# Showing papers in "Journal of Machine Learning Research in 2003"

••

[...]

TL;DR: This work proposes a generative model for text and other collections of discrete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams, and Hofmann's aspect model.

Abstract: We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

27,392 citations

••

[...]

TL;DR: The contributions of this special issue cover a wide range of aspects of variable selection: providing a better definition of the objective function, feature construction, feature ranking, multivariate feature selection, efficient search methods, and feature validity assessment methods.

Abstract: Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. These areas include text processing of internet documents, gene expression array analysis, and combinatorial chemistry. The objective of variable selection is three-fold: improving the prediction performance of the predictors, providing faster and more cost-effective predictors, and providing a better understanding of the underlying process that generated the data. The contributions of this special issue cover a wide range of aspects of such problems: providing a better definition of the objective function, feature construction, feature ranking, multivariate feature selection, efficient search methods, and feature validity assessment methods.

13,554 citations

••

[...]

TL;DR: The authors propose to learn a distributed representation for words which allows each training sentence to inform the model about an exponential number of semantically neighboring sentences, which can be expressed in terms of these representations.

Abstract: A goal of statistical language modeling is to learn the joint probability function of sequences of words in a language. This is intrinsically difficult because of the curse of dimensionality: a word sequence on which the model will be tested is likely to be different from all the word sequences seen during training. Traditional but very successful approaches based on n-grams obtain generalization by concatenating very short overlapping sequences seen in the training set. We propose to fight the curse of dimensionality by learning a distributed representation for words which allows each training sentence to inform the model about an exponential number of semantically neighboring sentences. The model learns simultaneously (1) a distributed representation for each word along with (2) the probability function for word sequences, expressed in terms of these representations. Generalization is obtained because a sequence of words that has never been seen before gets high probability if it is made of words that are similar (in the sense of having a nearby representation) to words forming an already seen sentence. Training such large models (with millions of parameters) within a reasonable time is itself a significant challenge. We report on experiments using neural networks for the probability function, showing on two text corpora that the proposed approach significantly improves on state-of-the-art n-gram models, and that the proposed approach allows to take advantage of longer contexts.

6,194 citations

••

[...]

TL;DR: This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings and proposes three effective and efficient techniques for obtaining high-quality combiners (consensus functions).

Abstract: This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse' framework that we call cluster ensembles. The cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information. In addition to a direct maximization approach, we propose three effective and efficient techniques for obtaining high-quality combiners (consensus functions). The first combiner induces a similarity measure from the partitionings and then reclusters the objects. The second combiner is based on hypergraph partitioning. The third one collapses groups of clusters into meta-clusters which then compete for each object to determine the combined clustering. Due to the low computational costs of our techniques, it is quite feasible to use a supra-consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation. We evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios: (i) where the original clusters were formed based on non-identical sets of features, (ii) where the original clustering algorithms worked on non-identical sets of objects, and (iii) where a common data-set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution. Promising results are obtained in all three situations for synthetic as well as real data-sets.

4,008 citations

•

[...]

Hewlett-Packard

^{1}TL;DR: An empirical comparison of twelve feature selection methods evaluated on a benchmark of 229 text classification problem instances, revealing that a new feature selection metric, called 'Bi-Normal Separation' (BNS), outperformed the others by a substantial margin in most situations and was the top single choice for all goals except precision.

Abstract: Machine learning for text classification is the cornerstone of document categorization, news filtering, document routing, and personalization. In text domains, effective feature selection is essential to make the learning task efficient and more accurate. This paper presents an empirical comparison of twelve feature selection methods (e.g. Information Gain) evaluated on a benchmark of 229 text classification problem instances that were gathered from Reuters, TREC, OHSUMED, etc. The results are analyzed from multiple goal perspectives-accuracy, F-measure, precision, and recall-since each is appropriate in different situations. The results reveal that a new feature selection metric we call 'Bi-Normal Separation' (BNS), outperformed the others by a substantial margin in most situations. This margin widened in tasks with high class skew, which is rampant in text classification problems and is particularly challenging for induction algorithms. A new evaluation methodology is offered that focuses on the needs of the data mining practitioner faced with a single dataset who seeks to choose one (or a pair of) metrics that are most likely to yield the best performance. From this perspective, BNS was the top single choice for all goals except precision, for which Information Gain yielded the best result most often. This analysis also revealed, for example, that Information Gain and Chi-Squared have correlated failures, and so they work poorly together. When choosing optimal pairs of metrics for each of the four performance goals, BNS is consistently a member of the pair---e.g., for greatest recall, the pair BNS + F1-measure yielded the best performance on the greatest number of tasks by a considerable margin.

