No Internal Regret via Neighborhood Watch

We present an algorithm which attains O(\sqrt{T}) internal (and thus external) regret for finite games with partial monitoring under the local observability condition. Recently, this condition has been shown by (Bartok, Pal, and Szepesvari, 2011) to imply the O(\sqrt{T}) rate for partial monitoring games against an i.i.d. opponent, and the authors conjectured that the same holds for non-stochastic adversaries. Our result is in the affirmative, and it completes the characterization of possible rates for finite partial-monitoring games, an open question stated by (Cesa-Bianchi, Lugosi, and Stoltz, 2006). Our regret guarantees also hold for the more general model of partial monitoring with random signals.


Transfer from Multiple MDPs

Transfer reinforcement learning (RL) methods leverage on the experience collected on a set of source tasks to speed-up RL algorithms. A simple and effective approach is to transfer samples from source tasks and include them into the training set used to solve a given target task. In this paper, we investigate the theoretical properties of this transfer method and we introduce novel algorithms adapting the transfer process on the basis of the similarity between source and target tasks. Finally, we report illustrative experimental results in a continuous chain problem.


Infinite Tucker Decomposition: Nonparametric Bayesian Models for Multiway Data Analysis

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g. missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models, coupled with efficient inference methods, for multiway data analysis. We name these models InfTucker. Using these InfTucker, we conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or $t$ processes with nonlinear covariance functions. To efficiently learn the InfTucker from data, we develop a variational inference technique on tensors. Compared with classical implementation, the new technique reduces both time and space complexities by several orders of magnitude. Our experimental results on chemometrics and social network datasets demonstrate that our new models achieved significantly higher prediction accuracy than the most state-of-art tensor decomposition


Local Component Analysis

Kernel density estimation, a.k.a. Parzen windows, is a popular density estimation method, which can be used for outlier detection or clustering. With multivariate data, its performance is heavily reliant on the metric used within the kernel. Most earlier work has focused on learning only the bandwidth of the kernel (i.e., a scalar multiplicative factor). In this paper, we propose to learn a full Euclidean metric through an expectation-minimization (EM) procedure, which can be seen as an unsupervised counterpart to neighbourhood component analysis (NCA). In order to avoid overfitting with a fully nonparametric density estimator in high dimensions, we also consider a semi-parametric Gaussian-Parzen density model, where some of the variables are modelled through a jointly Gaussian density, while others are modelled through Parzen windows. For these two models, EM leads to simple closed-form updates based on matrix inversions and eigenvalue decompositions. We show empirically that our method leads to density estimators with higher test-likelihoods than natural competing methods, and that the metrics may be used within most unsupervised learning techniques that rely on such metrics, such as spectral clustering or manifold learning methods. Finally, we present a stochastic approximation scheme which allows for the use of this method in a large-scale setting.


Differentially Private Online Learning

In this paper, we consider the problem of preserving privacy in the online learning setting. We study the problem in the online convex programming (OCP) framework---a popular online learning setting with several interesting theoretical and practical implications---while using differential privacy as the formal privacy measure. For this problem, we distill two critical attributes that a private OCP algorithm should have in order to provide reasonable privacy as well as utility guarantees: 1) linearly decreasing sensitivity, i.e., as new data points arrive their effect on the learning model decreases, 2) sub-linear regret bound---regret bound is a popular goodness/utility measure of an online learning algorithm. Given an OCP algorithm that satisfies these two conditions, we provide a general framework to convert the given algorithm into a privacy preserving OCP algorithm with good (sub-linear) regret. We then illustrate our approach by converting two popular online learning algorithms into their differentially private variants while guaranteeing sub-linear regret ($O(\sqrt{T})$). Next, we consider the special case of online linear regression problems, a practically important class of online learning problems, for which we generalize an approach by Dwork et al. to provide a differentially private algorithm with just $O(\log^{1.5} T)$ regret. Finally, we show that our online learning framework can be used to provide differentially private algorithms for offline learning as well. For the offline learning problem, our approach obtains better error bounds as well as can handle larger class of problems than the existing state-of-the-art methods Chaudhuri et al.


Quantum adiabatic machine learning

We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. We apply and illustrate this approach in detail to the problem of software verification and validation.


Gradient-based kernel dimension reduction for supervised learning

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The proposed method uses an estimator for the gradient of regression function, based on the covariance operators on reproducing kernel Hilbert spaces. In comparison with other existing methods, the proposed one has wide applicability without strong assumptions on the distributions or the type of variables, and uses computationally simple eigendecomposition. Experimental results show that the proposed method successfully finds the effective directions with efficient computation.


The Variational Garrote

In this paper, we present a new variational method for sparse regression using $L_0$ regularization. The variational parameters appear in the approximate model in a way that is similar to Breiman's Garrote model. We refer to this method as the variational Garrote (VG). We show that the combination of the variational approximation and $L_0$ regularization has the effect of making the problem effectively of maximal rank even when the number of samples is small compared to the number of variables. The VG is compared numerically with the Lasso method, ridge regression and the recently introduced paired mean field method (PMF) (M. Titsias & M. L\'azaro-Gredilla., NIPS 2012). Numerical results show that the VG and PMF yield more accurate predictions and more accurately reconstruct the true model than the other methods. It is shown that the VG finds correct solutions when the Lasso solution is inconsistent due to large input correlations. Globally, VG is significantly faster than PMF and tends to perform better as the problems become denser and in problems with strongly correlated inputs. The naive implementation of the VG scales cubic with the number of features. By introducing Lagrange multipliers we obtain a dual formulation of the problem that scales cubic in the number of samples, but close to linear in the number of features.


How Open Should Open Source Be?

Many open-source projects land security fixes in public repositories before shipping these patches to users. This paper presents attacks on such projects - taking Firefox as a case-study - that exploit patch metadata to efficiently search for security patches prior to shipping. Using access-restricted bug reports linked from patch descriptions, security patches can be immediately identified for 260 out of 300 days of Firefox 3 development. In response to Mozilla obfuscating descriptions, we show that machine learning can exploit metadata such as patch author to search for security patches, extending the total window of vulnerability by 5 months in an 8 month period when examining up to two patches daily. Finally we present strong evidence that further metadata obfuscation is unlikely to prevent information leaks, and we argue that open-source projects instead ought to keep security patches secret until they are ready to be released.


ShareBoost: Efficient Multiclass Learning with Feature Sharing

Multiclass prediction is the problem of classifying an object into a relevant target class. We consider the problem of learning a multiclass predictor that uses only few features, and in particular, the number of used features should increase sub-linearly with the number of possible classes. This implies that features should be shared by several classes. We describe and analyze the ShareBoost algorithm for learning a multiclass predictor that uses few shared features. We prove that ShareBoost efficiently finds a predictor that uses few shared features (if such a predictor exists) and that it has a small generalization error. We also describe how to use ShareBoost for learning a non-linear predictor that has a fast evaluation time. In a series of experiments with natural data sets we demonstrate the benefits of ShareBoost and evaluate its success relatively to other state-of-the-art approaches.


Nonlinear Channel Estimation for OFDM System by Complex LS-SVM under High Mobility Conditions

A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the highly selective multipath channel in the presence of non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm maps trained data into a high dimensional feature space and uses the structural risk minimization (SRM) principle to carry out the regression estimation for the frequency response function of the highly selective channel. The simulations show the effectiveness of the proposed method which has good performance and high precision to track the variations of the fading channels compared to the conventional LS method and it is robust at high speed mobility.


Review on Feature Selection Techniques and the Impact of SVM for Cancer Classification using Gene Expression Profile

The DNA microarray technology has modernized the approach of biology research in such a way that scientists can now measure the expression levels of thousands of genes simultaneously in a single experiment. Gene expression profiles, which represent the state of a cell at a molecular level, have great potential as a medical diagnosis tool. But compared to the number of genes involved, available training data sets generally have a fairly small sample size for classification. These training data limitations constitute a challenge to certain classification methodologies. Feature selection techniques can be used to extract the marker genes which influence the classification accuracy effectively by eliminating the un wanted noisy and redundant genes This paper presents a review of feature selection techniques that have been employed in micro array data based cancer classification and also the predominant role of SVM for cancer classification.


