Results 1  10
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27
Empirical Analysis of Predictive Algorithm for Collaborative Filtering
 Proceedings of the 14 th Conference on Uncertainty in Artificial Intelligence
, 1998
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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 260 (24 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...
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 189 (6 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 Bayes Net Toolbox for MATLAB
 Computing Science and Statistics
, 2001
"... The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the ..."
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Cited by 176 (2 self)
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The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the web page has received over 28,000 hits since May 2000. In this paper, we discuss a broad spectrum of issues related to graphical models (directed and undirected), and describe, at a highlevel, how BNT was designed to cope with them all. We also compare BNT to other software packages for graphical models, and to the nascent OpenBayes effort.
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 136 (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...
An experimental comparison of several clustering and intialization methods
, 1998
"... We examine methods for clustering in high dimensions. In the first part of the paper, we perform an experimental comparison between three batch clustering algorithms: the Expectation–Maximization (EM) algorithm, a “winner take all ” version of the EM algorithm reminiscent of the Kmeans algorithm, a ..."
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Cited by 78 (0 self)
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We examine methods for clustering in high dimensions. In the first part of the paper, we perform an experimental comparison between three batch clustering algorithms: the Expectation–Maximization (EM) algorithm, a “winner take all ” version of the EM algorithm reminiscent of the Kmeans algorithm, and modelbased hierarchical agglomerative clustering. We learn naiveBayes models with a hidden root node, using highdimensional discretevariable data sets (both real and synthetic). We find that the EM algorithm significantly outperforms the other methods, and proceed to investigate the effect of various initialization schemes on the final solution produced by the EM algorithm. The initializations that we consider are (1) parameters sampled from an uninformative prior, (2) random perturbations of the marginal distribution of the data, and (3) the output of hierarchical agglomerative clustering. Although the methods are substantially different, they lead to learned models that are strikingly similar in quality. 1
The role of Occam’s Razor in knowledge discovery
 Data Mining and Knowledge Discovery
, 1999
"... Abstract. Many KDD systems incorporate an implicit or explicit preference for simpler models, but this use of “Occam’s razor ” has been strongly criticized by several authors (e.g., Schaffer, 1993; Webb, 1996). This controversy arises partly because Occam’s razor has been interpreted in two quite di ..."
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Cited by 78 (3 self)
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Abstract. Many KDD systems incorporate an implicit or explicit preference for simpler models, but this use of “Occam’s razor ” has been strongly criticized by several authors (e.g., Schaffer, 1993; Webb, 1996). This controversy arises partly because Occam’s razor has been interpreted in two quite different ways. The first interpretation (simplicity is a goal in itself) is essentially correct, but is at heart a preference for more comprehensible models. The second interpretation (simplicity leads to greater accuracy) is much more problematic. A critical review of the theoretical arguments for and against it shows that it is unfounded as a universal principle, and demonstrably false. A review of empirical evidence shows that it also fails as a practical heuristic. This article argues that its continued use in KDD risks causing significant opportunities to be missed, and should therefore be restricted to the comparatively few applications where it is appropriate. The article proposes and reviews the use of domain constraints as an alternative for avoiding overfitting, and examines possible methods for handling the accuracy–comprehensibility tradeoff.
Bayesian Averaging of Classifiers and the Overfitting Problem
 IN PROC. 17TH INTERNATIONAL CONF. ON MACHINE LEARNING
, 2000
"... Although Bayesian model averaging is theoretically the optimal method for combining learned models, it has seen very little use in machine learning. In this paper we study its application to combining rule sets, and compare it with bagging and partitioning, two popular but more ad hoc alternativ ..."
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Cited by 41 (2 self)
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Although Bayesian model averaging is theoretically the optimal method for combining learned models, it has seen very little use in machine learning. In this paper we study its application to combining rule sets, and compare it with bagging and partitioning, two popular but more ad hoc alternatives. Our experiments show that, surprisingly, Bayesian model averaging's error rates are consistently higher than the other methods'. Further investigation shows this to be due to a marked tendency to overfit on the part of Bayesian model averaging, contradicting previous beliefs that it solves (or avoids) the overfitting problem.
Accelerating EM for large databases
 Machine Learning
, 2001
"... The EM algorithm is a popular method for parameter estimation in a variety of problems involving missing data. However, the EM algorithm often requires signi cant computational resources and has been dismissed as impractical for large databases. We presenttwo approaches that signi cantly reduce the ..."
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Cited by 35 (1 self)
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The EM algorithm is a popular method for parameter estimation in a variety of problems involving missing data. However, the EM algorithm often requires signi cant computational resources and has been dismissed as impractical for large databases. We presenttwo approaches that signi cantly reduce the computational cost of applying the EM algorithm to databases with a large number of cases, including databases with large dimensionality. Both approaches are based on partial Esteps for which we can use the results of Neal and Hinton (1998) to obtain the standard convergence guarantees of EM. The rst approach is a version of the incremental EM, described in Neal and Hinton (1998), which cycles through data cases in blocks. The number of cases in each block dramatically e ects the e ciency of the algorithm. We provide a method for selecting a near optimal block size. The second approach, which we call lazy EM, will, at scheduled iterations, evaluate the signi cance of each data case and then proceed for several iterations actively using only the signi cant cases. We demonstrate that both methods can signi cantly reduce computational costs through their application to highdimensional realworld and synthetic mixture modeling problems for large databases. Keywords: Expectation Maximization Algorithm, incremental EM, lazy EM, online EM, data blocking, mixture models, clustering.