2,523 citations

••

[...]

TL;DR: This work describes and analyze an efficient algorithm called RankBoost for combining preferences based on the boosting approach to machine learning, and gives theoretical results describing the algorithm's behavior both on the training data, and on new test data not seen during training.

Abstract: We study the problem of learning to accurately rank a set of objects by combining a given collection of ranking or preference functions. This problem of combining preferences arises in several applications, such as that of combining the results of different search engines, or the "collaborative-filtering" problem of ranking movies for a user based on the movie rankings provided by other users. In this work, we begin by presenting a formal framework for this general problem. We then describe and analyze an efficient algorithm called RankBoost for combining preferences based on the boosting approach to machine learning. We give theoretical results describing the algorithm's behavior both on the training data, and on new test data not seen during training. We also describe an efficient implementation of the algorithm for a particular restricted but common case. We next discuss two experiments we carried out to assess the performance of RankBoost. In the first experiment, we used the algorithm to combine different web search strategies, each of which is a query expansion for a given domain. The second experiment is a collaborative-filtering task for making movie recommendations.

1,821 citations

••

[...]

TL;DR: A new approach for modeling multi-modal data sets, focusing on the specific case of segmented images with associated text, is presented, and a number of models for the joint distribution of image regions and words are developed, including several which explicitly learn the correspondence between regions and Words.

Abstract: We present a new approach for modeling multi-modal data sets, focusing on the specific case of segmented images with associated text. Learning the joint distribution of image regions and words has many applications. We consider in detail predicting words associated with whole images (auto-annotation) and corresponding to particular image regions (region naming). Auto-annotation might help organize and access large collections of images. Region naming is a model of object recognition as a process of translating image regions to words, much as one might translate from one language to another. Learning the relationships between image regions and semantic correlates (words) is an interesting example of multi-modal data mining, particularly because it is typically hard to apply data mining techniques to collections of images. We develop a number of models for the joint distribution of image regions and words, including several which explicitly learn the correspondence between regions and words. We study multi-modal and correspondence extensions to Hofmann's hierarchical clustering/aspect model, a translation model adapted from statistical machine translation (Brown et al.), and a multi-modal extension to mixture of latent Dirichlet allocation (MoM-LDA). All models are assessed using a large collection of annotated images of real scenes. We study in depth the difficult problem of measuring performance. For the annotation task, we look at prediction performance on held out data. We present three alternative measures, oriented toward different types of task. Measuring the performance of correspondence methods is harder, because one must determine whether a word has been placed on the right region of an image. We can use annotation performance as a proxy measure, but accurate measurement requires hand labeled data, and thus must occur on a smaller scale. We show results using both an annotation proxy, and manually labeled data.

1,700 citations

••

[...]

TL;DR: A class of algorithms for independent component analysis which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space is presented, showing that these algorithms outperform many of the presently known algorithms.

Abstract: We present a class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence. On the other hand, building on recent developments in kernel methods, we show that these criteria and their derivatives can be computed efficiently. Minimizing these criteria leads to flexible and robust algorithms for ICA. We illustrate with simulations involving a wide variety of source distributions, showing that our algorithms outperform many of the presently known algorithms.

1,641 citations

••

[...]

TL;DR: Locally linear embedding (LLE), an unsupervised learning algorithm that computes low dimensional, neighborhood preserving embeddings of high dimensional data, is described and several extensions that enhance its performance are discussed.