Localization on low-order eigenvectors of data matrices

Eigenvector localization refers to the situation when most of the components of an eigenvector are zero or near-zero. This phenomenon has been observed on eigenvectors associated with extremal eigenvalues, and in many of those cases it can be meaningfully interpreted in terms of "structural heterogeneities" in the data. For example, the largest eigenvectors of adjacency matrices of large complex networks often have most of their mass localized on high-degree nodes; and the smallest eigenvectors of the Laplacians of such networks are often localized on small but meaningful community-like sets of nodes. Here, we describe localization associated with low-order eigenvectors, i.e., eigenvectors corresponding to eigenvalues that are not extremal but that are "buried" further down in the spectrum. Although we have observed it in several unrelated applications, this phenomenon of low-order eigenvector localization defies common intuitions and simple explanations, and it creates serious difficulties for the applicability of popular eigenvector-based machine learning and data analysis tools. After describing two examples where low-order eigenvector localization arises, we present a very simple model that qualitatively reproduces several of the empirically-observed results. This model suggests certain coarse structural similarities among the seemingly-unrelated applications where we have observed low-order eigenvector localization, and it may be used as a diagnostic tool to help extract insight from data graphs when such low-order eigenvector localization is present.


Gossip Learning with Linear Models on Fully Distributed Data

Machine learning over fully distributed data poses an important problem in peer-to-peer (P2P) applications. In this model we have one data record at each network node, but without the possibility to move raw data due to privacy considerations. For example, user profiles, ratings, history, or sensor readings can represent this case. This problem is difficult, because there is no possibility to learn local models, the system model offers almost no guarantees for reliability, yet the communication cost needs to be kept low. Here we propose gossip learning, a generic approach that is based on multiple models taking random walks over the network in parallel, while applying an online learning algorithm to improve themselves, and getting combined via ensemble learning methods. We present an instantiation of this approach for the case of classification with linear models. Our main contribution is an ensemble learning method which---through the continuous combination of the models in the network---implements a virtual weighted voting mechanism over an exponential number of models at practically no extra cost as compared to independent random walks. We prove the convergence of the method theoretically, and perform extensive experiments on benchmark datasets. Our experimental analysis demonstrates the performance and robustness of the proposed approach.


Dynamics of Boltzmann Q-Learning in Two-Player Two-Action Games

We consider the dynamics of Q-learning in two-player two-action games with a Boltzmann exploration mechanism. For any non-zero exploration rate the dynamics is dissipative, which guarantees that agent strategies converge to rest points that are generally different from the game's Nash Equlibria (NE). We provide a comprehensive characterization of the rest point structure for different games, and examine the sensitivity of this structure with respect to the noise due to exploration. Our results indicate that for a class of games with multiple NE the asymptotic behavior of learning dynamics can undergo drastic changes at critical exploration rates. Furthermore, we demonstrate that for certain games with a single NE, it is possible to have additional rest points (not corresponding to any NE) that persist for a finite range of the exploration rates and disappear when the exploration rates of both players tend to zero.


The Non-Bayesian Restless Multi-Armed Bandit: A Case of Near-Logarithmic Strict Regret

In the classic Bayesian restless multi-armed bandit (RMAB) problem, there are $N$ arms, with rewards on all arms evolving at each time as Markov chains with known parameters. A player seeks to activate $K \geq 1$ arms at each time in order to maximize the expected total reward obtained over multiple plays. RMAB is a challenging problem that is known to be PSPACE-hard in general. We consider in this work the even harder non-Bayesian RMAB, in which the parameters of the Markov chain are assumed to be unknown \emph{a priori}. We develop an original approach to this problem that is applicable when the corresponding Bayesian problem has the structure that, depending on the known parameter values, the optimal solution is one of a prescribed finite set of policies. In such settings, we propose to learn the optimal policy for the non-Bayesian RMAB by employing a suitable meta-policy which treats each policy from this finite set as an arm in a different non-Bayesian multi-armed bandit problem for which a single-arm selection policy is optimal. We demonstrate this approach by developing a novel sensing policy for opportunistic spectrum access over unknown dynamic channels. We prove that our policy achieves near-logarithmic regret (the difference in expected reward compared to a model-aware genie), which leads to the same average reward that can be achieved by the optimal policy under a known model. This is the first such result in the literature for a non-Bayesian RMAB. For our proof, we also develop a novel generalization of the Chernoff-Hoeffding bound.


Efficient Online Learning for Opportunistic Spectrum Access

The problem of opportunistic spectrum access in cognitive radio networks has been recently formulated as a non-Bayesian restless multi-armed bandit problem. In this problem, there are N arms (corresponding to channels) and one player (corresponding to a secondary user). The state of each arm evolves as a finite-state Markov chain with unknown parameters. At each time slot, the player can select K < N arms to play and receives state-dependent rewards (corresponding to the throughput obtained given the activity of primary users). The objective is to maximize the expected total rewards (i.e., total throughput) obtained over multiple plays. The performance of an algorithm for such a multi-armed bandit problem is measured in terms of regret, defined as the difference in expected reward compared to a model-aware genie who always plays the best K arms. In this paper, we propose a new continuous exploration and exploitation (CEE) algorithm for this problem. When no information is available about the dynamics of the arms, CEE is the first algorithm to guarantee near-logarithmic regret uniformly over time. When some bounds corresponding to the stationary state distributions and the state-dependent rewards are known, we show that CEE can be easily modified to achieve logarithmic regret over time. In contrast, prior algorithms require additional information concerning bounds on the second eigenvalues of the transition matrices in order to guarantee logarithmic regret. Finally, we show through numerical simulations that CEE is more efficient than prior algorithms.


On Clustering on Graphs with Multiple Edge Types

We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where they are published, keyword similarity, citations, etc. As such, graphs with multiple edges is a more accurate model to describe similarities between objects. Each edge/metric provides only partial information about the data; recovering full information requires aggregation of all the similarity metrics. Clustering becomes much more challenging in this context, since in addition to the difficulties of the traditional clustering problem, we have to deal with a space of clusterings. We generalize the concept of clustering in single-edge graphs to multi-edged graphs and investigate problems such as: Can we find a clustering that remains good, even if we change the relative weights of metrics? How can we describe the space of clusterings efficiently? Can we find unexpected clusterings (a good clustering that is distant from all given clusterings)? If given the ground-truth clustering, can we recover how the weights for edge types were aggregated? %In this paper, we discuss these problems and the underlying algorithmic challenges and propose some solutions. We also present two case studies: one based on papers on Arxiv and one based on CIA World Factbook.


Online Learning for Combinatorial Network Optimization with Restless Markovian Rewards

Combinatorial network optimization algorithms that compute optimal structures taking into account edge weights form the foundation for many network protocols. Examples include shortest path routing, minimal spanning tree computation, maximum weighted matching on bipartite graphs, etc. We present CLRMR, the first online learning algorithm that efficiently solves the stochastic version of these problems where the underlying edge weights vary as independent Markov chains with unknown dynamics. The performance of an online learning algorithm is characterized in terms of regret, defined as the cumulative difference in rewards between a suitably-defined genie, and that obtained by the given algorithm. We prove that, compared to a genie that knows the Markov transition matrices and uses the single-best structure at all times, CLRMR yields regret that is polynomial in the number of edges and nearly-logarithmic in time.


Anomaly Sequences Detection from Logs Based on Compression

Mining information from logs is an old and still active research topic. In recent years, with the rapid emerging of cloud computing, log mining becomes increasingly important to industry. This paper focus on one major mission of log mining: anomaly detection, and proposes a novel method for mining abnormal sequences from large logs. Different from previous anomaly detection systems which based on statistics, probabilities and Markov assumption, our approach measures the strangeness of a sequence using compression. It first trains a grammar about normal behaviors using grammar-based compression, then measures the information quantities and densities of questionable sequences according to incrementation of grammar length. We have applied our approach on mining some real bugs from fine grained execution logs. We have also tested its ability on intrusion detection using some publicity available system call traces. The experiments show that our method successfully selects the strange sequences which related to bugs or attacking.


