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

Learning algorithms are based on samples which are often drawn independently from an identical distribution (i.i.d.). In this paper we consider a different setting with samples drawn according to a non-identical sequence of probability distributions. Each time a sample is drawn from a different distribution. In this setting we investigate a fully online learning algorithm associated with a general convex loss function and a reproducing kernel Hilbert space (RKHS). Error analysis is conducted under the assumption that the sequence of marginal distributions converges polynomially in the dual of a Höolder space. For regression with least square or insensitive loss, learning rates are given in both the RKHS norm and the L² norm. For classification with hinge loss and support vector machine q-norm loss, rates are explicitly stated with respect to the excess misclassification error. [ABSTRACT FROM AUTHOR]

A common problem of kernel-based online algorithms, such as the kernel-based Perceptron algorithm, is the amount of memory required to store the online hypothesis, which may increase without bound as the algorithm progresses. Furthermore, the computational load of such algorithms grows linearly with the amount of memory used to store the hypothesis. To attack these problems, most previous work has focused on discarding some of the instances, in order to keep the memory bounded. In this paper we present a new algorithm, in which the instances are not discarded, but are instead projected onto the space spanned by the previous online hypothesis. We call this algorithm Projectron. While the memory size of the Projectron solution cannot be predicted before training, we prove that its solution is guaranteed to be bounded. We derive a relative mistake bound for the proposed algorithm, and deduce from it a slightly different algorithm which outperforms the Perceptron. We call this second algorithm Projectron++. We show that this algorithm can be extended to handle the multiclass and the structured output settings, resulting, as far as we know, in the first online bounded algorithm that can learn complex classification tasks. The method of bounding the hypothesis representation can be applied to any conservative online algorithm and to other online algorithms, as it is demonstrated for ALMA2. Experimental results on various data sets show the empirical advantage of our technique compared to various bounded online algorithms, both in terms of memory and accuracy. [ABSTRACT FROM AUTHOR]

We consider a general class of regularization methods which learn a vector of parameters on the basis of linear measurements. It is well known that if the regularizer is a nondecreasing function of the L2 norm, then the learned vector is a linear combination of the input data. This result, known as the representer theorem, lies at the basis of kernel-based methods in machine learning. In this paper, we prove the necessity of the above condition, in the case of differentiable regularizers. We further extend our analysis to regularization methods which learn a matrix, a problem which is motivated by the application to multi-task learning. In this context, we study a more general representer theorem, which holds for a larger class of regularizers. We provide a necessary and sufficient condition characterizing this class of matrix regularizers and we highlight some concrete examples of practical importance. Our analysis uses basic principles from matrix theory, especially the useful notion of matrix nondecreasing functions. [ABSTRACT FROM AUTHOR]

The growth of information available to learning systems and the increasing complexity of learning tasks determine the need for devising algorithms that scale well with respect to all learning parameters. In the context of supervised sequential learning, the Viterbi algorithm plays a fundamental role, by allowing the evaluation of the best (most probable) sequence of labels with a time complexity linear in the number of time events, and quadratic in the number of labels. In this paper we propose CarpeDiem, a novel algorithm allowing the evaluation of the best possible sequence of labels with a sub-quadratic time complexity. We provide theoretical grounding together with solid empirical results supporting two chief facts. CarpeDiem always finds the optimal solution requiring, in most cases, only a small fraction of the time taken by the Viterbi algorithm; meantime, CarpeDiem is never asymptotically worse than the Viterbi algorithm, thus confirming it as a sound replacement. [ABSTRACT FROM AUTHOR]

This paper presents Model Monitor (M²), a Java toolkit for robustly evaluating machine learning algorithms in the presence of changing data distributions. M² provides a simple and intuitive framework in which users can evaluate classifiers under hypothesized shifts in distribution and therefore determine the best model (or models) for their data under a number of potential scenarios. Additionally, M² is fully integrated with the WEKA machine learning environment, so that a variety of commodity classifiers can be used if desired. [ABSTRACT FROM AUTHOR]