Abstract: The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. Here we describe locally linear embedding (LLE), an unsupervised learning algorithm that computes low dimensional, neighborhood preserving embeddings of high dimensional data. The data, assumed to be sampled from an underlying manifold, are mapped into a single global coordinate system of lower dimensionality. The mapping is derived from the symmetries of locally linear reconstructions, and the actual computation of the embedding reduces to a sparse eigenvalue problem. Notably, the optimizations in LLE---though capable of generating highly nonlinear embeddings---are simple to implement, and they do not involve local minima. In this paper, we describe the implementation of the algorithm in detail and discuss several extensions that enhance its performance. We present results of the algorithm applied to data sampled from known manifolds, as well as to collections of images of faces, lips, and handwritten digits. These examples are used to provide extensive illustrations of the algorithm's performance---both successes and failures---and to relate the algorithm to previous and ongoing work in nonlinear dimensionality reduction.

1,570 citations

••

[...]

Duke University

^{1}TL;DR: The new algorithm, least-squares policy iteration (LSPI), learns the state-action value function which allows for action selection without a model and for incremental policy improvement within a policy-iteration framework.

Abstract: We propose a new approach to reinforcement learning for control problems which combines value-function approximation with linear architectures and approximate policy iteration. This new approach is motivated by the least-squares temporal-difference learning algorithm (LSTD) for prediction problems, which is known for its efficient use of sample experiences compared to pure temporal-difference algorithms. Heretofore, LSTD has not had a straightforward application to control problems mainly because LSTD learns the state value function of a fixed policy which cannot be used for action selection and control without a model of the underlying process. Our new algorithm, least-squares policy iteration (LSPI), learns the state-action value function which allows for action selection without a model and for incremental policy improvement within a policy-iteration framework. LSPI is a model-free, off-policy method which can use efficiently (and reuse in each iteration) sample experiences collected in any manner. By separating the sample collection method, the choice of the linear approximation architecture, and the solution method, LSPI allows for focused attention on the distinct elements that contribute to practical reinforcement learning. LSPI is tested on the simple task of balancing an inverted pendulum and the harder task of balancing and riding a bicycle to a target location. In both cases, LSPI learns to control the pendulum or the bicycle by merely observing a relatively small number of trials where actions are selected randomly. LSPI is also compared against Q-learning (both with and without experience replay) using the same value function architecture. While LSPI achieves good performance fairly consistently on the difficult bicycle task, Q-learning variants were rarely able to balance for more than a small fraction of the time needed to reach the target location.

1,316 citations

••

[...]

TL;DR: This work finds that LSTM augmented by "peephole connections" from its internal cells to its multiplicative gates can learn the fine distinction between sequences of spikes spaced either 50 or 49 time steps apart without the help of any short training exemplars.

Abstract: The temporal distance between events conveys information essential for numerous sequential tasks such as motor control and rhythm detection. While Hidden Markov Models tend to ignore this information, recurrent neural networks (RNNs) can in principle learn to make use of it. We focus on Long Short-Term Memory (LSTM) because it has been shown to outperform other RNNs on tasks involving long time lags. We find that LSTM augmented by "peephole connections" from its internal cells to its multiplicative gates can learn the fine distinction between sequences of spikes spaced either 50 or 49 time steps apart without the help of any short training exemplars. Without external resets or teacher forcing, our LSTM variant also learns to generate stable streams of precisely timed spikes and other highly nonlinear periodic patterns. This makes LSTM a promising approach for tasks that require the accurate measurement or generation of time intervals.

•

[...]

TL;DR: It is shown how a standard tool from statistics, namely confidence bounds, can be used to elegantly deal with situations which exhibit an exploitation-exploration trade-off, and improves the regret from O(T3/4) to T1/2.

Abstract: We show how a standard tool from statistics --- namely confidence bounds --- can be used to elegantly deal with situations which exhibit an exploitation-exploration trade-off. Our technique for designing and analyzing algorithms for such situations is general and can be applied when an algorithm has to make exploitation-versus-exploration decisions based on uncertain information provided by a random process. We apply our technique to two models with such an exploitation-exploration trade-off. For the adversarial bandit problem with shifting our new algorithm suffers only O((ST)1/2) regret with high probability over T trials with S shifts. Such a regret bound was previously known only in expectation. The second model we consider is associative reinforcement learning with linear value functions. For this model our technique improves the regret from O(T3/4) to O(T1/2).

••

[...]

Microsoft

^{1}TL;DR: This paper proves the so-called "Meek Conjecture", which shows that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that H remains anindependence map of G and after all modifications G =H.

Abstract: In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.

••

[...]

