. We also consider general lp costs and show that near-optimal evasion on the family of convex-inducing classifiers is generally efficient for both positive and negative convexity for all levels of approximation if p=1.


Computational Model of Music Sight Reading: A Reinforcement Learning Approach

Although the Music Sight Reading process has been studied from the cognitive psychology view points, but the computational learning methods like the Reinforcement Learning have not yet been used to modeling of such processes. In this paper, with regards to essential properties of our specific problem, we consider the value function concept and will indicate that the optimum policy can be obtained by the method we offer without to be getting involved with computing of the complex value functions. Also, we will offer a normative behavioral model for the interaction of the agent with the musical pitch environment and by using a slightly different version of Partially observable Markov decision processes we will show that our method helps for faster learning of state-action pairs in our implemented agents.


A Reinforcement Learning Model Using Neural Networks for Music Sight Reading Learning Problem

Music Sight Reading is a complex process in which when it is occurred in the brain some learning attributes would be emerged. Besides giving a model based on actor-critic method in the Reinforcement Learning, the agent is considered to have a neural network structure. We studied on where the sight reading process is happened and also a serious problem which is how the synaptic weights would be adjusted through the learning process. The model we offer here is a computational model on which an updated weights equation to fix the weights is accompanied too.


Minimax Manifold Estimation

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D given a noisy sample from the manifold. We assume that the manifold satisfies a smoothness condition and that the noise distribution has compact support. We show that the optimal rate of convergence is n^{-2/(2+d)}. Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.


The Latent Bernoulli-Gauss Model for Data Analysis

We present a new latent-variable model employing a Gaussian mixture integrated with a feature selection procedure (the Bernoulli part of the model) which together form a "Latent Bernoulli-Gauss" distribution. The model is applied to MAP estimation, clustering, feature selection and collaborative filtering and fares favorably with the state-of-the-art latent-variable models.


Filtrage vaste marge pour l'\'etiquetage s\'equentiel \`a noyaux de signaux

We address in this paper the problem of multi-channel signal sequence labeling. In particular, we consider the problem where the signals are contaminated by noise or may present some dephasing with respect to their labels. For that, we propose to jointly learn a SVM sample classifier with a temporal filtering of the channels. This will lead to a large margin filtering that is adapted to the specificity of each channel (noise and time-lag). We derive algorithms to solve the optimization problem and we discuss different filter regularizations for automated scaling or selection of channels. Our approach is tested on a non-linear toy example and on a BCI dataset. Results show that the classification performance on these problems can be improved by learning a large margin filtering.


A note on sample complexity of learning binary output neural networks under fixed input distributions

We show that the learning sample complexity of a sigmoidal neural network constructed by Sontag (1992) required to achieve a given misclassification error under a fixed purely atomic distribution can grow arbitrarily fast: for any prescribed rate of growth there is an input distribution having this rate as the sample complexity, and the bound is asymptotically tight. The rate can be superexponential, a non-recursive function, etc. We further observe that Sontag's ANN is not Glivenko-Cantelli under any input distribution having a non-atomic part.


Reinforcement Learning via AIXI Approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This 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 Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.


Consistency of Feature Markov Processes

We are studying long term sequence prediction (forecasting). We approach this by investigating criteria for choosing a compact useful state representation. The state is supposed to summarize useful information from the history. We want a method that is asymptotically consistent in the sense it will provably eventually only choose between alternatives that satisfy an optimality property related to the used criterion. We extend our work to the case where there is side information that one can take advantage of and, furthermore, we briefly discuss the active setting where an agent takes actions to achieve desirable outcomes.


Online Algorithms for the Multi-Armed Bandit Problem with Markovian Rewards

We consider the classical multi-armed bandit problem with Markovian rewards. When played an arm changes its state in a Markovian fashion while it remains frozen when not played. The player receives a state-dependent reward each time it plays an arm. The number of states and the state transition probabilities of an arm are unknown to the player. The player's objective is to maximize its long-term total reward by learning the best arm over time. We show that under certain conditions on the state transition probabilities of the arms, a sample mean based index policy achieves logarithmic regret uniformly over the total number of trials. The result shows that sample mean based index policies can be applied to learning problems under the rested Markovian bandit model without loss of optimality in the order. Moreover, comparision between Anantharam's index policy and UCB shows that by choosing a small exploration parameter UCB can have a smaller regret than Anantharam's index policy.


A Brief Introduction to Temporality and Causality

Causality is a non-obvious concept that is often considered to be related to temporality. In this paper we present a number of past and present approaches to the definition of temporality and causality from philosophical, physical, and computational points of view. We note that time is an important ingredient in many relationships and phenomena. The topic is then divided into the two main areas of temporal discovery, which is concerned with finding relations that are stretched over time, and causal discovery, where a claim is made as to the causal influence of certain events on others. We present a number of computational tools used for attempting to automatically discover temporal and causal relations in data.