We propose a novel framework for supervised learning of discrete concepts. Since the 1970's, the standard computational primitive has been to find the most consistent hypothesis in a given complexity class. In contrast, in this paper we propose a new basic operation: for each pair of input instances, count how many concepts of bounded complexity contain both of them. Our approach maps instances to a Hilbert space, whose metric is induced by a universal kernel coinciding with our computational primitive, and identifies concepts with half-spaces. We prove that all concepts are linearly separable under this mapping. Hence, given a labeled sample and an oracle for evaluating the universal kernel, we can efficiently compute a linear classifier (via SVM, for example) and use margin bounds to control its generalization error. Even though exact evaluation of the universal kernel may be infeasible, in various natural situations it is efficiently approximable. Though our approach is general, our main application is to regular languages. Our approach presents a substantial departure from current learning paradigms and in particular yields a novel method for learning this fundamental concept class. Unlike existing techniques, we make no structural assumptions on the corresponding unknown automata, the string distribution or the completeness of the training set. Instead, given a labeled sample our algorithm outputs a classifier with guaranteed distribution-free generalization bounds; to our knowledge, the proposed framework is the only one capable of achieving the latter. Along the way, we touch upon several fundamental questions in complexity, automata, and machine learning. [ABSTRACT FROM AUTHOR]

This paper reviews and extends the field of similarity-based classification, presenting new analyses, algorithms, data sets, and a comprehensive set of experimental results for a rich collection of classification problems. Specifically, the generalizability of using similarities as features is analyzed, design goals and methods for weighting nearest-neighbors for similarity-based learning are proposed, and different methods for consistently converting similarities into kernels are compared. Experiments on eight real data sets compare eight approaches and their variants to similarity-based learning. [ABSTRACT FROM AUTHOR]

In this paper, we study low-rank matrix nearness problems, with a focus on learning low-rank positive semidefinite (kernel) matrices for machine learning applications. We propose efficient algorithms that scale linearly in the number of data points and quadratically in the rank of the input matrix. Existing algorithms for learning kernel matrices often scale poorly, with running times that are cubic in the number of data points. We employ Bregman matrix divergences as the measures of nearness--these divergences are natural for learning low-rank kernels since they preserve rank as well as positive semidefiniteness. Special cases of our framework yield faster algorithms for various existing learning problems, and experimental results demonstrate that our algorithms can effectively learn both low-rank and full-rank kernel matrices. [ABSTRACT FROM AUTHOR]

In real world applications, graphical statistical models are not only a tool for operations such as classification or prediction, but usually the network structures of the models themselves are also of great interest (e.g., in modeling brain connectivity). The false discovery rate (FDR), the expected ratio of falsely claimed connections to all those claimed, is often a reasonable error-rate criterion in these applications. However, current learning algorithms for graphical models have not been adequately adapted to the concerns of the FDR. The traditional practice of controlling the type I error rate and the type II error rate under a conventional level does not necessarily keep the FDR low, especially in the case of sparse networks. In this paper, we propose embedding an FDR-control procedure into the PC algorithm to curb the FDR of the skeleton of the learned graph. We prove that the proposed method can control the FDR under a user-specified level at the limit of large sample sizes. In the cases of moderate sample size (about several hundred), empirical experiments show that the method is still able to control the FDR under the user-specified level, and a heuristic modification of the method is able to control the FDR more accurately around the user-specified level. The proposed method is applicable to any models for which statistical tests of conditional independence are available, such as discrete models and Gaussian models. [ABSTRACT FROM AUTHOR]

This paper proposes the application of particle swarm optimization (PSO) to the problem of full model selection, FMS, for classification tasks. FMS is defined as follows: given a pool of pre-processing methods, feature selection and learning algorithms, to select the combination of these that obtains the lowest classification error for a given data set; the task also includes the selection of hyperparameters for the considered methods. This problem generates a vast search space to be explored, well suited for stochastic optimization techniques. FMS can be applied to any classification domain as it does not require domain knowledge. Different model types and a variety of algorithms can be considered under this formulation. Furthermore, competitive yet simple models can be obtained with FMS. We adopt PSO for the search because of its proven performance in different problems and because of its simplicity, since neither expensive computations nor complicated operations are needed. Interestingly, the way the search is guided allows PSO to avoid overfitting to some extend. Experimental results on benchmark data sets give evidence that the proposed approach is very effective, despite its simplicity. Furthermore, results obtained in the framework of a model selection challenge show the competitiveness of the models selected with PSO, compared to models selected with other techniques that focus on a single algorithm and that use domain knowledge. [ABSTRACT FROM AUTHOR]