Weighted Clustering

One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the identification of succinct, user-friendly properties that formally capture when certain clustering methods are preferred over others. Until now these properties focused on advantages of classical Linkage-Based algorithms, failing to identify when other clustering paradigms, such as popular center-based methods, are preferable. We present surprisingly simple new properties that delineate the differences between common clustering paradigms, which clearly and formally demonstrates advantages of center-based approaches for some applications. These properties address how sensitive algorithms are to changes in element frequencies, which we capture in a generalized setting where every element is associated with a real-valued weight.


Trace Lasso: a trace norm regularization for correlated designs

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, called the trace Lasso, uses the trace norm, which is a convex surrogate of the rank, of the selected covariates as the criterion of model complexity. We analyze the properties of our norm, describe an optimization algorithm based on reweighted least-squares, and illustrate the behavior of this norm on synthetic data, showing that it is more adapted to strong correlations than competing methods such as the elastic net.


Learning Sequence Neighbourhood Metrics

Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector space of arbitrary dimensionality. Subsequently, the resulting features are meaningful and can be used for visualization or nearest neighbour classification in linear time. This kind of metric learning for sequential data enables the use of algorithms tailored towards fixed length vector spaces such as R^n.


Learning From Labeled And Unlabeled Data: An Empirical Study Across Techniques And Domains

There has been increased interest in devising learning techniques that combine unlabeled data with labeled data ? i.e. semi-supervised learning. However, to the best of our knowledge, no study has been performed across various techniques and different types and amounts of labeled and unlabeled data. Moreover, most of the published work on semi-supervised learning techniques assumes that the labeled and unlabeled data come from the same distribution. It is possible for the labeling process to be associated with a selection bias such that the distributions of data points in the labeled and unlabeled sets are different. Not correcting for such bias can result in biased function approximation with potentially poor performance. In this paper, we present an empirical study of various semi-supervised learning techniques on a variety of datasets. We attempt to answer various questions such as the effect of independence or relevance amongst features, the effect of the size of the labeled and unlabeled sets and the effect of noise. We also investigate the impact of sample-selection bias on the semi-supervised learning techniques under study and implement a bivariate probit technique particularly designed to correct for such bias.


Online Learning Algorithms for Stochastic Water-Filling

Water-filling is the term for the classic solution to the problem of allocating constrained power to a set of parallel channels to maximize the total data-rate. It is used widely in practice, for example, for power allocation to sub-carriers in multi-user OFDM systems such as WiMax. The classic water-filling algorithm is deterministic and requires perfect knowledge of the channel gain to noise ratios. In this paper we consider how to do power allocation over stochastically time-varying (i.i.d.) channels with unknown gain to noise ratio distributions. We adopt an online learning framework based on stochastic multi-armed bandits. We consider two variations of the problem, one in which the goal is to find a power allocation to maximize $\sum\limits_i \mathbb{E}[\log(1 + SNR_i)]$, and another in which the goal is to find a power allocation to maximize $\sum\limits_i \log(1 + \mathbb{E}[SNR_i])$. For the first problem, we propose a \emph{cognitive water-filling} algorithm that we call CWF1. We show that CWF1 obtains a regret (defined as the cumulative gap over time between the sum-rate obtained by a distribution-aware genie and this policy) that grows polynomially in the number of channels and logarithmically in time, implying that it asymptotically achieves the optimal time-averaged rate that can be obtained when the gain distributions are known. For the second problem, we present an algorithm called CWF2, which is, to our knowledge, the first algorithm in the literature on stochastic multi-armed bandits to exploit non-linear dependencies between the arms. We prove that the number of times CWF2 picks the incorrect power allocation is bounded by a function that is polynomial in the number of channels and logarithmic in time, implying that its frequency of incorrect allocation tends to zero.


Efficiency versus Convergence of Boolean Kernels for On-Line Learning Algorithms

The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses in this context is to expand the feature set to include conjunctions of basic features. This can be done explicitly or where possible by using a kernel function. Focusing on the well known Perceptron and Winnow algorithms, the paper demonstrates a tradeoff between the computational efficiency with which the algorithm can be run over the expanded feature space and the generalization ability of the corresponding learning algorithm. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Perceptron algorithm over a feature space of exponentially many conjunctions; however we also show that using such kernels, the Perceptron algorithm can provably make an exponential number of mistakes even when learning simple functions. We then consider the question of whether kernel functions can analogously be used to run the multiplicative-update Winnow algorithm over an expanded feature space of exponentially many conjunctions. Known upper bounds imply that the Winnow algorithm can learn Disjunctive Normal Form (DNF) formulae with a polynomial mistake bound in this setting. However, we prove that it is computationally hard to simulate Winnows behavior for learning DNF over such a feature set. This implies that the kernel functions which correspond to running Winnow for this problem are not efficiently computable, and that there is no general construction that can run Winnow with kernels.


Risk-Sensitive Reinforcement Learning Applied to Control under Constraints

In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state when the policy is pursued. We consider the problem of finding good policies whose risk is smaller than some user-specified threshold, and formalize it as a constrained MDP with two criteria. The first criterion corresponds to the value function originally given. We will show that the risk can be formulated as a second criterion function based on a cumulative return, whose definition is independent of the original value function. We present a model free, heuristic reinforcement learning algorithm that aims at finding good deterministic policies. It is based on weighting the original value function and the risk. The weight parameter is adapted in order to find a feasible solution for the constrained problem that has a good performance with respect to the value function. The algorithm was successfully applied to the control of a feed tank with stochastic inflows that lies upstream of a distillation column. This control task was originally formulated as an optimal control problem with chance constraints, and it was solved under certain assumptions on the model to obtain an optimal solution. The power of our learning algorithm is that it can be used even when some of these restrictive assumptions are relaxed.


A Learning Theory Approach to Non-Interactive Database Privacy

In this paper we demonstrate that, ignoring computational constraints, it is possible to privately release synthetic databases that are useful for large classes of queries -- much larger in size than the database itself. Specifically, we give a mechanism that privately releases synthetic data for a class of queries over a discrete domain with error that grows as a function of the size of the smallest net approximately representing the answers to that class of queries. We show that this in particular implies a mechanism for counting queries that gives error guarantees that grow only with the VC-dimension of the class of queries, which itself grows only logarithmically with the size of the query class. We also show that it is not possible to privately release even simple classes of queries (such as intervals and their generalizations) over continuous domains. Despite this, we give a privacy-preserving polynomial time algorithm that releases information useful for all halfspace queries, given a slight relaxation of the utility guarantee. This algorithm does not release synthetic data, but instead another data structure capable of representing an answer for each query. We also give an efficient algorithm for releasing synthetic data for the class of interval queries and axis-aligned rectangles of constant dimension. Finally, inspired by learning theory, we introduce a new notion of data privacy, which we call distributional privacy, and show that it is strictly stronger than the prevailing privacy notion, differential privacy.


Bandits with an Edge

We consider a bandit problem over a graph where the rewards are not directly observed. Instead, the decision maker can compare two nodes and receive (stochastic) information pertaining to the difference in their value. The graph structure describes the set of possible comparisons. Consequently, comparing between two nodes that are relatively far requires estimating the difference between every pair of nodes on the path between them. We analyze this problem from the perspective of sample complexity: How many queries are needed to find an approximately optimal node with probability more than $1-\delta$ in the PAC setup? We show that the topology of the graph plays a crucial in defining the sample complexity: graphs with a low diameter have a much better sample complexity.


MIS-Boost: Multiple Instance Selection Boosting

In this paper, we present a new multiple instance learning (MIL) method, called MIS-Boost, which learns discriminative instance prototypes by explicit instance selection in a boosting framework. Unlike previous instance selection based MIL methods, we do not restrict the prototypes to a discrete set of training instances but allow them to take arbitrary values in the instance feature space. We also do not restrict the total number of prototypes and the number of selected-instances per bag; these quantities are completely data-driven. We show that MIS-Boost outperforms state-of-the-art MIL methods on a number of benchmark datasets. We also apply MIS-Boost to large-scale image classification, where we show that the automatically selected prototypes map to visually meaningful image regions.