A Machine Learning Approach to Recovery of Scene Geometry from Images

Recovering the 3D structure of the scene from images yields useful information for tasks such as shape and scene recognition, object detection, or motion planning and object grasping in robotics. In this thesis, we introduce a general machine learning approach called unsupervised CRF learning based on maximizing the conditional likelihood. We apply our approach to computer vision systems that recover the 3-D scene geometry from images. We focus on recovering 3D geometry from single images, stereo pairs and video sequences. Building these systems requires algorithms for doing inference as well as learning the parameters of conditional Markov random fields (MRF). Our system is trained unsupervisedly without using ground-truth labeled data. We employ a slanted-plane stereo vision model in which we use a fixed over-segmentation to segment the left image into coherent regions called superpixels, then assign a disparity plane for each superpixel. Plane parameters are estimated by solving an MRF labelling problem, through minimizing an energy fuction. We demonstrate the use of our unsupervised CRF learning algorithm for a parameterized slanted-plane stereo vision model involving shape from texture cues. Our stereo model with texture cues, only by unsupervised training, outperforms the results in related work on the same stereo dataset. In this thesis, we also formulate structure and motion estimation as an energy minimization problem, in which the model is an extension of our slanted-plane stereo vision model that also handles surface velocity. Velocity estimation is achieved by solving an MRF labeling problem using Loopy BP. Performance analysis is done using our novel evaluation metrics based on the notion of view prediction error. Experiments on road-driving stereo sequences show encouraging results.


Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.


A generalized risk approach to path inference based on hidden Markov models

Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework. While the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have long been around, other path estimators, or decoders, have been either only hinted at or applied more recently and in dedicated applications generally unfamiliar to the statistical learning community. Over a decade ago, however, a family of algorithmically defined decoders aiming to hybridize the two standard ones was proposed (Brushe et al., 1998). The present paper gives a careful analysis of this hybridization approach, identifies several problems and issues with it and other previously proposed approaches, and proposes practical resolutions of those. Furthermore, simple modifications of the classical criteria for hidden path recognition are shown to lead to a new class of decoders. Dynamic programming algorithms to compute these decoders in the usual forward-backward manner are presented. A particularly interesting subclass of such estimators can be also viewed as hybrids of the MAP and PD estimators. Similar to previously proposed MAP-PD hybrids, the new class is parameterized by a small number of tunable parameters. Unlike their algorithmic predecessors, the new risk-based decoders are more clearly interpretable, and, most importantly, work "out of the box" in practice, which is demonstrated on some real bioinformatics tasks and data. Some further generalizations and applications are discussed in conclusion.


Adapting to the Shifting Intent of Search Queries

Search engines today present results that are often oblivious to abrupt shifts in intent. For example, the query `independence day' usually refers to a US holiday, but the intent of this query abruptly changed during the release of a major film by that name. While no studies exactly quantify the magnitude of intent-shifting traffic, studies suggest that news events, seasonal topics, pop culture, etc account for 50% of all search queries. This paper shows that the signals a search engine receives can be used to both determine that a shift in intent has happened, as well as find a result that is now more relevant. We present a meta-algorithm that marries a classifier with a bandit algorithm to achieve regret that depends logarithmically on the number of query impressions, under certain assumptions. We provide strong evidence that this regret is close to the best achievable. Finally, via a series of experiments, we demonstrate that our algorithm outperforms prior approaches, particularly as the amount of intent-shifting traffic increases.


CHR(PRISM)-based Probabilistic Logic Learning

PRISM is an extension of Prolog with probabilistic predicates and built-in support for expectation-maximization learning. Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules. In this paper, we introduce a new probabilistic logic formalism, called CHRiSM, based on a combination of CHR and PRISM. It can be used for high-level rapid prototyping of complex statistical models by means of "chance rules". The underlying PRISM system can then be used for several probabilistic inference tasks, including probability computation and parameter learning. We define the CHRiSM language in terms of syntax and operational semantics, and illustrate it with examples. We define the notion of ambiguous programs and define a distribution semantics for unambiguous programs. Next, we describe an implementation of CHRiSM, based on CHR(PRISM). We discuss the relation between CHRiSM and other probabilistic logic programming languages, in particular PCHR. Finally we identify potential application domains.


Comparison of Support Vector Machine and Back Propagation Neural Network in Evaluating the Enterprise Financial Distress

Recently, applying the novel data mining techniques for evaluating enterprise financial distress has received much research alternation. Support Vector Machine (SVM) and back propagation neural (BPN) network has been applied successfully in many areas with excellent generalization results, such as rule extraction, classification and evaluation. In this paper, a model based on SVM with Gaussian RBF kernel is proposed here for enterprise financial distress evaluation. BPN network is considered one of the simplest and are most general methods used for supervised training of multilayered neural network. The comparative results show that through the difference between the performance measures is marginal; SVM gives higher precision and lower error rates.


Close Clustering Based Automated Color Image Annotation

Most image-search approaches today are based on the text based tags associated with the images which are mostly human generated and are subject to various kinds of errors. The results of a query to the image database thus can often be misleading and may not satisfy the requirements of the user. In this work we propose our approach to automate this tagging process of images, where image results generated can be fine filtered based on a probabilistic tagging mechanism. We implement a tool which helps to automate the tagging process by maintaining a training database, wherein the system is trained to identify certain set of input images, the results generated from which are used to create a probabilistic tagging mechanism. Given a certain set of segments in an image it calculates the probability of presence of particular keywords. This probability table is further used to generate the candidate tags for input images.