Most approaches to structured output prediction rely on a hypothesis space of prediction functions that compute their output by maximizing a linear scoring function. In this paper we present two novel learning algorithms for this hypothesis class, and a statistical analysis of their performance. The methods rely on efficiently computing the first two moments of the scoring function over the output space, and using them to create convex objective functions for training. We report extensive experimental results for sequence alignment, named entity recognition, and RNA secondary structure prediction. [ABSTRACT FROM AUTHOR]

Chain graphs present a broad class of graphical models for description of conditional independence structures, including both Markov networks and Bayesian networks as special cases. In this paper, we propose a computationally feasible method for the structural learning of chain graphs based on the idea of decomposing the learning problem into a set of smaller scale problems on its decomposed subgraphs. The decomposition requires conditional independencies but does not require the separators to be complete subgraphs. Algorithms for both skeleton recovery and complex arrow orientation are presented. Simulations under a variety of settings demonstrate the competitive performance of our method, especially when the underlying graph is sparse. [ABSTRACT FROM AUTHOR]

In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective functions. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NP-complete problems admit efficient algorithms. We show how our algorithm can be extended to handle complex cost functions (incorporating non-unit observation cost or communication and path costs). We also show how the algorithm can be used to near-optimally trade off expected-case (e.g., the Mean Square Prediction Error in Gaussian Process regression) and worst-case (e.g., maximum predictive variance) performance. We show that many important machine learning problems fit our robust submodular observation selection formalism, and provide extensive empirical evaluation on several real-world problems. For Gaussian Process regression, our algorithm compares favorably with state-of-the-art heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDP-based algorithms. [ABSTRACT FROM AUTHOR]

Harmonic analysis and diffusion on discrete data has been shown to lead to state-of-the-art algorithms for machine learning tasks, especially in the context of semi-supervised and transductive learning. The success of these algorithms rests on the assumption that the function(s) to be studied (learned, interpolated, etc.) are smooth with respect to the geometry of the data. In this paper we present a method for modifying the given geometry so the function(s) to be studied are smoother with respect to the modified geometry, and thus more amenable to treatment using harmonic analysis methods. Among the many possible applications, we consider the problems of image denoising and transductive classification. In both settings, our approach improves on standard diffusion based methods. [ABSTRACT FROM AUTHOR]

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or maxmargin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods. [ABSTRACT FROM AUTHOR]

Linear support vector machines (SVM) are useful for classifying large-scale sparse data. Problems with sparse features are common in applications such as document classification and natural language processing. In this paper, we propose a novel coordinate descent algorithm for training linear SVM with the L2-loss function. At each step, the proposed method minimizes a one-variable sub-problem while fixing other variables. The sub-problem is solved by Newton steps with the line search technique. The procedure globally converges at the linear rate. As each sub-problem involves only values of a corresponding feature, the proposed approach is suitable when accessing a feature is more convenient than accessing an instance. Experiments show that our method is more efficient and stable than state of the art methods such as Pegasos and TRON. [ABSTRACT FROM AUTHOR]

In structured classification problems, there is a direct conflict between expressive models and efficient inference: while graphical models such as Markov random fields or factor graphs can represent arbitrary dependences among instance labels, the cost of inference via belief propagation in these models grows rapidly as the graph structure becomes more complicated. One important source of complexity in belief propagation is the need to marginalize large factors to compute messages. This operation takes time exponential in the number of variables in the factor, and can limit the expressiveness of the models we can use. In this paper, we study a new class of potential functions, which we call decomposable k-way potentials, and provide efficient algorithms for computing messages from these potentials during belief propagation. We believe these new potentials provide a good balance between expressive power and efficient inference in practical structured classification problems. We discuss three instances of decomposable potentials: the associative Markov network potential, the nested junction tree, and a new type of potential which we call the voting potential. We use these potentials to classify images of protein subcellular location patterns in groups of cells. Classifying subcellular location patterns can help us answer many important questions in computational biology, including questions about how various treatments affect the synthesis and behavior of proteins and networks of proteins within a cell. Our new representation and algorithm lead to substantial improvements in both inference speed and classification accuracy. [ABSTRACT FROM AUTHOR]