A Probabilistic Framework for Discriminative Dictionary Learning

In this paper, we address the problem of discriminative dictionary learning (DDL), where sparse linear representation and classification are combined in a probabilistic framework. As such, a single discriminative dictionary and linear binary classifiers are learned jointly. By encoding sparse representation and discriminative classification models in a MAP setting, we propose a general optimization framework that allows for a data-driven tradeoff between faithful representation and accurate classification. As opposed to previous work, our learning methodology is capable of incorporating a diverse family of classification cost functions (including those used in popular boosting methods), while avoiding the need for involved optimization techniques. We show that DDL can be solved by a sequence of updates that make use of well-known and well-studied sparse coding and dictionary learning algorithms from the literature. To validate our DDL framework, we apply it to digit classification and face recognition and test it on standard benchmarks.


Structured sparsity through convex optimization

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the regularization by the $\ell_1$-norm. In this paper, we consider situations where we are not only interested in sparsity, but where some structural prior knowledge is available as well. We show that the $\ell_1$-norm can then be extended to structured norms built on either disjoint or overlapping groups of variables, leading to a flexible framework that can deal with various structures. We present applications to unsupervised learning, for structured sparse principal component analysis and hierarchical dictionary learning, and to supervised learning in the context of non-linear variable selection.


Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems.


Active Learning for Node Classification in Assortative and Disassortative Networks

In many real-world networks, nodes have class labels, attributes, or variables that affect the network's topology. If the topology of the network is known but the labels of the nodes are hidden, we would like to select a small subset of nodes such that, if we knew their labels, we could accurately predict the labels of all the other nodes. We develop an active learning algorithm for this problem which uses information-theoretic techniques to choose which nodes to explore. We test our algorithm on networks from three different domains: a social network, a network of English words that appear adjacently in a novel, and a marine food web. Our algorithm makes no initial assumptions about how the groups connect, and performs well even when faced with quite general types of network structure. In particular, we do not assume that nodes of the same class are more likely to be connected to each other---only that they connect to the rest of the network in similar ways.


Reconstruction of sequential data with density models

We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is independent of the sequence index. The problem is hard because it involves possibly multivalued mappings at each vector in the sequence, where the missing variables can take more than one value given the present variables; and the set of missing variables can vary from one vector to the next. To solve this problem, we propose an algorithm based on two redundancy assumptions: vector redundancy (the data live in a low-dimensional manifold), so that the present variables constrain the missing ones; and sequence redundancy (e.g. continuity), so that consecutive vectors constrain each other. We capture the low-dimensional nature of the data in a probabilistic way with a joint density model, here the generative topographic mapping, which results in a Gaussian mixture. Candidate reconstructions at each vector are obtained as all the modes of the conditional distribution of missing variables given present variables. The reconstructed sequence is obtained by minimising a global constraint, here the sequence length, by dynamic programming. We present experimental results for a toy problem and for inverse kinematics of a robot arm.


Distributed User Profiling via Spectral Methods

User profiling is a useful primitive for constructing personalised services, such as content recommendation. In the present paper we investigate the feasibility of user profiling in a distributed setting, with no central authority and only local information exchanges between users. We compute a profile vector for each user (i.e., a low-dimensional vector that characterises her taste) via spectral transformation of observed user-produced ratings for items. Our two main contributions follow: i) We consider a low-rank probabilistic model of user taste. More specifically, we consider that users and items are partitioned in a constant number of classes, such that users and items within the same class are statistically identical. We prove that without prior knowledge of the compositions of the classes, based solely on few random observed ratings (namely $O(N\log N)$ such ratings for $N$ users), we can predict user preference with high probability for unrated items by running a local vote among users with similar profile vectors. In addition, we provide empirical evaluations characterising the way in which spectral profiling performance depends on the dimension of the profile space. Such evaluations are performed on a data set of real user ratings provided by Netflix. ii) We develop distributed algorithms which provably achieve an embedding of users into a low-dimensional space, based on spectral transformation. These involve simple message passing among users, and provably converge to the desired embedding. Our method essentially relies on a novel combination of gossiping and the algorithm proposed by Oja and Karhunen.


Learning Topic Models by Belief Propagation

Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational biology. This paper represents LDA as a factor graph within the Markov random field (MRF) framework, which enables the classic loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Although two commonly-used approximate inference methods, such as variational Bayes (VB) and collapsed Gibbs sampling (GS), have gained great successes in learning LDA, the proposed BP is competitive in both speed and accuracy as validated by encouraging experimental results on four large-scale document data sets. Furthermore, the BP algorithm has the potential to become a generic learning scheme for variants of LDA-based topic models. To this end, we show how to learn two typical variants of LDA-based topic models, such as author-topic models (ATM) and relational topic models (RTM), using BP based on the factor graph representation.


Active Ranking using Pairwise Comparisons

This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Specifically, we assume that the objects can be embedded into a $d$-dimensional Euclidean space and that the rankings reflect their relative distances from a common reference point in $R^d$. We show that under this assumption the number of possible rankings grows like $n^{2d}$ and demonstrate an algorithm that can identify a randomly selected ranking using just slightly more than $d log n$ adaptively selected pairwise comparisons, on average. If instead the comparisons are chosen at random, then almost all pairwise comparisons must be made in order to identify any ranking. In addition, we propose a robust, error-tolerant algorithm that only requires that the pairwise comparisons are probably correct. Experimental studies with synthetic and real datasets support the conclusions of our theoretical analysis.


Fast approximation of matrix coherence and statistical leverage

The statistical leverage scores of a matrix $A$ are the squared row-norms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities are of interest in recently-popular problems such as matrix completion and Nystr\"{o}m-based low-rank matrix approximation as well as in large-scale statistical data analysis applications more generally; moreover, they are of interest since they define the key structural nonuniformity that must be dealt with in developing fast randomized matrix algorithms. Our main result is a randomized algorithm that takes as input an arbitrary $n \times d$ matrix $A$, with $n \gg d$, and that returns as output relative-error approximations to all $n$ of the statistical leverage scores. The proposed algorithm runs (under assumptions on the precise values of $n$ and $d$) in $O(n d \log n)$ time, as opposed to the $O(nd^2)$ time required by the na\"{i}ve algorithm that involves computing an orthogonal basis for the range of $A$. Our analysis may be viewed in terms of computing a relative-error approximation to an underconstrained least-squares approximation problem, or, relatedly, it may be viewed as an application of Johnson-Lindenstrauss type ideas. Several practically-important extensions of our basic result are also described, including the approximation of so-called cross-leverage scores, the extension of these ideas to matrices with $n \approx d$, and the extension to streaming environments.


Learning Discriminative Metrics via Generative Models and Kernel Learning

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework. Specifically, we learn local metrics optimized from parametric generative models. These are then used as base kernels to construct a global kernel that minimizes a discriminative training criterion. We consider both linear and nonlinear combinations of local metric kernels. Our empirical results show that these combinations significantly improve performance on classification tasks. The proposed learning algorithm is also very efficient, achieving order of magnitude speedup in training time compared to previous discriminative baseline methods.


VC dimension of ellipsoids

We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^2+3d)/2. Keywords: VC dimension; finite dimensional ellipsoid; Gaussian mixture model


Manifold estimation and singular deconvolution under Hausdorff loss

We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.


Memristive fuzzy edge detector

Fuzzy inference systems always suffer from the lack of efficient structures or platforms for their hardware implementation. In this paper, we tried to overcome this problem by proposing new method for the implementation of those fuzzy inference systems which use fuzzy rule base to make inference. To achieve this goal, we have designed a multi-layer neuro-fuzzy computing system based on the memristor crossbar structure by introducing some new concepts like fuzzy minterms. Although many applications can be realized through the use of our proposed system, in this study we show how the fuzzy XOR function can be constructed and how it can be used to extract edges from grayscale images. Our memristive fuzzy edge detector (implemented in analog form) compared with other common edge detectors has this advantage that it can extract edges of any given image all at once in real-time.


Robust estimation of latent tree graphical models: Inferring hidden states with inexact parameters

Latent tree graphical models are widely used in computational biology, signal and image processing, and network tomography. Here we design a new efficient, estimation procedure for latent tree models, including Gaussian and discrete, reversible models, that significantly improves on previous sample requirement bounds. Our techniques are based on a new hidden state estimator which is robust to inaccuracies in estimated parameters. More precisely, we prove that latent tree models can be estimated with high probability in the so-called Kesten-Stigum regime with $O(log^2 n)$ samples where $n$ is the number of nodes.