Bounded Coordinate-Descent for Biological Sequence Classification in High Dimensional Predictor Space

We present a framework for discriminative sequence classification where the learner works directly in the high dimensional predictor space of all subsequences in the training set. This is possible by employing a new coordinate-descent algorithm coupled with bounding the magnitude of the gradient for selecting discriminative subsequences fast. We characterize the loss functions for which our generic learning algorithm can be applied and present concrete implementations for logistic regression (binomial log-likelihood loss) and support vector machines (squared hinge loss). Application of our algorithm to protein remote homology detection and remote fold recognition results in performance comparable to that of state-of-the-art methods (e.g., kernel support vector machines). Unlike state-of-the-art classifiers, the resulting classification models are simply lists of weighted discriminative subsequences and can thus be interpreted and related to the biological problem.


Semi-Supervised Kernel PCA

We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher discriminant analysis. The second, LSKPCA is a hybrid of least squares regression and kernel PCA. The final LR-KPCA is an iteratively reweighted version of the previous which achieves a sigmoid loss function on the labeled points. We provide a theoretical risk bound as well as illustrative experiments on real and toy data sets.


Separate Training for Conditional Random Fields Using Co-occurrence Rate Factorization

The standard training method of Conditional Random Fields (CRFs) is very slow for large-scale applications. As an alternative, piecewise training divides the full graph into pieces, trains them independently, and combines the learned weights at test time. In this paper, we present \emph{separate} training for undirected models based on the novel Co-occurrence Rate Factorization (CR-F). Separate training is a local training method. In contrast to MEMMs, separate training is unaffected by the label bias problem. Experiments show that separate training (i) is unaffected by the label bias problem; (ii) reduces the training time from weeks to seconds; and (iii) obtains competitive results to the standard and piecewise training on linear-chain CRFs.


A Learning Algorithm based on High School Teaching Wisdom

A learning algorithm based on primary school teaching and learning is presented. The methodology is to continuously evaluate a student and to give them training on the examples for which they repeatedly fail, until, they can correctly answer all types of questions. This incremental learning procedure produces better learning curves by demanding the student to optimally dedicate their learning time on the failed examples. When used in machine learning, the algorithm is found to train a machine on a data with maximum variance in the feature space so that the generalization ability of the network improves. The algorithm has interesting applications in data mining, model evaluations and rare objects discovery.


Submodular Functions: Learnability, Structure, and Optimization

Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In this work we study submodular functions from a learning theoretic angle. We provide algorithms for learning submodular functions, as well as lower bounds on their learnability. In doing so, we uncover several novel structural results revealing ways in which submodular functions can be both surprisingly structured and surprisingly unstructured. We provide several concrete implications of our work in other domains including algorithmic game theory and combinatorial optimization. At a technical level, this research combines ideas from many areas, including learning theory (distributional learning and PAC-style analyses), combinatorics and optimization (matroids and submodular functions), and pseudorandomness (lossless expander graphs).


Learning Functions of Few Arbitrary Linear Parameters in High Dimensions

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in \mathbb N$ of possible point evaluations $f(x_i)$, $i=1,...,m$, of $f$, which we are allowed to query in order to construct a uniform approximating function. Under certain smoothness and variation assumptions on the function $g$, and an {\it arbitrary} choice of the matrix $A$, we present in this paper 1. a sampling choice of the points $\{x_i\}$ drawn at random for each function approximation; 2. algorithms (Algorithm 1 and Algorithm 2) for computing the approximating function, whose complexity is at most polynomial in the dimension $d$ and in the number $m$ of points. Due to the arbitrariness of $A$, the choice of the sampling points will be according to suitable random distributions and our results hold with overwhelming probability. Our approach uses tools taken from the {\it compressed sensing} framework, recent Chernoff bounds for sums of positive-semidefinite matrices, and classical stability bounds for invariant subspaces of singular value decompositions.


Polynomial-Time Approximation Schemes for Knapsack and Related Counting Problems using Branching Programs

We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm produces a (1 + eps)-multiplicative approximation in time poly(n,log W,1/eps). We also give algorithms with identical guarantees for general integer knapsack, the multidimensional knapsack problem (with a constant number of constraints) and for contingency tables (with a constant number of rows). Previously, only randomized approximation schemes were known for these problems due to work by Morris and Sinclair and work by Dyer. Our algorithms work by constructing small-width, read-once branching programs for approximating the underlying solution space under a carefully chosen distribution. As a byproduct of this approach, we obtain new query algorithms for learning functions of k halfspaces with respect to the uniform distribution on {0,1}^n. The running time of our algorithm is polynomial in the accuracy parameter eps. Previously even for the case of k=2, only algorithms with an exponential dependence on eps were known.


Ultrametric and Generalized Ultrametric in Computational Logic and in Data Analysis

Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes are then developed based on the use of metric, ultrametric and generalized ultrametric in logic. In particular we study approximation chains in an ultrametric or generalized ultrametric context. Our aim in this work is to extend the scope of data analysis by facilitating reasoning based on the data analysis; and to show how quantitative and qualitative data analysis can be incorporated into logic programming.


Belief Propagation Algorithm for Portfolio Optimization Problems

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. M\'ezard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.