In this paper we introduce an improved implementation of locally weighted projection regression (LWPR), a supervised learning algorithm that is capable of handling high-dimensional input data. As the key features, our code supports multi-threading, is available for multiple platforms, and provides wrappers for several programming languages. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) is one of the most popular and promising classification algorithms. After a classification rule is constructed via the SVM, it is essential to evaluate its prediction accuracy. In this paper, we develop procedures for obtaining both point and interval estimators for the prediction error. Under mild regularity conditions, we derive the consistency and asymptotic normality of the prediction error estimators for SVM with finite-dimensional kernels. A perturbationresampling procedure is proposed to obtain interval estimates for the prediction error in practice. With numerical studies on simulated data and a benchmark repository, we recommend the use of interval estimates centered at the cross-validated point estimates for the prediction error. Further applications of the proposed procedure in model evaluation and feature selection are illustrated with two examples. [ABSTRACT FROM AUTHOR]

Ensemble learning algorithms such as boosting can achieve better performance by averaging over the predictions of some base hypotheses. Nevertheless, most existing algorithms are limited to combining only a finite number of hypotheses, and the generated ensemble is usually sparse. Thus, it is not clear whether we should construct an ensemble classifier with a larger or even an infinite number of hypotheses. In addition, constructing an infinite ensemble itself is a challenging task. In this paper, we formulate an infinite ensemble learning framework based on the support vector machine (SVM). The framework can output an infinite and nonsparse ensemble through embedding infinitely many hypotheses into an SVM kernel. We use the framework to derive two novel kernels, the stump kernel and the perceptron kernel. The stump kernel embodies infinitely many decision stumps, and the perceptron kernel embodies infinitely many perceptrons. We also show that the Laplacian radial basis function kernel embodies infinitely many decision trees, and can thus be explained through infinite ensemble learning. Experimental results show that SVM with these kernels is superior to boosting with the same base hypothesis set. In addition, SVM with the stump kernel or the perceptron kernel performs similarly to SVM with the Gaussian radial basis function kernel, but enjoys the benefit of faster parameter selection. These properties make the novel kernels favorable choices in practice. [ABSTRACT FROM AUTHOR]

The authors comment on the article "Evidence Contrary to Statistical View of Boosting," by David Mease and Abraham Wyner that was published within the issue. The three important properties that contribute to the success of boosting methods are mentioned. The authors claim that the paper attributes consequences of statistical view that are not the case, including the requirement that test error have a unique minimum as a function of the number of included terms.

The authors present a response to comments on their paper "Evidence Contrary to the Statistical View of Boosting." They state that Kristin P. Bennett provided a useful perspective on the situation by examining the convergence of boosting algorithms from the optimization point of view. Moreover, the authors agree with Andreas Buja and Werner Stuetzle that a complete view of boosting should explain both its ability to reduce bias and variance.

Due to its wide applicability, the problem of semi-supervised classification is attracting increasing attention in machine learning. Semi-Supervised Support Vector Machines (S³VMs) are based on applying the margin maximization principle to both labeled and unlabeled examples. Unlike SVMs, their formulation leads to a non-convex optimization problem. A suite of algorithms have recently been proposed for solving S³VMs. This paper reviews key ideas in this literature. The performance and behavior of various S³VM algorithms is studied together, under a common experimental setting. [ABSTRACT FROM AUTHOR]

Classifiers favoring sparse solutions, such as support vector machines, relevance vector machines, LASSO-regression based classifiers, etc., provide competitive methods for classification problems in high dimensions. However, current algorithms for training sparse classifiers typically scale quite unfavorably with respect to the number of training examples. This paper proposes online and multi-pass algorithms for training sparse linear classifiers for high dimensional data. These algorithms have computational complexity and memory requirements that make learning on massive data sets feasible. The central idea that makes this possible is a straightforward quadratic approximation to the likelihood function. [ABSTRACT FROM AUTHOR]