Exhaustive and Efficient Constraint Propagation: A Semi-Supervised Learning Perspective and Its Applications

This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised learning subproblems which can be solved in quadratic time using label propagation based on k-nearest neighbor graphs. Considering that this time cost is proportional to the number of all possible pairwise constraints, our approach actually provides an efficient solution for exhaustively propagating pairwise constraints throughout the entire dataset. The resulting exhaustive set of propagated pairwise constraints are further used to adjust the similarity matrix for constrained spectral clustering. Other than the traditional constraint propagation on single-source data, our approach is also extended to more challenging constraint propagation on multi-source data where each pairwise constraint is defined over a pair of data points from different sources. This multi-source constraint propagation has an important application to cross-modal multimedia retrieval. Extensive results have shown the superior performance of our approach.


Latent Semantic Learning with Structured Sparse Representation for Human Action Recognition

This paper proposes a novel latent semantic learning method for extracting high-level features (i.e. latent semantics) from a large vocabulary of abundant mid-level features (i.e. visual keywords) with structured sparse representation, which can help to bridge the semantic gap in the challenging task of human action recognition. To discover the manifold structure of midlevel features, we develop a spectral embedding approach to latent semantic learning based on L1-graph, without the need to tune any parameter for graph construction as a key step of manifold learning. More importantly, we construct the L1-graph with structured sparse representation, which can be obtained by structured sparse coding with its structured sparsity ensured by novel L1-norm hypergraph regularization over mid-level features. In the new embedding space, we learn latent semantics automatically from abundant mid-level features through spectral clustering. The learnt latent semantics can be readily used for human action recognition with SVM by defining a histogram intersection kernel. Different from the traditional latent semantic analysis based on topic models, our latent semantic learning method can explore the manifold structure of mid-level features in both L1-graph construction and spectral embedding, which results in compact but discriminative high-level features. The experimental results on the commonly used KTH action dataset and unconstrained YouTube action dataset show the superior performance of our method.


Application of distances between terms for flat and hierarchical data

In machine learning, distance-based algorithms, and other approaches, use information that is represented by propositional data. However, this kind of representation can be quite restrictive and, in many cases, it requires more complex structures in order to represent data in a more natural way. Terms are the basis for functional and logic programming representation. Distances between terms are a useful tool not only to compare terms, but also to determine the search space in many of these applications. This dissertation applies distances between terms, exploiting the features of each distance and the possibility to compare from propositional data types to hierarchical representations. The distances between terms are applied through the k-NN (k-nearest neighbor) classification algorithm using XML as a common language representation. To be able to represent these data in an XML structure and to take advantage of the benefits of distance between terms, it is necessary to apply some transformations. These transformations allow the conversion of flat data into hierarchical data represented in XML, using some techniques based on intuitive associations between the names and values of variables and associations based on attribute similarity. Several experiments with the distances between terms of Nienhuys-Cheng and Estruch et al. were performed. In the case of originally propositional data, these distances are compared to the Euclidean distance. In all cases, the experiments were performed with the distance-weighted k-nearest neighbor algorithm, using several exponents for the attraction function (weighted distance). It can be seen that in some cases, the term distances can significantly improve the results on approaches applied to flat representations.


Noise Tolerance under Risk Minimization

In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an ${\bf unobservable}$ training set which is noise-free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with the ideal noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper we analyze the noise tolerance properties of risk minimization (under different loss functions), which is a generic method for learning classifiers. We show that risk minimization under 0-1 loss function has impressive noise tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude the paper with some discussion on implications of these theoretical results.


Simultaneous Codeword Optimization (SimCO) for Dictionary Update and Learning

We consider the data-driven dictionary learning problem. The goal is to seek an over-complete dictionary from which every training signal can be best approximated by a linear combination of only a few codewords. This task is often achieved by iteratively executing two operations: sparse coding and dictionary update. In the literature, there are two benchmark mechanisms to update a dictionary. The first approach, such as the MOD algorithm, is characterized by searching for the optimal codewords while fixing the sparse coefficients. In the second approach, represented by the K-SVD method, one codeword and the related sparse coefficients are simultaneously updated while all other codewords and coefficients remain unchanged. We propose a novel framework that generalizes the aforementioned two methods. The unique feature of our approach is that one can update an arbitrary set of codewords and the corresponding sparse coefficients simultaneously: when sparse coefficients are fixed, the underlying optimization problem is similar to that in the MOD algorithm; when only one codeword is selected for update, it can be proved that the proposed algorithm is equivalent to the K-SVD method; and more importantly, our method allows us to update all codewords and all sparse coefficients simultaneously, hence the term simultaneous codeword optimization (SimCO). Under the proposed framework, we design two algorithms, namely, primitive and regularized SimCO. We implement these two algorithms based on a simple gradient descent mechanism. Simulations are provided to demonstrate the performance of the proposed algorithms, as compared with two baseline algorithms MOD and K-SVD. Results show that regularized SimCO is particularly appealing in terms of both learning performance and running speed.


Bias Plus Variance Decomposition for Survival Analysis Problems

Bias - variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -variance parts of the expected error for two algorithms: original Cox proportional hazard regression and CoxPath, path algorithm for L1-regularized Cox regression, on the series of increased training sets. The experiments demonstrate that, contrary expectations, CoxPath does not necessarily have an advantage over Cox regression.


Higher-Order Markov Tag-Topic Models for Tagged Documents and Images

This paper studies the topic modeling problem of tagged documents and images. Higher-order relations among tagged documents and images are major and ubiquitous characteristics, and play positive roles in extracting reliable and interpretable topics. In this paper, we propose the tag-topic models (TTM) to depict such higher-order topic structural dependencies within the Markov random field (MRF) framework. First, we use the novel factor graph representation of latent Dirichlet allocation (LDA)-based topic models from the MRF perspective, and present an efficient loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Second, we propose the factor hypergraph representation of TTM, and focus on both pairwise and higher-order relation modeling among tagged documents and images. Efficient loopy BP algorithm is developed to learn TTM, which encourages the topic labeling smoothness among tagged documents and images. Extensive experimental results confirm the incorporation of higher-order relations to be effective in enhancing the overall topic modeling performance, when compared with current state-of-the-art topic models, in many text and image mining tasks of broad interests such as word and link prediction, document classification, and tag recommendation.


Making Gradient Descent Optimal for Strongly Convex Stochastic Optimization

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for T iterations and returning the average point. However, recent results showed that using a different algorithm, one can get an optimal O(1/T) rate. This might lead one to believe that standard SGD is suboptimal, and maybe should even be replaced as a method of choice. In this paper, we investigate the optimality of SGD in a stochastic setting. We show that for smooth problems, the algorithm attains the optimal O(1/T) rate. However, for non-smooth problems, the convergence rate with averaging might really be \Omega(\log(T)/T), and this is not just an artifact of the analysis. On the flip side, we show that a simple modification of the averaging step suffices to recover the O(1/T) rate, and no other change of the algorithm is necessary. We also present experimental results which support our findings, and point out open problems.


Deterministic Feature Selection for $k$-means Clustering

We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these algorithms are randomized and fail with, say, a constant probability. We address this issue by presenting a deterministic feature selection algorithm for k-means with theoretical guarantees. At the heart of our algorithm lies a deterministic method for decompositions of the identity.


Learning Item Trees for Probabilistic Modelling of Implicit Feedback

User preferences for items can be inferred from either explicit feedback, such as item ratings, or implicit feedback, such as rental histories. Research in collaborative filtering has concentrated on explicit feedback, resulting in the development of accurate and scalable models. However, since explicit feedback is often difficult to collect it is important to develop effective models that take advantage of the more widely available implicit feedback. We introduce a probabilistic approach to collaborative filtering with implicit feedback based on modelling the user's item selection process. In the interests of scalability, we restrict our attention to tree-structured distributions over items and develop a principled and efficient algorithm for learning item trees from data. We also identify a problem with a widely used protocol for evaluating implicit feedback models and propose a way of addressing it using a small quantity of explicit feedback data.