Approximate Judgement Aggregation

In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them(e.g., transitivity when describing preferences). We consider the issue of judgement aggregation from the perspective of approximation. That is, we generalize the previous results by studying approximate judgement aggregation. We relax the main two constraints assumed in the current literature, Consistency and Independence and consider mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small portion of the inputs. The main question we raise is whether the relaxation of these notions significantly alters the class of satisfying aggregation mechanisms. The recent works for preference aggregation of Kalai, Mossel, and Keller fit into this framework. The main result of this paper is that, as in the case of preference aggregation, in the case of a subclass of a natural class of aggregation problems termed `truth-functional agendas', the set of satisfying aggregation mechanisms does not extend non-trivially when relaxing the constraints. Our proof techniques involve Boolean Fourier transform and analysis of voter influences for voting protocols. The question we raise for Approximate Aggregation can be stated in terms of Property Testing. For instance, as a corollary from our result we get a generalization of the classic result for property testing of linearity of Boolean functions. An updated version (RePEc:huj:dispap:dp574R) is available at http://www.ratio.huji.ac.il/dp_files/dp574R.pdf


NESVM: a Fast Gradient Method for Support Vector Machines

Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a great deal of samples as well as a large number of features. In this paper, thus, we present NESVM, a fast gradient SVM solver that can optimize various SVM models, e.g., classical SVM, linear programming SVM and least square SVM. Compared against SVM-Perf \cite{SVM_Perf}\cite{PerfML} (its convergence rate in solving the dual SVM is upper bounded by $\mathcal O(1/\sqrt{k})$, wherein $k$ is the number of iterations.) and Pegasos \cite{Pegasos} (online SVM that converges at rate $\mathcal O(1/k)$ for the primal SVM), NESVM achieves the optimal convergence rate at $\mathcal O(1/k^{2})$ and a linear time complexity. In particular, NESVM smoothes the non-differentiable hinge loss and $\ell_1$-norm in the primal SVM. Then the optimal gradient method without any line search is adopted to solve the optimization. In each iteration round, the current gradient and historical gradients are combined to determine the descent direction, while the Lipschitz constant determines the step size. Only two matrix-vector multiplications are required in each iteration round. Therefore, NESVM is more efficient than existing SVM solvers. In addition, NESVM is available for both linear and nonlinear kernels. We also propose "homotopy NESVM" to accelerate NESVM by dynamically decreasing the smooth parameter and using the continuation method. Our experiments on census income categorization, indoor/outdoor scene classification, event recognition and scene recognition suggest the efficiency and the effectiveness of NESVM. The MATLAB code of NESVM will be available on our website for further assessment.


Structured sparsity-inducing norms through submodular functions

Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by replacing the cardinality function by its convex envelope (tightest convex lower bound), in this case the L1-norm. In this paper, we investigate more general set-functions than the cardinality, that may incorporate prior knowledge or structural constraints which are common in many applications: namely, we show that for nondecreasing submodular set-functions, the corresponding convex envelope can be obtained from its \lova extension, a common tool in submodular analysis. This defines a family of polyhedral norms, for which we provide generic algorithmic tools (subgradients and proximal operators) and theoretical results (conditions for support recovery or high-dimensional inference). By selecting specific submodular functions, we can give a new interpretation to known norms, such as those based on rank-statistics or grouped norms with potentially overlapping groups; we also define new norms, in particular ones that can be used as non-factorial priors for supervised learning.


Online Learning in Case of Unbounded Losses Using the Follow Perturbed Leader Algorithm

In this paper the sequential prediction problem with expert advice is considered for the case where losses of experts suffered at each step cannot be bounded in advance. We present some modification of Kalai and Vempala algorithm of following the perturbed leader where weights depend on past losses of the experts. New notions of a volume and a scaled fluctuation of a game are introduced. We present a probabilistic algorithm protected from unrestrictedly large one-step losses. This algorithm has the optimal performance in the case when the scaled fluctuations of one-step losses of experts of the pool tend to zero.


Structural Solutions to Dynamic Scheduling for Multimedia Transmission in Unknown Wireless Environments

In this paper, we propose a systematic solution to the problem of scheduling delay-sensitive media data for transmission over time-varying wireless channels. We first formulate the dynamic scheduling problem as a Markov decision process (MDP) that explicitly considers the users' heterogeneous multimedia data characteristics (e.g. delay deadlines, distortion impacts and dependencies etc.) and time-varying channel conditions, which are not simultaneously considered in state-of-the-art packet scheduling algorithms. This formulation allows us to perform foresighted decisions to schedule multiple data units for transmission at each time in order to optimize the long-term utilities of the multimedia applications. The heterogeneity of the media data enables us to express the transmission priorities between the different data units as a priority graph, which is a directed acyclic graph (DAG). This priority graph provides us with an elegant structure to decompose the multi-data unit foresighted decision at each time into multiple single-data unit foresighted decisions which can be performed sequentially, from the high priority data units to the low priority data units, thereby significantly reducing the computation complexity. When the statistical knowledge of the multimedia data characteristics and channel conditions is unknown a priori, we develop a low-complexity online learning algorithm to update the value functions which capture the impact of the current decision on the future utility. The simulation results show that the proposed solution significantly outperforms existing state-of-the-art scheduling solutions.


Switching between Hidden Markov Models using Fixed Share

In prediction with expert advice the goal is to design online prediction algorithms that achieve small regret (additional loss on the whole data) compared to a reference scheme. In the simplest such scheme one compares to the loss of the best expert in hindsight. A more ambitious goal is to split the data into segments and compare to the best expert on each segment. This is appropriate if the nature of the data changes between segments. The standard fixed-share algorithm is fast and achieves small regret compared to this scheme. Fixed share treats the experts as black boxes: there are no assumptions about how they generate their predictions. But if the experts are learning, the following question arises: should the experts learn from all data or only from data in their own segment? The original algorithm naturally addresses the first case. Here we consider the second option, which is more appropriate exactly when the nature of the data changes between segments. In general extending fixed share to this second case will slow it down by a factor of T on T outcomes. We show, however, that no such slowdown is necessary if the experts are hidden Markov models.


