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644
Statistical pattern recognition: A review
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2000
"... The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques ..."
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Cited by 998 (30 self)
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The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have bean receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the wellknown methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.
Stochastic volatility: likelihood inference and comparison with ARCH models
 Review of Economic Studies
, 1998
"... In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihoodbased framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offse ..."
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Cited by 582 (41 self)
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In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihoodbased framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offset mixture model, followed by an importance reweighting procedure. This approach is compared with several alternative methods using real data. The paper also develops simulationbased methods for filtering, likelihood evaluation and model failure diagnostics. The issue of model choice using nonnested likelihood ratios and Bayes factors is also investigated. These methods are used to compare the fit of stochastic volatility and GARCH models. All the procedures are illustrated in detail. 1.
ModelBased Clustering, Discriminant Analysis, and Density Estimation
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little ..."
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Cited by 557 (28 self)
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Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as \How many clusters are there?", "Which clustering method should be used?" and \How should outliers be handled?". We outline a general methodology for modelbased clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology, a...
Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
"... [Read before The Royal Statistical Society at a meeting organized by the Research ..."
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Cited by 435 (4 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research
Unsupervised learning of finite mixture models
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectationmaximization (EM) alg ..."
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Cited by 415 (22 self)
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This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectationmaximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models; instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm; in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach.
A Variational Bayesian Framework for Graphical Models
 In Advances in Neural Information Processing Systems 12
, 2000
"... This paper presents a novel practical framework for Bayesian model averaging and model selection in probabilistic graphical models. Our approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner. These posteriors ..."
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Cited by 271 (7 self)
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This paper presents a novel practical framework for Bayesian model averaging and model selection in probabilistic graphical models. Our approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner. These posteriors fall out of a freeform optimization procedure, which naturally incorporates conjugate priors. Unlike in large sample approximations, the posteriors are generally nonGaussian and no Hessian needs to be computed. Predictive quantities are obtained analytically. The resulting algorithm generalizes the standard Expectation Maximization algorithm, and its convergence is guaranteed. We demonstrate that this approach can be applied to a large class of models in several domains, including mixture models and source separation. 1 Introduction A standard method to learn a graphical model 1 from data is maximum likelihood (ML). Given a training dataset, ML estimates a single optimal value f...
The Infinite Gaussian Mixture Model
 In Advances in Neural Information Processing Systems 12
, 2000
"... In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the difficult problem of finding the "right" number of mixture components. Inference in the model is ..."
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Cited by 256 (8 self)
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In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the difficult problem of finding the "right" number of mixture components. Inference in the model is done using an efficient parameterfree Markov Chain that relies entirely on Gibbs sampling.
Recognizing Imprecisely Localized, Partially Occluded and Expression Variant Faces from a Single Sample per Class
, 2002
"... The classical way of attempting to solve the face (or object) recognition problem is by using large and representative datasets. In many applications though, only one sample per class is available to the system. In this contribution, we describe a probabilistic approach that is able to compensate fo ..."
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Cited by 212 (8 self)
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The classical way of attempting to solve the face (or object) recognition problem is by using large and representative datasets. In many applications though, only one sample per class is available to the system. In this contribution, we describe a probabilistic approach that is able to compensate for imprecisely localized, partially occluded and expression variant faces even when only one single training sample per class is available to the system. To solve the localization problem, we find the subspace (within the feature space, e.g. eigenspace) that represents this error for each of the training images. To resolve the occlusion problem, each face is divided into k local regions which are analyzed in isolation. In contrast with other approaches, where a simple voting space is used, we present a probabilistic method that analyzes how "good" a local match is. To make the recognition system less sensitive to the differences between the facial expression displayed on the training and the testing images, we weight the results obtained on each local area on the bases of how much of this local area is affected by the expression displayed on the current test image.
Inferring Parameters and Structure of Latent Variable Models by Variational Bayes
, 1999
"... Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior ..."
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Cited by 196 (1 self)
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Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior distributions over the parameters remains a difficult problem. Moreover, learning the structure of models with latent variables, for which the Bayesian approach is crucial, is yet a harder problem. In this paper I present the Variational Bayes framework, which provides a solution to these problems. This approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner without resorting to sampling methods. Unlike in the Laplace approximation, these posteriors are generally nonGaussian and no Hessian needs to be computed. The resulting algorithm generalizes the standard Expectation Maximization a...