Domain Adaptation for Statistical Classifiers

The most basic assumption used in statistical learning theory is that training data and test data are drawn from the same underlying distribution. Unfortunately, in many applications, the "in-domain" test data is drawn from a distribution that is related, but not identical, to the "out-of-domain" distribution of the training data. We consider the common case in which labeled out-of-domain data is plentiful, but labeled in-domain data is scarce. We introduce a statistical formulation of this problem in terms of a simple mixture model and present an instantiation of this framework to maximum entropy classifiers and their linear chain counterparts. We present efficient inference algorithms for this special case based on the technique of conditional expectation maximization. Our experimental results show that our approach leads to improved performance on three real world tasks on four different data sets from the natural language processing domain.


Learning image transformations without training examples

The use of image transformations is essential for efficient modeling and learning of visual data. But the class of relevant transformations is large: affine transformations, projective transformations, elastic deformations, ... the list goes on. Therefore, learning these transformations, rather than hand coding them, is of great conceptual interest. To the best of our knowledge, all the related work so far has been concerned with either supervised or weakly supervised learning (from correlated sequences, video streams, or image-transform pairs). In this paper, on the contrary, we present a simple method for learning affine and elastic transformations when no examples of these transformations are explicitly given, and no prior knowledge of space (such as ordering of pixels) is included either. The system has only access to a moderately large database of natural images arranged in no particular order.


Eclectic Extraction of Propositional Rules from Neural Networks

Artificial Neural Network is among the most popular algorithm for supervised learning. However, Neural Networks have a well-known drawback of being a "Black Box" learner that is not comprehensible to the Users. This lack of transparency makes it unsuitable for many high risk tasks such as medical diagnosis that requires a rational justification for making a decision. Rule Extraction methods attempt to curb this limitation by extracting comprehensible rules from a trained Network. Many such extraction algorithms have been developed over the years with their respective strengths and weaknesses. They have been broadly categorized into three types based on their approach to use internal model of the Network. Eclectic Methods are hybrid algorithms that combine the other approaches to attain more performance. In this paper, we present an Eclectic method called HERETIC. Our algorithm uses Inductive Decision Tree learning combined with information of the neural network structure for extracting logical rules. Experiments and theoretical analysis show HERETIC to be better in terms of speed and performance.


Group Lasso with Overlaps: the Latent Group Lasso approach

We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the usual group Lasso penalty on a set of latent variables. A detailed analysis of the norm and its properties is presented and we characterize conditions under which the set of groups associated with latent variables are correctly identi ed. We motivate and discuss the delicate choice of weights associated to each group, and illustrate this approach on simulated data and on the problem of breast cancer prognosis from gene expression data.


Two Projection Pursuit Algorithms for Machine Learning under Non-Stationarity

This thesis derives, tests and applies two linear projection algorithms for machine learning under non-stationarity. The first finds a direction in a linear space upon which a data set is maximally non-stationary. The second aims to robustify two-way classification against non-stationarity. The algorithm is tested on a key application scenario, namely Brain Computer Interfacing.


Directed information and Pearl's causal calculus

Probabilistic graphical models are a fundamental tool in statistics, machine learning, signal processing, and control. When such a model is defined on a directed acyclic graph (DAG), one can assign a partial ordering to the events occurring in the corresponding stochastic system. Based on the work of Judea Pearl and others, these DAG-based "causal factorizations" of joint probability measures have been used for characterization and inference of functional dependencies (causal links). This mostly expository paper focuses on several connections between Pearl's formalism (and in particular his notion of "intervention") and information-theoretic notions of causality and feedback (such as causal conditioning, directed stochastic kernels, and directed information). As an application, we show how conditional directed information can be used to develop an information-theoretic version of Pearl's "back-door" criterion for identifiability of causal effects from passive observations. This suggests that the back-door criterion can be thought of as a causal analog of statistical sufficiency.


Linearized Additive Classifiers

We revisit the additive model learning literature and adapt a penalized spline formulation due to Eilers and Marx, to train additive classifiers efficiently. We also propose two new embeddings based two classes of orthogonal basis with orthogonal derivatives, which can also be used to efficiently learn additive classifiers. This paper follows the popular theme in the current literature where kernel SVMs are learned much more efficiently using a approximate embedding and linear machine. In this paper we show that spline basis are especially well suited for learning additive models because of their sparsity structure and the ease of computing the embedding which enables one to train these models in an online manner, without incurring the memory overhead of precomputing the storing the embeddings. We show interesting connections between B-Spline basis and histogram intersection kernel and show that for a particular choice of regularization and degree of the B-Splines, our proposed learning algorithm closely approximates the histogram intersection kernel SVM. This enables one to learn additive models with almost no memory overhead compared to fast a linear solver, such as LIBLINEAR, while being only 5-6X slower on average. On two large scale image classification datasets, MNIST and Daimler Chrysler pedestrians, the proposed additive classifiers are as accurate as the kernel SVM, while being two orders of magnitude faster to train.


Dictionary Learning for Deblurring and Digital Zoom

This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some large set (dictionary) of candidates, have proven well adapted to several image restoration tasks. A key to their success has been to learn dictionaries adapted to the reconstruction of small image patches. In contrast, recent works have proposed instead to learn dictionaries which are not only adapted to data reconstruction, but also tuned for a specific task. We introduce here such an approach to deblurring and digital zoom, using pairs of blurry/sharp (or low-/high-resolution) images for training, as well as an effective stochastic gradient algorithm for solving the corresponding optimization task. Although this learning problem is not convex, once the dictionaries have been learned, the sharp/high-resolution image can be recovered via convex optimization at test time. Experiments with synthetic and real data demonstrate the effectiveness of the proposed approach, leading to state-of-the-art performance for non-blind image deblurring and digital zoom.


Active Learning with Multiple Views

Active learners alleviate the burden of labeling large amounts of data by detecting and asking the user to label only the most informative examples in the domain. We focus here on active learning for multi-view domains, in which there are several disjoint subsets of features (views), each of which is sufficient to learn the target concept. In this paper we make several contributions. First, we introduce Co-Testing, which is the first approach to multi-view active learning. Second, we extend the multi-view learning framework by also exploiting weak views, which are adequate only for learning a concept that is more general/specific than the target concept. Finally, we empirically show that Co-Testing outperforms existing active learners on a variety of real world domains such as wrapper induction, Web page classification, advertisement removal, and discourse tree parsing.


The Augmented Complex Kernel LMS

Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex Reproducing Kernel Hilbert Spaces, developed a suitable Wirtinger-like Calculus for general Hilbert Spaces. In this short paper, the extended Wirtinger's calculus is adopted to derive complex kernel-based widely-linear estimation filters. Furthermore, we illuminate several important characteristics of the widely linear filters. We show that, although in many cases the gains from adopting widely linear estimation filters, as alternatives to ordinary linear ones, are rudimentary, for the case of kernel based widely linear filters significant performance improvements can be obtained.


Blackwell Approachability and Minimax Theory

This manuscript investigates the relationship between Blackwell Approachability, a stochastic vector-valued repeated game, and minimax theory, a single-play scalar-valued scenario. First, it is established in a general setting --- one not permitting invocation of minimax theory --- that Blackwell's Approachability Theorem and its generalization due to Hou are still valid. Second, minimax structure grants a result in the spirit of Blackwell's weak-approachability conjecture, later resolved by Vieille, that any set is either approachable by one player, or avoidable by the opponent. This analysis also reveals a strategy for the opponent.


On the trade-off between complexity and correlation decay in structural learning algorithms

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


A Study of Unsupervised Adaptive Crowdsourcing

We consider unsupervised crowdsourcing performance based on the model wherein the responses of end-users are essentially rated according to how their responses correlate with the majority of other responses to the same subtasks/questions. In one setting, we consider an independent sequence of identically distributed crowdsourcing assignments (meta-tasks), while in the other we consider a single assignment with a large number of component subtasks. Both problems yield intuitive results in which the overall reliability of the crowd is a factor.