Freezing and Sleeping: Tracking Experts that Learn by Evolving Past Posteriors

A problem posed by Freund is how to efficiently track a small pool of experts out of a much larger set. This problem was solved when Bousquet and Warmuth introduced their mixing past posteriors (MPP) algorithm in 2001. In Freund's problem the experts would normally be considered black boxes. However, in this paper we re-examine Freund's problem in case the experts have internal structure that enables them to learn. In this case the problem has two possible interpretations: should the experts learn from all data or only from the subsequence on which they are being tracked? The MPP algorithm solves the first case. Our contribution is to generalise MPP to address the second option. The results we obtain apply to any expert structure that can be formalised using (expert) hidden Markov models. Curiously enough, for our interpretation there are \emph{two} natural reference schemes: freezing and sleeping. For each scheme, we provide an efficient prediction strategy and prove the relevant loss bound.


An Architecture of Active Learning SVMs with Relevance Feedback for Classifying E-mail

In this paper, we have proposed an architecture of active learning SVMs with relevance feedback (RF)for classifying e-mail. This architecture combines both active learning strategies where instead of using a randomly selected training set, the learner has access to a pool of unlabeled instances and can request the labels of some number of them and relevance feedback where if any mail misclassified then the next set of support vectors will be different from the present set otherwise the next set will not change. Our proposed architecture will ensure that a legitimate e-mail will not be dropped in the event of overflowing mailbox. The proposed architecture also exhibits dynamic updating characteristics making life as difficult for the spammer as possible.


Entropy-Based Search Algorithm for Experimental Design

The scientific method relies on the iterated processes of inference and inquiry. The inference phase consists of selecting the most probable models based on the available data; whereas the inquiry phase consists of using what is known about the models to select the most relevant experiment. Optimizing inquiry involves searching the parameterized space of experiments to select the experiment that promises, on average, to be maximally informative. In the case where it is important to learn about each of the model parameters, the relevance of an experiment is quantified by Shannon entropy of the distribution of experimental outcomes predicted by a probable set of models. If the set of potential experiments is described by many parameters, we must search this high-dimensional entropy space. Brute force search methods will be slow and computationally expensive. We present an entropy-based search algorithm, called nested entropy sampling, to select the most informative experiment for efficient experimental design. This algorithm is inspired by Skilling's nested sampling algorithm used in inference and borrows the concept of a rising threshold while a set of experiment samples are maintained. We demonstrate that this algorithm not only selects highly relevant experiments, but also is more efficient than brute force search. Such entropic search techniques promise to greatly benefit autonomous experimental design.


Prediction by Compression

It is well known that text compression can be achieved by predicting the next symbol in the stream of text data based on the history seen up to the current symbol. The better the prediction the more skewed the conditional probability distribution of the next symbol and the shorter the codeword that needs to be assigned to represent this next symbol. What about the opposite direction ? suppose we have a black box that can compress text stream. Can it be used to predict the next symbol in the stream ? We introduce a criterion based on the length of the compressed data and use it to predict the next symbol. We examine empirically the prediction error rate and its dependency on some compression parameters.


Fixed-point and coordinate descent algorithms for regularized kernel methods

In this paper, we study two general classes of optimization algorithms for kernel methods with convex loss function and quadratic norm regularization, and analyze their convergence. The first approach, based on fixed-point iterations, is simple to implement and analyze, and can be easily parallelized. The second, based on coordinate descent, exploits the structure of additively separable loss functions to compute solutions of line searches in closed form. Instances of these general classes of algorithms are already incorporated into state of the art machine learning software for large scale problems. We start from a solution characterization of the regularized problem, obtained using sub-differential calculus and resolvents of monotone operators, that holds for general convex loss functions regardless of differentiability. The two methodologies described in the paper can be regarded as instances of non-linear Jacobi and Gauss-Seidel algorithms, and are both well-suited to solve large scale problems.


Indexability, concentration, and VC theory

Degrading performance of indexing schemes for exact similarity search in high dimensions has long since been linked to histograms of distributions of distances and other 1-Lipschitz functions getting concentrated. We discuss this observation in the framework of the phenomenon of concentration of measure on the structures of high dimension and the Vapnik-Chervonenkis theory of statistical learning.


Memristor Crossbar-based Hardware Implementation of IDS Method

Ink Drop Spread (IDS) is the engine of Active Learning Method (ALM), which is the methodology of soft computing. IDS, as a pattern-based processing unit, extracts useful information from a system subjected to modeling. In spite of its excellent potential in solving problems such as classification and modeling compared to other soft computing tools, finding its simple and fast hardware implementation is still a challenge. This paper describes a new hardware implementation of IDS method based on the memristor crossbar structure. In addition of simplicity, being completely real-time, having low latency and the ability to continue working after the occurrence of power breakdown are some of the advantages of our proposed circuit.