Hierarchical reinforcement learning (HRL) is a general framework for scaling reinforcement learning (RL) to problems with large state and action spaces by using the task (or action) structure to restrict the space of policies. Prior work in HRL including HAMs, options, MAXQ, and PHAMs has been limited to the discrete-time discounted reward semi-Markov decision process (SMDP) model. The average reward optimality criterion has been recognized to be more appropriate for a wide class of continuing tasks than the discounted framework. Although average reward RL has been studied for decades, prior work has been largely limited to flat policy representations. In this paper, we develop a framework for HRL based on the average reward optimality criterion. We investigate two formulations of HRL based on the average reward SMDP model, both for discrete-time and continuous-time. These formulations correspond to two notions of optimality that have been previously explored in HRL: hierarchical optimality and recursive optimality. We present algorithms that learn to find hierarchically and recursively optimal average reward policies under discrete-time and continuous-time average reward SMDP models. We use two automated guided vehicle (AGV) scheduling tasks as experimental testbeds to study the empirical performance of the proposed algorithms. The first problem is a relatively simple AGV scheduling task, in which the hierarchically and recursively optimal policies are different. We compare the proposed algorithms with three other HRL methods, including a hierarchically optimal discounted reward algorithm and a recursively optimal discounted reward algorithm on this problem. The second problem is a larger AGV scheduling task. We model this problem using both discrete-time and continuous-time models. We use a hierarchical task decomposition in which the hierarchically and recursively optimal policies are the same for this problem. We compare the performance of the proposed algorithms with a hierarchically optimal discounted reward algorithm and a recursively optimal discounted reward algorithm, as well as a non-hierarchical average reward algorithm. The results show that the proposed hierarchical average reward algorithms converge to the same performance as their discounted reward counterparts. [ABSTRACT FROM AUTHOR]

Marchand and Shawe-Taylor (2002) have proposed a loss bound for the set covering machine that has the property to depend on the observed fraction of positive examples and on what the classifier achieves on the positive training examples. We show that this loss bound is incorrect. We then propose a loss bound, valid for any sample-compression learning algorithm (including the set covering machine), that depends on the observed fraction of positive examples and on what the classifier achieves on them. We also compare numerically the loss bound proposed in this paper with the incorrect bound, the original SCM bound and a recently proposed loss bound of Marchand and Sokolova (2005) (which does not depend on the observed fraction of positive examples) and show that the latter loss bounds can be substantially larger than the new bound in the presence of imbalanced misclassifications. [ABSTRACT FROM AUTHOR]

Temporal difference (TD) learning (Sutton and Barto, 1998) has become a popular reinforcement learning technique in recent years. TD methods, relying on function approximators to generalize learning to novel situations, have had some experimental successes and have been shown to exhibit some desirable properties in theory, but the most basic algorithms have often been found slow in practice. This empirical result has motivated the development of many methods that speed up reinforcement learning by modifying a task for the learner or helping the learner better generalize to novel situations. This article focuses on generalizing across tasks, thereby speeding up learning, via a novel form of transfer using handcoded task relationships. We compare learning on a complex task with three function approximators, a cerebellar model arithmetic computer (CMAC), an artificial neural network (ANN), and a radial basis function (RBF), and empirically demonstrate that directly transferring the action-value function can lead to a dramatic speedup in learning with all three. Using transfer via inter-task mapping (TVITM), agents are able to learn one task and then markedly reduce the time it takes to learn a more complex task. Our algorithms are fully implemented and tested in the RoboCup soccer Keepaway domain. This article contains and extends material published in two conference papers (Taylor and Stone, 2005; Taylor et al., 2005). [ABSTRACT FROM AUTHOR]

Center-based partitioning clustering algorithms rely on minimizing an appropriately formulated objective function, and different formulations suggest different possible algorithms. In this paper, we start with the standard nonconvex and nonsmooth formulation of the partitioning clustering problem. We demonstrate that within this elementary formulation, convex analysis tools and optimization theory provide a unifying language and framework to design, analyze and extend hard and soft center-based clustering algorithms, through a generic algorithm which retains the computational simplicity of the popular k-means scheme. We show that several well known and more recent center-based clustering algorithms, which have been derived either heuristically, or/and have emerged from intuitive analogies in physics, statistical techniques and information theoretic perspectives can be recovered as special cases of the proposed analysis and we streamline their relationships. [ABSTRACT FROM AUTHOR]