A Behavior-based Approach for Multi-agent Q-learning for Autonomous Exploration

The use of mobile robots is being popular over the world mainly for autonomous explorations in hazardous/ toxic or unknown environments. This exploration will be more effective and efficient if the explorations in unknown environment can be aided with the learning from past experiences. Currently reinforcement learning is getting more acceptances for implementing learning in robots from the system-environment interactions. This learning can be implemented using the concept of both single-agent and multiagent. This paper describes such a multiagent approach for implementing a type of reinforcement learning using a priority based behaviour-based architecture. This proposed methodology has been successfully tested in both indoor and outdoor environments.


Dynamic Matrix Factorization: A State Space Approach

Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle changing user preferences over time. Recent proposals to address this issue are heuristic in nature and do not fully exploit the time-dependent structure of the problem. As a principled and general temporal formulation, we propose a dynamical state space model of matrix factorization. Our proposal builds upon probabilistic matrix factorization, a Bayesian model with Gaussian priors. We utilize results in state tracking, such as the Kalman filter, to provide accurate recommendations in the presence of both process and measurement noise. We show how system parameters can be learned via expectation-maximization and provide comparisons to current published techniques.


Active Learning Using Smooth Relative Regret Approximations with Applications

The disagreement coefficient of Hanneke has become a central data independent invariant in proving active learning rates. It has been shown in various ways that a concept class with low complexity together with a bound on the disagreement coefficient at an optimal solution allows active learning rates that are superior to passive learning ones. We present a different tool for pool based active learning which follows from the existence of a certain uniform version of low disagreement coefficient, but is not equivalent to it. In fact, we present two fundamental active learning problems of significant interest for which our approach allows nontrivial active learning bounds. However, any general purpose method relying on the disagreement coefficient bounds only fails to guarantee any useful bounds for these problems. The tool we use is based on the learner's ability to compute an estimator of the difference between the loss of any hypotheses and some fixed "pivotal" hypothesis to within an absolute error of at most $\eps$ times the


Large-Margin Learning of Submodular Summarization Methods

In this paper, we present a supervised learning approach to training submodular scoring functions for extractive multi-document summarization. By taking a structured predicition approach, we provide a large-margin method that directly optimizes a convex relaxation of the desired performance measure. The learning method applies to all submodular summarization methods, and we demonstrate its effectiveness for both pairwise as well as coverage-based scoring functions on multiple datasets. Compared to state-of-the-art functions that were tuned manually, our method significantly improves performance and enables high-fidelity models with numbers of parameters well beyond what could reasonbly be tuned by hand.


Learning Symbolic Models of Stochastic Domains

In this article, we work towards the goal of developing agents that can learn to act in complex worlds. We develop a probabilistic, relational planning rule representation that compactly models noisy, nondeterministic action effects, and show how such rules can be effectively learned. Through experiments in simple planning domains and a 3D simulated blocks world with realistic physics, we demonstrate that this learning algorithm allows agents to effectively model world dynamics.


Ground Metric Learning

Transportation distances have been used for more than a decade now in machine learning to compare histograms of features. They have one parameter: the ground metric, which can be any metric between the features themselves. As is the case for all parameterized distances, transportation distances can only prove useful in practice when this parameter is carefully chosen. To date, the only option available to practitioners to set the ground metric parameter was to rely on a priori knowledge of the features, which limited considerably the scope of application of transportation distances. We propose to lift this limitation and consider instead algorithms that can learn the ground metric using only a training set of labeled histograms. We call this approach ground metric learning. We formulate the problem of learning the ground metric as the minimization of the difference of two polyhedral convex functions over a convex set of distance matrices. We follow the presentation of our algorithms with promising experimental results on binary classification tasks using GIST descriptors of images taken in the Caltech-256 set.


A Variant of Azuma's Inequality for Martingales with Subgaussian Tails

We provide a variant of Azuma's concentration inequality for martingales, in which the standard boundedness requirement is replaced by the milder requirement of a subgaussian tail.


Supervised learning of short and high-dimensional temporal sequences for life science measurements

The analysis of physiological processes over time are often given by spectrometric or gene expression profiles over time with only few time points but a large number of measured variables. The analysis of such temporal sequences is challenging and only few methods have been proposed. The information can be encoded time independent, by means of classical expression differences for a single time point or in expression profiles over time. Available methods are limited to unsupervised and semi-supervised settings. The predictive variables can be identified only by means of wrapper or post-processing techniques. This is complicated due to the small number of samples for such studies. Here, we present a supervised learning approach, termed Supervised Topographic Mapping Through Time (SGTM-TT). It learns a supervised mapping of the temporal sequences onto a low dimensional grid. We utilize a hidden markov model (HMM) to account for the time domain and relevance learning to identify the relevant feature dimensions most predictive over time. The learned mapping can be used to visualize the temporal sequences and to predict the class of a new sequence. The relevance learning permits the identification of discriminating masses or gen expressions and prunes dimensions which are unnecessary for the classification task or encode mainly noise. In this way we obtain a very efficient learning system for temporal sequences. The results indicate that using simultaneous supervised learning and metric adaptation significantly improves the prediction accuracy for synthetically and real life data in comparison to the standard techniques. The discriminating features, identified by relevance learning, compare favorably with the results of alternative methods. Our method permits the visualization of the data on a low dimensional grid, highlighting the observed temporal structure.


The Generalization Ability of Online Algorithms for Dependent Data

We study the generalization performance of online learning algorithms trained on samples coming from a dependent source of data. We show that the generalization error of any stable online algorithm concentrates around its regret--an easily computable statistic of the online performance of the algorithm--when the underlying ergodic process is $\beta$- or $\phi$-mixing. We show high probability error bounds assuming the loss function is convex, and we also establish sharp convergence rates and deviation bounds for strongly convex losses and several linear prediction problems such as linear and logistic regression, least-squares SVM, and boosting on dependent data. In addition, our results have straightforward applications to stochastic optimization with dependent data, and our analysis requires only martingale convergence arguments; we need not rely on more powerful statistical tools such as empirical process theory.


Issues,Challenges and Tools of Clustering Algorithms

Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure. This paper has captured the problems that are faced in real when clustering algorithms are implemented .It also considers the most extensively used tools which are readily available and support functions which ease the programming. Once algorithms have been implemented, they also need to be tested for its validity. There exist several validation indexes for testing the performance and accuracy which have also been discussed here.


Analysis of Heart Diseases Dataset using Neural Network Approach

One of the important techniques of Data mining is Classification. Many real world problems in various fields such as business, science, industry and medicine can be solved by using classification approach. Neural Networks have emerged as an important tool for classification. The advantages of Neural Networks helps for efficient classification of given data. In this study a Heart diseases dataset is analyzed using Neural Network approach. To increase the efficiency of the classification process parallel approach is also adopted in the training phase.


Efficient Tracking of Large Classes of Experts

In the framework of prediction of individual sequences, sequential prediction methods are to be constructed that perform nearly as well as the best expert from a given class. We consider prediction strategies that compete with the class of switching strategies that can segment a given sequence into several blocks, and follow the advice of a different "base" expert in each block. As usual, the performance of the algorithm is measured by the regret defined as the excess loss relative to the best switching strategy selected in hindsight for the particular sequence to be predicted. In this paper we construct prediction strategies of low computational cost for the case where the set of base experts is large. In particular we provide a method that can transform any prediction algorithm $\A$ that is designed for the base class into a tracking algorithm. The resulting tracking algorithm can take advantage of the prediction performance and potential computational efficiency of $\A$ in the sense that it can be implemented with time and space complexity only $O(n^{\gamma} \ln n)$ times larger than that of $\A$, where $n$ is the time horizon and $\gamma \ge 0$ is a parameter of the algorithm. With $\A$ properly chosen, our algorithm achieves a regret bound of optimal order for $\gamma>0$, and only $O(\ln n)$ times larger than the optimal order for $\gamma=0$ for all typical regret bound types we examined. For example, for predicting binary sequences with switching parameters under the logarithmic loss, our method achieves the optimal $O(\ln n)$ regret rate with time complexity $O(n^{1+\gamma}\ln n)$ for any $\gamma\in (0,1)$.


A tail inequality for quadratic forms of subgaussian random vectors

We prove an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.