A Smoothing Stochastic Gradient Method for Composite Optimization

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting applications in machine learning. We propose a stochastic gradient descent algorithm for this class of optimization problem. When the non-smooth component has a particular structure, we propose another stochastic gradient descent algorithm by incorporating a smoothing method into our first algorithm. The proofs of the convergence rates of these two algorithms are given and we show the numerical performance of our algorithm by applying them to regularized linear regression problems with different sets of synthetic data.


Network Flow Algorithms for Structured Sparsity

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when the groups are disjoint or embedded in a specific hierarchical structure, we address here the case of general overlapping groups. To this end, we show that the corresponding optimization problem is related to network flow optimization. More precisely, the proximal problem associated with the norm we consider is dual to a quadratic min-cost flow problem. We propose an efficient procedure which computes its solution exactly in polynomial time. Our algorithm scales up to millions of variables, and opens up a whole new range of applications for structured sparse models. We present several experiments on image and video data, demonstrating the applicability and scalability of our approach for various problems.


The adaptive projected subgradient method constrained by families of quasi-nonexpansive mappings and its application to online learning

Many online, i.e., time-adaptive, inverse problems in signal processing and machine learning fall under the wide umbrella of the asymptotic minimization of a sequence of non-negative, convex, and continuous functions. To incorporate a-priori knowledge into the design, the asymptotic minimization task is usually constrained on a fixed closed convex set, which is dictated by the available a-priori information. To increase versatility towards the usage of the available information, the present manuscript extends the Adaptive Projected Subgradient Method (APSM) by introducing an algorithmic scheme which incorporates a-priori knowledge in the design via a sequence of strongly attracting quasi-nonexpansive mappings in a real Hilbert space. In such a way, the benefits offered to online learning tasks by the proposed method unfold in two ways: 1) the rich class of quasi-nonexpansive mappings provides a plethora of ways to cast a-priori knowledge, and 2) by introducing a sequence of such mappings, the proposed scheme is able to capture the time-varying nature of a-priori information. The convergence properties of the algorithm are studied, several special cases of the method with wide applicability are shown, and the potential of the proposed scheme is demonstrated by considering an increasingly important, nowadays, online sparse system/signal recovery task.


Inference with Multivariate Heavy-Tails in Linear Models

Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we propose a novel simple linear graphical model for independent latent random variables, called linear characteristic model (LCM), defined in the characteristic function domain. Using stable distributions, a heavy-tailed family of distributions which is a generalization of Cauchy, L\'evy and Gaussian distributions, we show for the first time, how to compute both exact and approximate inference in such a linear multivariate graphical model. LCMs are not limited to stable distributions, in fact LCMs are always defined for any random variables (discrete, continuous or a mixture of both). We provide a realistic problem from the field of computer networks to demonstrate the applicability of our construction. Other potential application is iterative decoding of linear channels with non-Gaussian noise.


Penalty Decomposition Methods for $L0$-Norm Minimization

In this paper we consider general l0-norm minimization problems, that is, the problems with l0-norm appearing in either objective function or constraint. In particular, we first reformulate the l0-norm constrained problem as an equivalent rank minimization problem and then apply the penalty decomposition (PD) method proposed in [33] to solve the latter problem. By utilizing the special structures, we then transform all matrix operations of this method to vector operations and obtain a PD method that only involves vector operations. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the PD method satisfies a first-order optimality condition that is generally stronger than one natural optimality condition. We further extend the PD method to solve the problem with the l0-norm appearing in objective function. Finally, we test the performance of our PD methods by applying them to compressed sensing, sparse logistic regression and sparse inverse covariance selection. The computational results demonstrate that our methods generally outperform the existing methods in terms of solution quality and/or speed.


Penalty Decomposition Methods for Rank Minimization

In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result, we then propose penalty decomposition methods for general rank minimization problems in which each subproblem is solved by a block coordinate descend method. Under some suitable assumptions, we show that any accumulation point of the sequence generated by the penalty decomposition methods satisfies the first-order optimality conditions of a nonlinear reformulation of the problems. Finally, we test the performance of our methods by applying them to the matrix completion and nearest low-rank correlation matrix problems. The computational results demonstrate that our methods are generally comparable or superior to the existing methods in terms of solution quality.


Mixed Cumulative Distribution Networks

Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional independencies, and are especially useful in modeling the effects of latent variables implicitly. Unfortunately there are currently no good parameterizations of general ADMGs. In this paper, we apply recent work on cumulative distribution networks and copulas to propose one one general construction for ADMG models. We consider a simple parameter estimation approach, and report some encouraging experimental results.


Applications of Machine Learning Methods to Quantifying Phenotypic Traits that Distinguish the Wild Type from the Mutant Arabidopsis Thaliana Seedlings during Root Gravitropism

Post-genomic research deals with challenging problems in screening genomes of organisms for particular functions or potential for being the targets of genetic engineering for desirable biological features. 'Phenotyping' of wild type and mutants is a time-consuming and costly effort by many individuals. This article is a preliminary progress report in research on large-scale automation of phenotyping steps (imaging, informatics and data analysis) needed to study plant gene-proteins networks that influence growth and development of plants. Our results undermine the significance of phenotypic traits that are implicit in patterns of dynamics in plant root response to sudden changes of its environmental conditions, such as sudden re-orientation of the root tip against the gravity vector. Including dynamic features besides the common morphological ones has paid off in design of robust and accurate machine learning methods to automate a typical phenotyping scenario, i.e. to distinguish the wild type from the mutants.