An ensemble is a group of learning models that jointly solve a problem. However, the ensembles generated by existing techniques are sometimes unnecessarily large, which can lead to extra memory usage, computational costs, and occasional decreases in effectiveness. The purpose of ensemble pruning is to search for a good subset of ensemble members that performs as well as, or better than, the original ensemble. This subset selection problem is a combinatorial optimization problem and thus finding the exact optimal solution is computationally prohibitive. Various heuristic methods have been developed to obtain an approximate solution. However, most of the existing heuristics use simple greedy search as the optimization method, which lacks either theoretical or empirical quality guarantees. In this paper, the ensemble subset selection problem is formulated as a quadratic integer programming problem. By applying semi-definite programming (SDP) as a solution technique, we are able to get better approximate solutions. Computational experiments show that this SDP-based pruning algorithm outperforms other heuristics in the literature. Its application in a classifier-sharing study also demonstrates the effectiveness of the method. [ABSTRACT FROM AUTHOR]

The task of learning models for many real-world problems requires incorporating domain knowledge into learning algorithms, to enable accurate learning from a realistic volume of training data. This paper considers a variety of types of domain knowledge for constraining parameter estimates when learning Bayesian networks. In particular, we consider domain knowledge that constrains the values or relationships among subsets of parameters in a Bayesian network with known structure. We incorporate a wide variety of parameter constraints into learning procedures for Bayesian networks, by formulating this task as a constrained optimization problem. The assumptions made in module networks, dynamic Bayes nets and context specific independence models can be viewed as particular cases of such parameter constraints. We present closed form solutions or fast iterative algorithms for estimating parameters subject to several specific classes of parameter constraints, including equalities and inequalities among parameters, constraints on individual parameters, and constraints on sums and ratios of parameters, for discrete and continuous variables. Our methods cover learning from both frequentist and Bayesian points of view, from both complete and incomplete data. We present formal guarantees for our estimators, as well as methods for automatically learning useful parameter constraints from data. To validate our approach, we apply it to the domain of fMRI brain image analysis. Here we demonstrate the ability of our system to first learn useful relationships among parameters, and then to use them to constrain the training of the Bayesian network, resulting in improved cross-validated accuracy of the learned model. Experiments on synthetic data are also presented. [ABSTRACT FROM AUTHOR]

A classical approach in multi-class pattern classification is the following. Estimate the probability distributions that generated the observations for each label class, and then label new instances by applying the Bayes classifier to the estimated distributions. That approach provides more useful information than just a class label; it also provides estimates of the conditional distribution of class labels, in situations where there is class overlap. We would like to know whether it is harder to build accurate classifiers via this approach, than by techniques that may process all data with distinct labels together. In this paper we make that question precise by considering it in the context of PAC learnability. We propose two restrictions on the PAC learning framework that are intended to correspond with the above approach, and consider their relationship with standard PAC learning. Our main restriction of interest leads to some interesting algorithms that show that the restriction is not stronger (more restrictive) than various other well-known restrictions on PAC learning. An alternative slightly milder restriction turns out to be almost equivalent to unrestricted PAC learning. [ABSTRACT FROM AUTHOR]

The Bradley-Terry model for obtaining individual skill from paired comparisons has been popular in many areas. In machine learning, this model is related to multi-class probability estimates by coupling all pairwise classification results. Error correcting output codes (ECOC) are a general framework to decompose a multi-class problem to several binary problems. To obtain probability estimates under this framework, this paper introduces a generalized Bradley-Terry model in which paired individual comparisons are extended to paired team comparisons. We propose a simple algorithm with convergence proofs to solve the model and obtain individual skill. Experiments on synthetic and real data demonstrate that the algorithm is useful for obtaining multi-class probability estimates. Moreover, we discuss four extensions of the proposed model: 1) weighted individual skill, 2) home-field advantage, 3) ties, and 4) comparisons with more than two teams. [ABSTRACT FROM AUTHOR]

One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting. [ABSTRACT FROM AUTHOR]

Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary issue of designing classification algorithms that can deal with more complex outputs, such as trees, sequences, or sets. More generally, we consider problems involving multiple dependent output variables, structured output spaces, and classification problems with class attributes. In order to accomplish this, we propose to appropriately generalize the well-known notion of a separation margin and derive a corresponding maximum-margin formulation. While this leads to a quadratic program with a potentially prohibitive, i.e. exponential, number of constraints, we present a cutting plane algorithm that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval/extraction, and optical character recognition. Experiments from various domains involving different types of output spaces emphasize the breadth and generality of our approach. [ABSTRACT FROM AUTHOR]

Typical recommender systems adopt a static view of the recommendation process and treat it as a prediction problem. We argue that it is more appropriate to view the problem of generating recommendations as a sequential optimization problem and, consequently, that Markov decision processes (MDPs) provide a more appropriate model for recommender systems. MDPs introduce two benefits: they take into account the long-term effects of each recommendation and the expected value of each recommendation. To succeed in practice, an MDP-based recommender system must employ a strong initial model, must be solvable quickly, and should not consume too much memory. In this paper, we describe our particular MDP model, its initialization using a predictive model, the solution and update algorithm, and its actual performance on a commercial site. We also describe the particular predictive model we used which outperforms previous models. Our system is one of a small number of commercially deployed recommender systems. As far as we know, it is the first to report experimental analysis conducted on a real commercial site. These results validate the commercial value of recommender systems, and in particular, of our MDP-based approach. [ABSTRACT FROM AUTHOR]

Winner-take-all multiclass classifiers are built on the top of a set of prototypes each representing one of the available classes. A pattern is then classified with the label associated to the most 'similar' prototype. Recent proposal of SVM extensions to multiclass can be considered instances of the same strategy with one prototype per class. The multi-prototype SVM proposed in this paper extends multiclass SVM to multiple prototypes per class. It allows to combine several vectors in a principled way to obtain large margin decision functions. For this problem, we give a compact constrained quadratic formulation and we propose a greedy optimization algorithm able to find locally optimal solutions for the non convex objective function. This algorithm proceeds by reducing the overall problem into a series of simpler convex problems. For the solution of these reduced problems an efficient optimization algorithm is proposed. A number of pattern selection strategies are then discussed to speed-up the optimization process. In addition, given the combinatorial nature of the overall problem, stochastic search strategies are suggested to escape from local minima which are not globally optimal. Finally, we report experiments on a number of datasets. The performance obtained using few simple linear prototypes is comparable to that obtained by state-of-the-art kernel-based methods but with a significant reduction (of one or two orders) in response time. [ABSTRACT FROM AUTHOR]

Standard SVM training has O(m³) time and O(m²) space complexities, where m is the training set size. It is thus computationally infeasible on very large data sets. By observing that practical SVM implementations only approximate the optimal solution by an iterative strategy, we scale up kernel methods by exploiting such "approximateness" in this paper. We first show that many kernel methods can be equivalently formulated as minimum enclosing ball (MEB) problems in computational geometry. Then, by adopting an efficient approximate MEB algorithm, we obtain provably approximately optimal solutions with the idea of core sets. Our proposed Core Vector Machine (CVM) algorithm can be used with nonlinear kernels and has a time complexity that is linear in m and a space complexity that is independent of m. Experiments on large toy and real-world data sets demonstrate that the CVM is as accurate as existing SVM implementations, but is much faster and can handle much larger data sets than existing scale-up methods. For example, CVM with the Gaussian kernel produces superior results on the KDDCUP-99 intrusion detection data, which has about five million training patterns, in only 1.4 seconds on a 3.2GHz Pentium-4 PC. [ABSTRACT FROM AUTHOR]

A blind separation problem where the sources are not independent, but have variance dependencies is discussed. For this scenario Hyvärinen and Hurri (2004) proposed an algorithm which requires no assumption on distributions of sources and no parametric model of dependencies between components. In this paper, we extend the semiparametric approach of Amari and Cardoso (1997) to variance dependencies and study estimating functions for blind separation of such dependent sources. In particular, we show that many ICA algorithms are applicable to the variance-dependent model as well under mild conditions, although they should in principle not. Our results indicate that separation can be done based only on normalized sources which are adjusted to have stationary variances and is not affected by the dependent activity levels. We also study the asymptotic distribution of the quasi maximum likelihood method and the stability of the natural gradient learning in detail. Simulation results of artificial and realistic examples match well with our theoretical findings. [ABSTRACT FROM AUTHOR]