TL;DR: This work introduces kernels defined over shallow parse representations of text, and design efficient algorithms for computing the kernels, and uses the devised kernels in conjunction with Support Vector Machine and Voted Perceptron learning algorithms for the task of extracting person-affiliation and organization-location relations from text.

Abstract: We present an application of kernel methods to extracting relations from unstructured natural language sources. We introduce kernels defined over shallow parse representations of text, and design efficient algorithms for computing the kernels. We use the devised kernels in conjunction with Support Vector Machine and Voted Perceptron learning algorithms for the task of extracting person-affiliation and organization-location relations from text. We experimentally evaluate the proposed methods and compare them with feature-based learning algorithms, with promising results.

••

[...]

TL;DR: R-MAX is a very simple model-based reinforcement learning algorithm which can attain near-optimal average reward in polynomial time and formally justifies the ``optimism under uncertainty'' bias used in many RL algorithms.

Abstract: R-MAX is a very simple model-based reinforcement learning algorithm which can attain near-optimal average reward in polynomial time. In R-MAX, the agent always maintains a complete, but possibly inaccurate model of its environment and acts based on the optimal policy derived from this model. The model is initialized in an optimistic fashion: all actions in all states return the maximal possible reward (hence the name). During execution, it is updated based on the agent's observations. R-MAX improves upon several previous algorithms: (1) It is simpler and more general than Kearns and Singh's E3 algorithm, covering zero-sum stochastic games. (2) It has a built-in mechanism for resolving the exploration vs. exploitation dilemma. (3) It formally justifies the ``optimism under uncertainty'' bias used in many RL algorithms. (4) It is simpler, more general, and more efficient than Brafman and Tennenholtz's LSG algorithm for learning in single controller stochastic games. (5) It generalizes the algorithm by Monderer and Tennenholtz for learning in repeated games. (6) It is the only algorithm for learning in repeated games, to date, which is provably efficient, considerably improving and simplifying previous algorithms by Banos and by Megiddo.

••

[...]

TL;DR: This work extends Q-learning to a noncooperative multiagent context, using the framework of general-sum stochastic games, and implements an online version of Nash Q- learning that balances exploration with exploitation, yielding improved performance.

Abstract: We extend Q-learning to a noncooperative multiagent context, using the framework of general-sum stochastic games. A learning agent maintains Q-functions over joint actions, and performs updates based on assuming Nash equilibrium behavior over the current Q-values. This learning protocol provably converges given certain restrictions on the stage games (defined by Q-values) that arise during learning. Experiments with a pair of two-player grid games suggest that such restrictions on the game structure are not necessarily required. Stage games encountered during learning in both grid environments violate the conditions. However, learning consistently converges in the first grid game, which has a unique equilibrium Q-function, but sometimes fails to converge in the second, which has three different equilibrium Q-functions. In a comparison of offline learning performance in both games, we find agents are more likely to reach a joint optimal path with Nash Q-learning than with a single-agent Q-learning method. When at least one agent adopts Nash Q-learning, the performance of both agents is better than using single-agent Q-learning. We have also implemented an online version of Nash Q-learning that balances exploration with exploitation, yielding improved performance.

•

[...]

TL;DR: In this article, the authors explore the use of the zero-norm of the parameters of linear models in learning and derive a simple but practical method for variable or feature selection, minimizing training error and ensuring sparsity in solutions.

Abstract: We explore the use of the so-called zero-norm of the parameters of linear models in learning. Minimization of such a quantity has many uses in a machine learning context: for variable or feature selection, minimizing training error and ensuring sparsity in solutions. We derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero-norm. The method boils down to implementing a simple modification of vanilla SVM, namely via an iterative multiplicative rescaling of the training data. Applications we investigate which aid our discussion include variable and feature selection on biological microarray data, and multicategory classification.

•

[...]

TL;DR: New methods to evaluate variable subset relevance with a view to variable selection based on weight vector derivative achieves good results and performs consistently well over the datasets used.

Abstract: We propose new methods to evaluate variable subset relevance with a view to variable selection. Relevance criteria are derived from Support Vector Machines and are based on weight vector ||w||2 or generalization error bounds sensitivity with respect to a variable. Experiments on linear and non-linear toy problems and real-world datasets have been carried out to assess the effectiveness of these criteria. Results show that the criterion based on weight vector derivative achieves good results and performs consistently well over the datasets we used.