Sparse Image Representation with Epitomes

Sparse coding, which is the decomposition of a vector using only a few basis elements, is widely used in machine learning and image processing. The basis set, also called dictionary, is learned to adapt to specific data. This approach has proven to be very effective in many image processing tasks. Traditionally, the dictionary is an unstructured "flat" set of atoms. In this paper, we study structured dictionaries which are obtained from an epitome, or a set of epitomes. The epitome is itself a small image, and the atoms are all the patches of a chosen size inside this image. This considerably reduces the number of parameters to learn and provides sparse image decompositions with shiftinvariance properties. We propose a new formulation and an algorithm for learning the structured dictionaries associated with epitomes, and illustrate their use in image denoising tasks.


Randomized Dimensionality Reduction for k-means Clustering

We study the topic of dimensionality reduction for $k$-means clustering. Dimensionality reduction encompasses the union of two approaches: \emph{feature selection} and \emph{feature extraction}. A feature selection based algorithm for $k$-means clustering selects a small subset of the input features and then applies $k$-means clustering on the selected features. A feature extraction based algorithm for $k$-means clustering constructs a small set of new artificial features and then applies $k$-means clustering on the constructed features. Despite the significance of $k$-means clustering as well as the wealth of heuristic methods addressing it, provably accurate feature selection methods for $k$-means clustering are not known. On the other hand, two provably accurate feature extraction methods for $k$-means clustering are known in the literature; one is based on random projections and the other is based on the singular value decomposition (SVD). This paper makes further progress towards a better understanding of dimensionality reduction for $k$-means clustering. Namely, we present the first provably accurate feature selection method for $k$-means clustering and, in addition, we present two feature extraction methods. The first feature extraction method is based on random projections and it improves upon the existing results in terms of time complexity and number of features needed to be extracted. The second feature extraction method is based on fast approximate SVD factorizations and it also improves upon the existing results in terms of time complexity. The proposed algorithms are randomized and provide constant-factor approximation guarantees with respect to the optimal $k$-means objective value.


Discovering Emerging Topics in Social Streams via Link Anomaly Detection

Detection of emerging topics are now receiving renewed interest motivated by the rapid growth of social networks. Conventional term-frequency-based approaches may not be appropriate in this context, because the information exchanged are not only texts but also images, URLs, and videos. We focus on the social aspects of theses networks. That is, the links between users that are generated dynamically intentionally or unintentionally through replies, mentions, and retweets. We propose a probability model of the mentioning behaviour of a social network user, and propose to detect the emergence of a new topic from the anomaly measured through the model. We combine the proposed mention anomaly score with a recently proposed change-point detection technique based on the Sequentially Discounting Normalized Maximum Likelihood (SDNML), or with Kleinberg's burst model. Aggregating anomaly scores from hundreds of users, we show that we can detect emerging topics only based on the reply/mention relationships in social network posts. We demonstrate our technique in a number of real data sets we gathered from Twitter. The experiments show that the proposed mention-anomaly-based approaches can detect new topics at least as early as the conventional term-frequency-based approach, and sometimes much earlier when the keyword is ill-defined.


Step size adaptation in first-order method for stochastic strongly convex programming

We propose a first-order method for stochastic strongly convex optimization that attains $O(1/n)$ rate of convergence, analysis show that the proposed method is simple, easily to implement, and in worst case, asymptotically four times faster than its peers. We derive this method from several intuitive observations that are generalized from existing first order optimization methods.


Efficient Latent Variable Graphical Model Selection via Split Bregman Method

We consider the problem of covariance matrix estimation in the presence of latent variables. Under suitable conditions, it is possible to learn the marginal covariance matrix of the observed variables via a tractable convex program, where the concentration matrix of the observed variables is decomposed into a sparse matrix (representing the graphical structure of the observed variables) and a low rank matrix (representing the marginalization effect of latent variables). We present an efficient first-order method based on split Bregman to solve the convex problem. The algorithm is guaranteed to converge under mild conditions. We show that our algorithm is significantly faster than the state-of-the-art algorithm on both artificial and real-world data. Applying the algorithm to a gene expression data involving thousands of genes, we show that most of the correlation between observed variables can be explained by only a few dozen latent factors.


Robust Image Analysis by L1-Norm Semi-supervised Learning

This paper presents a novel L1-norm semi-supervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm Laplacian regularization is defined directly over the eigenvectors of the normalized Laplacian matrix, we successfully formulate semi-supervised learning as an L1-norm linear reconstruction problem which can be effectively solved with sparse coding. By working with only a small subset of eigenvectors, we further develop a fast sparse coding algorithm for our L1-norm semi-supervised learning. Due to the sparsity induced by sparse coding, the proposed algorithm can deal with the noise in the data to some extent and thus has important applications to robust image analysis, such as noise-robust image classification and noise reduction for visual and textual bag-of-words (BOW) models. In particular, this paper is the first attempt to obtain robust image representation by sparse co-refinement of visual and textual BOW models. The experimental results have shown the promising performance of the proposed algorithm.


Improving parameter learning of Bayesian nets from incomplete data

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the maximum penalized log-likelihood and the maximum a posteriori estimate) has severe drawbacks, being affected both by overfitting and model uncertainty. Two ideas are discussed to overcome these issues: a maximum entropy approach and a Bayesian model averaging approach. Both ideas can be easily applied on top of EM, while the entropy idea can be also implemented in a more sophisticated way, through a dedicated non-linear solver. A vast set of experiments shows that these ideas produce significantly better estimates and inferences than the traditional and widely used maximum (penalized) log-likelihood and maximum a posteriori estimates. In particular, if EM is adopted as optimization engine, the model averaging approach is the best performing one; its performance is matched by the entropy approach when implemented using the non-linear solver. The results suggest that the applicability of these ideas is immediate (they are easy to implement and to integrate in currently available inference engines) and that they constitute a better way to learn Bayesian network parameters.


Dynamic Batch Bayesian Optimization

Bayesian optimization (BO) algorithms try to optimize an unknown function that is expensive to evaluate using minimum number of evaluations/experiments. Most of the proposed algorithms in BO are sequential, where only one experiment is selected at each iteration. This method can be time inefficient when each experiment takes a long time and more than one experiment can be ran concurrently. On the other hand, requesting a fix-sized batch of experiments at each iteration causes performance inefficiency in BO compared to the sequential policies. In this paper, we present an algorithm that asks a batch of experiments at each time step t where the batch size p_t is dynamically determined in each step. Our algorithm is based on the observation that the sequence of experiments selected by the sequential policy can sometimes be almost independent from each other. Our algorithm identifies such scenarios and request those experiments at the same time without degrading the performance. We evaluate our proposed method using the Expected Improvement policy and the results show substantial speedup with little impact on the performance in eight real and synthetic benchmarks.


Budget-Optimal Task Allocation for Reliable Crowdsourcing Systems

Crowdsourcing systems, in which numerous tasks are electronically distributed to numerous "information piece-workers", have emerged as an effective paradigm for human-powered solving of large scale problems in domains such as image classification, data entry, optical character recognition, recommendation, and proofreading. Because these low-paid workers can be unreliable, nearly all such systems must devise schemes to increase confidence in their answers, typically by assigning each task multiple times and combining the answers in an appropriate manner, e.g. majority voting. In this paper, we consider a general model of such crowdsourcing tasks and pose the problem of minimizing the total price (i.e., number of task assignments) that must be paid to achieve a target overall reliability. We give a new algorithm for deciding which tasks to assign to which workers and for inferring correct answers from the workers' answers. We show that our algorithm, inspired by belief propagation and low-rank matrix approximation, significantly outperforms majority voting and, in fact, is optimal through comparison to an oracle that knows the reliability of every worker. Further, we compare our approach with a more general class of algorithms which can dynamically assign tasks. By adaptively deciding which questions to ask to the next arriving worker, one might hope to reduce uncertainty more efficiently. We show that, perhaps surprisingly, the minimum price necessary to achieve a target reliability scales in the same manner under both adaptive and non-adaptive scenarios. Hence, our non-adaptive approach is order-optimal under both scenarios. This strongly relies on the fact that workers are fleeting and can not be exploited. Therefore, architecturally, our results suggest that building a reliable worker-reputation system is essential to fully harnessing the potential of adaptive designs.


Information, learning and falsification

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out. The third, statistical learning theory, has introduced measures of capacity that control (in part) the expected risk of classifiers. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies, counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information.