Exploring Language-Independent Emotional Acoustic Features via Feature Selection

We propose a novel feature selection strategy to discover language-independent acoustic features that tend to be responsible for emotions regardless of languages, linguistics and other factors. Experimental results suggest that the language-independent feature subset discovered yields the performance comparable to the full feature set on various emotional speech corpora.


Fast Overlapping Group Lasso

The group Lasso is an extension of the Lasso for feature selection on (predefined) non-overlapping groups of features. The non-overlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation, where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. We have performed empirical evaluations using the breast cancer gene expression data set, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results demonstrate the efficiency and effectiveness of the proposed algorithm.


A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering

We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph clustering with other possible ways to model the graph. We adapt the PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009) to derive a PAC-Bayesian generalization bound for graph clustering. The bound shows that graph clustering should optimize a trade-off between empirical data fit and the mutual information that clusters preserve on the graph nodes. A similar trade-off derived from information-theoretic considerations was already shown to produce state-of-the-art results in practice (Slonim et al., 2005; Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by providing a better theoretical foundation, suggesting formal generalization guarantees, and offering a more accurate way to deal with finite sample issues. We derive a bound minimization algorithm and show that it provides good results in real-life problems and that the derived PAC-Bayesian bound is reasonably tight.


Gaussian Process Bandits for Tree Search: Theory and Application to Planning in Discounted MDPs

We motivate and analyse a new Tree Search algorithm, GPTS, based on recent theoretical advances in the use of Gaussian Processes for Bandit problems. We consider tree paths as arms and we assume the target/reward function is drawn from a GP distribution. The posterior mean and variance, after observing data, are used to define confidence intervals for the function values, and we sequentially play arms with highest upper confidence bounds. We give an efficient implementation of GPTS and we adapt previous regret bounds by determining the decay rate of the eigenvalues of the kernel matrix on the whole set of tree paths. We consider two kernels in the feature space of binary vectors indexed by the nodes of the tree: linear and Gaussian. The regret grows in square root of the number of iterations T, up to a logarithmic factor, with a constant that improves with bigger Gaussian kernel widths. We focus on practical values of T, smaller than the number of arms. Finally, we apply GPTS to Open Loop Planning in discounted Markov Decision Processes by modelling the reward as a discounted sum of independent Gaussian Processes. We report similar regret bounds to those of the OLOP algorithm.


On the Estimation of Coherence

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of matrix entries in the context of these low-rank approximations and other sampling-based algorithms, e.g., matrix com- pletion, robust PCA. Since coherence is defined in terms of the singular vectors of a matrix and is expensive to compute, the practical significance of these results largely hinges on the following question: Can we efficiently and accurately estimate the coherence of a matrix? In this paper we address this question. We propose a novel algorithm for estimating coherence from a small number of columns, formally analyze its behavior, and derive a new coherence-based matrix approximation bound based on this analysis. We then present extensive experimental results on synthetic and real datasets that corroborate our worst-case theoretical analysis, yet provide strong support for the use of our proposed algorithm whenever low-rank approximation is being considered. Our algorithm efficiently and accurately estimates matrix coherence across a wide range of datasets, and these coherence estimates are excellent predictors of the effectiveness of sampling-based matrix approximation on a case-by-case basis.


PhishDef: URL Names Say It All

Phishing is an increasingly sophisticated method to steal personal user information using sites that pretend to be legitimate. In this paper, we take the following steps to identify phishing URLs. First, we carefully select lexical features of the URLs that are resistant to obfuscation techniques used by attackers. Second, we evaluate the classification accuracy when using only lexical features, both automatically and hand-selected, vs. when using additional features. We show that lexical features are sufficient for all practical purposes. Third, we thoroughly compare several classification algorithms, and we propose to use an online method (AROW) that is able to overcome noisy training data. Based on the insights gained from our analysis, we propose PhishDef, a phishing detection system that uses only URL names and combines the above three elements. PhishDef is a highly accurate method (when compared to state-of-the-art approaches over real datasets), lightweight (thus appropriate for online and client-side deployment), proactive (based on online classification rather than blacklists), and resilient to training data inaccuracies (thus enabling the use of large noisy training data).


Reinforcement Learning by Comparing Immediate Reward

This paper introduces an approach to Reinforcement Learning Algorithm by comparing their immediate rewards using a variation of Q-Learning algorithm. Unlike the conventional Q-Learning, the proposed algorithm compares current reward with immediate reward of past move and work accordingly. Relative reward based Q-learning is an approach towards interactive learning. Q-Learning is a model free reinforcement learning method that used to learn the agents. It is observed that under normal circumstances algorithm take more episodes to reach optimal Q-value due to its normal reward or sometime negative reward. In this new form of algorithm agents select only those actions which have a higher immediate reward signal in comparison to previous one. The contribution of this article is the presentation of new Q-Learning Algorithm in order to maximize the performance of algorithm and reduce the number of episode required to reach optimal Q-value. Effectiveness of proposed algorithm is simulated in a 20 x20 Grid world deterministic environment and the result for the two forms of Q-Learning Algorithms is given.