•

[...]

Motorola

^{1}TL;DR: A quadratic divergence measure is used instead of a commonly used mutual information measure based on Kullback-Leibler divergence, which allows for an efficient non-parametric implementation and requires no prior assumptions about class densities.

Abstract: We present a method for learning discriminative feature transforms using as criterion the mutual information between class labels and transformed features. Instead of a commonly used mutual information measure based on Kullback-Leibler divergence, we use a quadratic divergence measure, which allows us to make an efficient non-parametric implementation and requires no prior assumptions about class densities. In addition to linear transforms, we also discuss nonlinear transforms that are implemented as radial basis function networks. Extensions to reduce the computational complexity are also presented, and a comparison to greedy feature selection is made.

••

[...]

TL;DR: This paper describes a family of additive ultraconservative algorithms where each algorithm in the family updates its prototypes by finding a feasible solution for a set of linear constraints that depend on the instantaneous similarity-scores.

Abstract: In this paper we study a paradigm to generalize online classification algorithms for binary classification problems to multiclass problems. The particular hypotheses we investigate maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarity-score between each prototype and the input instance and sets the predicted label to be the index of the prototype achieving the highest similarity. To design and analyze the learning algorithms in this paper we introduce the notion of ultraconservativeness. Ultraconservative algorithms are algorithms that update only the prototypes attaining similarity-scores which are higher than the score of the correct label's prototype. We start by describing a family of additive ultraconservative algorithms where each algorithm in the family updates its prototypes by finding a feasible solution for a set of linear constraints that depend on the instantaneous similarity-scores. We then discuss a specific online algorithm that seeks a set of prototypes which have a small norm. The resulting algorithm, which we term MIRA (for Margin Infused Relaxed Algorithm) is ultraconservative as well. We derive mistake bounds for all the algorithms and provide further analysis of MIRA using a generalized notion of the margin for multiclass problems. We discuss the form the algorithms take in the binary case and show that all the algorithms from the first family reduce to the Perceptron algorithm while MIRA provides a new Perceptron-like algorithm with a margin-dependent learning rate. We then return to multiclass problems and describe an analogous multiplicative family of algorithms with corresponding mistake bounds. We end the formal part by deriving and analyzing a multiclass version of Li and Long's ROMMA algorithm. We conclude with a discussion of experimental results that demonstrate the merits of our algorithms.

••

[...]

TL;DR: A Bayesian approach is adopted in which some of the model parameters are shared and others more loosely connected through a joint prior distribution that can be learned from the data to combine the best parts of both the statistical multilevel approach and the neural network machinery.

Abstract: Modeling a collection of similar regression or classification tasks can be improved by making the tasks 'learn from each other'. In machine learning, this subject is approached through 'multitask learning', where parallel tasks are modeled as multiple outputs of the same network. In multilevel analysis this is generally implemented through the mixed-effects linear model where a distinction is made between 'fixed effects', which are the same for all tasks, and 'random effects', which may vary between tasks. In the present article we will adopt a Bayesian approach in which some of the model parameters are shared (the same for all tasks) and others more loosely connected through a joint prior distribution that can be learned from the data. We seek in this way to combine the best parts of both the statistical multilevel approach and the neural network machinery. The standard assumption expressed in both approaches is that each task can learn equally well from any other task. In this article we extend the model by allowing more differentiation in the similarities between tasks. One such extension is to make the prior mean depend on higher-level task characteristics. More unsupervised clustering of tasks is obtained if we go from a single Gaussian prior to a mixture of Gaussians. This can be further generalized to a mixture of experts architecture with the gates depending on task characteristics. All three extensions are demonstrated through application both on an artificial data set and on two real-world problems, one a school problem and the other involving single-copy newspaper sales.

••

[...]

TL;DR: A new information-theoretic divisive algorithm for feature/word clustering and apply it to text classification is proposed and it is shown that feature clustering is an effective technique for building smaller class models in hierarchical classification.