Policy gradient methods for reinforcement learning avoid some of the undesirable properties of the value function approaches, such as policy degradation (Baxter and Bartlett, 2001). However, the variance of the performance gradient estimates obtained from the simulation is sometimes excessive. In this paper, we consider variance reduction methods that were developed for Monte Carlo estimates of integrals. We study two commonly used policy gradient techniques, the baseline and actor-critic methods, from this perspective. Both can be interpreted as additive control variate variance reduction methods. We consider the expected average reward performance measure, and we focus on the GPOMDP algorithm for estimating performance gradients in partially observable Markov decision processes controlled by stochastic reactive policies. We give bounds for the estimation error of the gradient estimates for both baseline and actor-critic algorithms, in terms of the sample size and mixing properties of the controlled system. For the baseline technique, we compute the optimal baseline, and show that the popular approach of using the average reward to define the baseline can be suboptimal. For actor-critic algorithms, we show that using the true value function as the critic can be suboptimal. We also discuss algorithms for estimating the optimal baseline and approximate value function. [ABSTRACT FROM AUTHOR]

Model-based clustering techniques have been widely used and have shown promising results in many applications involving complex data. This paper presents a unified framework for probabilistic model-based clustering based on a bipartite graph view of data and models that highlights the commonalities and differences among existing model-based clustering algorithms. In this view, clusters are represented as probabilistic models in a model space that is conceptually separate from the data space. For partitional clustering, the view is conceptually similar to the ExpectationMaximization (EM) algorithm. For hierarchical clustering, the graph-based view helps to visualize critical/important distinctions between similarity-based approaches and model-based approaches. The framework also suggests several useful variations of existing clustering algorithms. Two new variations—balanced model-based clustering and hybrid model-based clustering—are discussed and empirically evaluated on a variety of data types. [ABSTRACT FROM AUTHOR]

So far, boosting has been used to improve the quality of moderately accurate learning algorithms, by weighting and combining many of their weak hypotheses into a final classifier with theoretically high accuracy. In a recent work (Sebban, Nock and Lallich, 2001), we have attempted to adapt boosting properties to data reduction techniques. In this particular context, the objective was not only to improve the success rate, but also to reduce the time and space complexities due to the storage requirements of some costly learning algorithms, such as nearest-neighbor classifiers. In that framework, each weak hypothesis, which is usually built and weighted from the learning set, is replaced by a single learning instance. The weight given by boosting defines in that case the relevance of the instance, and a statistical test allows one to decide whether it can be discarded without damaging further classification tasks. In Sebban, Nock and Lallich (2001), we addressed problems with two classes. It is the aim of the present paper to relax the class constraint, and extend our contribution to multiclass problems. Beyond data reduction, experimental results are also provided on twenty-three datasets, showing the benefits that our boosting-derived weighting rule brings to weighted nearest neighbor classifiers. [ABSTRACT FROM AUTHOR]

Cross-validation is a useful and generally applicable technique often employed in machine learning, including decision tree induction. An important disadvantage of straightforward implementation of the technique is its computational overhead. In this paper we show that, for decision trees, the computational overhead of cross-validation can be reduced significantly by integrating the cross-validation with the normal decision tree induction process. We discuss how existing decision tree algorithms can be adapted to this aim, and provide an analysis of the speedups these adaptations may yield. We identify a number of parameters that influence the obtainable speedups, and validate and refine our analysis with experiments on a variety of data sets with two different implementations. Besides cross-validation, we also briefly explore the usefulness of these techniques for bagging. We conclude with some guidelines concerning when these optimizations should be considered. [ABSTRACT FROM AUTHOR]

This paper demonstrates that standard algorithms for training support vector machines generally produce solutions with a greater number of support vectors than are strictly necessary. An algorithm is presented that allows unnecessary support vectors to be recognized and eliminated while leaving the solution otherwise unchanged. The algorithm is applied to a variety of benchmark data sets (for both classification and regression) and in most cases the procedure leads to a reduction in the number of support vectors. Insome cases the reduction is substantial. [ABSTRACT FROM AUTHOR]