A Unified View of Regularized Dual Averaging and Mirror Descent with Implicit Updates

We study three families of online convex optimization algorithms: follow-the-proximally-regularized-leader (FTRL-Proximal), regularized dual averaging (RDA), and composite-objective mirror descent. We first prove equivalence theorems that show all of these algorithms are instantiations of a general FTRL update. This provides theoretical insight on previous experimental observations. In particular, even though the FOBOS composite mirror descent algorithm handles L1 regularization explicitly, it has been observed that RDA is even more effective at producing sparsity. Our results demonstrate that FOBOS uses subgradient approximations to the L1 penalty from previous rounds, leading to less sparsity than RDA, which handles the cumulative penalty in closed form. The FTRL-Proximal algorithm can be seen as a hybrid of these two, and outperforms both on a large, real-world dataset. Our second contribution is a unified analysis which produces regret bounds that match (up to logarithmic terms) or improve the best previously known bounds. This analysis also extends these algorithms in two important ways: we support a more general type of composite objective and we analyze implicit updates, which replace the subgradient approximation of the current loss function with an exact optimization.


Conditional Random Fields and Support Vector Machines: A Hybrid Approach

We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a sufficient condition for when the hybrid loss is Fisher consistent for classification. This condition depends on a measure of dominance between labels - specifically, the gap in per observation probabilities between the most likely labels. We also prove Fisher consistency is necessary for parametric consistency when learning models such as CRFs. We demonstrate empirically that the hybrid loss typically performs as least as well as - and often better than - both of its constituent losses on variety of tasks. In doing so we also provide an empirical comparison of the efficacy of probabilistic and margin based approaches to multiclass and structured prediction and the effects of label dominance on these results.


Safe Feature Elimination in Sparse Supervised Learning

We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of variables prior to running the supervised learning algorithm. The methods are not heuristic: they only eliminate features that are {\em guaranteed} to be absent after solving the learning problem. Our framework applies to a large class of problems, including support vector machine classification, logistic regression and least-squares. The complexity of the feature elimination step is negligible compared to the typical computational effort involved in the sparse supervised learning problem: it grows linearly with the number of features times the number of examples, with much better count if data is sparse. We apply our method to data sets arising in text classification and observe a dramatic reduction of the dimensionality, hence in computational effort required to solve the learning problem, especially when very sparse classifiers are sought. Our method allows to immediately extend the scope of existing algorithms, allowing us to run them on data sets of sizes that were out of their reach before.


Deep Self-Taught Learning for Handwritten Character Recognition

Recent theoretical and empirical work in statistical machine learning has demonstrated the importance of learning algorithms for deep architectures, i.e., function classes obtained by composing multiple non-linear transformations. Self-taught learning (exploiting unlabeled examples or examples from other distributions) has already been applied to deep learners, but mostly to show the advantage of unlabeled examples. Here we explore the advantage brought by {\em out-of-distribution examples}. For this purpose we developed a powerful generator of stochastic variations and noise processes for character images, including not only affine transformations but also slant, local elastic deformations, changes in thickness, background images, grey level changes, contrast, occlusion, and various types of noise. The out-of-distribution examples are obtained from these highly distorted images or by including examples of object classes different from those in the target test set. We show that {\em deep learners benefit more from out-of-distribution examples than a corresponding shallow learner}, at least in the area of handwritten character recognition. In fact, we show that they beat previously published results and reach human-level performance on both handwritten digit classification and 62-class handwritten character recognition.


Geometric Decision Tree

In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy to assess the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node, are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree.


On the Doubt about Margin Explanation of Boosting

Margin theory provides one of the most popular explanations to the success of \texttt{AdaBoost}, where the central point lies in the recognition that \textit{margin} is the key for characterizing the performance of \texttt{AdaBoost}. This theory has been very influential, e.g., it has been used to argue that \texttt{AdaBoost} usually does not overfit since it tends to enlarge the margin even after the training error reaches zero. Previously the \textit{minimum margin bound} was established for \texttt{AdaBoost}, however, \cite{Breiman1999} pointed out that maximizing the minimum margin does not necessarily lead to a better generalization. Later, \cite{Reyzin:Schapire2006} emphasized that the margin distribution rather than minimum margin is crucial to the performance of \texttt{AdaBoost}. In this paper, we first present the \textit{$k$th margin bound} and further study on its relationship to previous work such as the minimum margin bound and Emargin bound. Then, we improve the previous empirical Bernstein bounds \citep{Maurer:Pontil2009,Audibert:Munos:Szepesvari2009}, and based on such findings, we defend the margin-based explanation against Breiman's doubts by proving a new generalization error bound that considers exactly the same factors as \cite{Schapire:Freund:Bartlett:Lee1998} but is sharper than \cite{Breiman1999}'s minimum margin bound. By incorporating factors such as average margin and variance, we present a generalization error bound that is heavily related to the whole margin distribution. We also provide margin distribution bounds for generalization error of voting classifiers in finite VC-dimension space.


Totally Corrective Multiclass Boosting with Binary Weak Learners

In this work, we propose a new optimization framework for multiclass boosting learning. In the literature, AdaBoost.MO and AdaBoost.ECC are the two successful multiclass boosting algorithms, which can use binary weak learners. We explicitly derive these two algorithms' Lagrange dual problems based on their regularized loss functions. We show that the Lagrange dual formulations enable us to design totally-corrective multiclass algorithms by using the primal-dual optimization technique. Experiments on benchmark data sets suggest that our multiclass boosting can achieve a comparable generalization capability with state-of-the-art, but the convergence speed is much faster than stage-wise gradient descent boosting. In other words, the new totally corrective algorithms can maximize the margin more aggressively.