Abstract: High dimensionality of text can be a deterrent in applying complex learners such as Support Vector Machines to the task of text classification. Feature clustering is a powerful alternative to feature selection for reducing the dimensionality of text data. In this paper we propose a new information-theoretic divisive algorithm for feature/word clustering and apply it to text classification. Existing techniques for such "distributional clustering" of words are agglomerative in nature and result in (i) sub-optimal word clusters and (ii) high computational cost. In order to explicitly capture the optimality of word clusters in an information theoretic framework, we first derive a global criterion for feature clustering. We then present a fast, divisive algorithm that monotonically decreases this objective function value. We show that our algorithm minimizes the "within-cluster Jensen-Shannon divergence" while simultaneously maximizing the "between-cluster Jensen-Shannon divergence". In comparison to the previously proposed agglomerative strategies our divisive algorithm is much faster and achieves comparable or higher classification accuracies. We further show that feature clustering is an effective technique for building smaller class models in hierarchical classification. We present detailed experimental results using Naive Bayes and Support Vector Machines on the 20Newsgroups data set and a 3-level hierarchy of HTML documents collected from the Open Directory project (www.dmoz.org).

•

[...]

TL;DR: This paper addresses a common methodological flaw in the comparison of variable selection methods by addressing the problem of cross-validation performance estimates of the different variable subsets used with computationally intensive search algorithms.

Abstract: This paper addresses a common methodological flaw in the comparison of variable selection methods. A practical approach to guide the search or the selection process is to compute cross-validation performance estimates of the different variable subsets. Used with computationally intensive search algorithms, these estimates may overfit and yield biased predictions. Therefore, they cannot be used reliably to compare two selection methods, as is shown by the empirical results of this paper. Instead, like in other instances of the model selection problem, independent test sets should be used for determining the final performance. The claims made in the literature about the superiority of more exhaustive search algorithms over simpler ones are also revisited, and some of them infirmed.

••

[...]

TL;DR: This work considers a binary classification problem where the mean and covariance matrix of each class are assumed to be known, and addresses the issue of robustness with respect to estimation errors via a simple modification of the input data.

Abstract: When constructing a classifier, the probability of correct classification of future data points should be maximized. We consider a binary classification problem where the mean and covariance matrix of each class are assumed to be known. No further assumptions are made with respect to the class-conditional distributions. Misclassification probabilities are then controlled in a worst-case setting: that is, under all possible choices of class-conditional densities with given mean and covariance matrix, we minimize the worst-case (maximum) probability of misclassification of future data points. For a linear decision boundary, this desideratum is translated in a very direct way into a (convex) second order cone optimization problem, with complexity similar to a support vector machine problem. The minimax problem can be interpreted geometrically as minimizing the maximum of the Mahalanobis distances to the two classes. We address the issue of robustness with respect to estimation errors (in the means and covariances of the classes) via a simple modification of the input data. We also show how to exploit Mercer kernels in this setting to obtain nonlinear decision boundaries, yielding a classifier which proves to be competitive with current methods, including support vector machines. An important feature of this method is that a worst-case bound on the probability of misclassification of future data is always obtained explicitly.

•

[...]

TL;DR: The method constructs a series of sparse linear SVMs to generate linear models that can generalize well, and uses a subset of nonzero weighted variables found by the linear models to produce a final nonlinear model.

Abstract: We describe a methodology for performing variable ranking and selection using support vector machines (SVMs). The method constructs a series of sparse linear SVMs to generate linear models that can generalize well, and uses a subset of nonzero weighted variables found by the linear models to produce a final nonlinear model. The method exploits the fact that a linear SVM (no kernels) with l1-norm regularization inherently performs variable selection as a side-effect of minimizing capacity of the SVM model. The distribution of the linear model weights provides a mechanism for ranking and interpreting the effects of variables. Starplots are used to visualize the magnitude and variance of the weights for each variable. We illustrate the effectiveness of the methodology on synthetic data, benchmark problems, and challenging regression problems in drug design. This method can dramatically reduce the number of variables and outperforms SVMs trained using all attributes and using the attributes selected according to correlation coefficients. The visualization of the resulting models is useful for understanding the role of underlying variables.

•

[...]

TL;DR: Grafting treats the selection of suitable features as an integral part of learning a predictor in a regularized learning framework, and operates in an incremental iterative fashion, gradually building up a feature set while training a predictor model using gradient descent.

Abstract: We present a novel and flexible approach to the problem of feature selection, called grafting. Rather than considering feature selection as separate from learning, grafting treats the selection of suitable features as an integral part of learning a predictor in a regularized learning framework. To make this regularized learning process sufficiently fast for large scale problems, grafting operates in an incremental iterative fashion, gradually building up a feature set while training a predictor model using gradient descent. At each iteration, a fast gradient-based heuristic is used to quickly assess which feature is most likely to improve the existing model, that feature is then added to the model, and the model is incrementally optimized using gradient descent. The algorithm scales linearly with the number of data points and at most quadratically with the number of features. Grafting can be used with a variety of predictor model classes, both linear and non-linear, and can be used for both classification and regression. Experiments are reported here on a variant of grafting for classification, using both linear and non-linear models, and using a logistic regression-inspired loss function. Results on a variety of synthetic and real world data sets are presented. Finally the relationship between grafting, stagewise additive modelling, and boosting is explored.

•

[...]

TL;DR: An approach to text categorization that combines distributional clustering of words and a Support Vector Machine (SVM) classifier with a word-cluster representation is studied, which significantly outperforms the word-based representation in terms of categorization accuracy or representation efficiency.

Abstract: We study an approach to text categorization that combines distributional clustering of words and a Support Vector Machine (SVM) classifier. This word-cluster representation is computed using the recently introduced Information Bottleneck method, which generates a compact and efficient representation of documents. When combined with the classification power of the SVM, this method yields high performance in text categorization. This novel combination of SVM with word-cluster representation is compared with SVM-based categorization using the simpler bag-of-words (BOW) representation. The comparison is performed over three known datasets. On one of these datasets (the 20 Newsgroups) the method based on word clusters significantly outperforms the word-based representation in terms of categorization accuracy or representation efficiency. On the two other sets (Reuters-21578 and WebKB) the word-based representation slightly outperforms the word-cluster representation. We investigate the potential reasons for this behavior and relate it to structural differences between the datasets.

••

[...]

TL;DR: 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 is presented.

Abstract: 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 Expectation-Maximization (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.

•

[...]

TL;DR: This paper proposes two mechanisms for representing a probabilistic distribution over link structures: reference uncertainty and existence uncertainty, and describes the appropriate conditions for using each model and present learning algorithms for each.

Abstract: Most real-world data is heterogeneous and richly interconnected. Examples include the Web, hypertext, bibliometric data and social networks. In contrast, most statistical learning methods work with "flat" data representations, forcing us to convert our data into a form that loses much of the link structure. The recently introduced framework of probabilistic relational models (PRMs) embraces the object-relational nature of structured data by capturing probabilistic interactions between attributes of related entities. In this paper, we extend this framework by modeling interactions between the attributes and the link structure itself. An advantage of our approach is a unified generative model for both content and relational structure. We propose two mechanisms for representing a probabilistic distribution over link structures: reference uncertainty and existence uncertainty. We describe the appropriate conditions for using each model and present learning algorithms for each. We present experimental results showing that the learned models can be used to predict link structure and, moreover, the observed link structure can be used to provide better predictions for the attributes in the model.

•

[...]

TL;DR: A new positive definite kernel f(A,B) defined over pairs of matrices A,B is derived based on the concept of principal angles between two linear subspaces and it is shown that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors to be mapped onto arbitrarily high-dimensional feature spaces.

Abstract: We consider the problem of learning with instances defined over a space of sets of vectors. We derive a new positive definite kernel f(A,B) defined over pairs of matrices A,B based on the concept of principal angles between two linear subspaces. We show that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors of A,B to be mapped onto arbitrarily high-dimensional feature spaces.We demonstrate the usage of the matrix-based kernel function f(A,B) with experiments on two visual tasks. The first task is the discrimination of "irregular" motion trajectory of an individual or a group of individuals in a video sequence. We use the SVM approach using f(A,B) where an input matrix represents the motion trajectory of a group of individuals over a certain (fixed) time frame. We show that the classification (irregular versus regular) greatly outperforms the conventional representation where all the trajectories form a single vector. The second application is the visual recognition of faces from input video sequences representing head motion and facial expressions where f(A,B) is used to compare two image sequences.