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Mixnets: Factored Mixtures of Gaussians in Bayesian Networks with Mixed Continuous And Discrete Variables
, 2000
"... Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in lowdimensional continuous spaces. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kdtrees ..."
Abstract

Cited by 7 (2 self)
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Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in lowdimensional continuous spaces. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kdtrees (Moore, 1999). In this paper, we propose a kind of Bayesian network in which lowdimensional mixtures of Gaussians over different subsets of the domain’s variables are combined into a coherent joint probability model over the entire domain. The network is also capable of modeling complex dependencies between discrete variables and continuous variables without requiring discretization of the continuous variables. We present efficient heuristic algorithms for automatically learning these networks from data, and perform comparative experiments illustrating how well these networks model real scientific data and synthetic data. We also briefly discuss some possible improvements to the networks, as well as possible applications.
Supervised Learning of Bayesian Network Parameters Made Easy
 Level Perspective on Branch Architecture Performance, IEEE Micro28
, 2002
"... Bayesian network models are widely used for supervised prediction tasks such as classification. Usually the parameters of such models are determined using `unsupervised' methods such as maximization of the joint likelihood. In many cases, the reason is that it is not clear how to find the parameters ..."
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Cited by 4 (1 self)
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Bayesian network models are widely used for supervised prediction tasks such as classification. Usually the parameters of such models are determined using `unsupervised' methods such as maximization of the joint likelihood. In many cases, the reason is that it is not clear how to find the parameters maximizing the supervised (conditional) likelihood. We show how the supervised learning problem can be solved e#ciently for a large class of Bayesian network models, including the Naive Bayes (NB) and treeaugmented NB (TAN) classifiers. We do this by showing that under a certain general condition on the network structure, the supervised learning problem is exactly equivalent to logistic regression. Hitherto this was known only for Naive Bayes models. Since logistic regression models have a concave loglikelihood surface, the global maximum can be easily found by local optimization methods.
Interpolating conditional density trees
 A. Darwiche, N. Friedman (Eds.), Uncertainty in Artificial Intelligence
, 2002
"... Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lowerdimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such models can be very computationally expensive when there are ..."
Abstract

Cited by 4 (0 self)
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Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lowerdimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such models can be very computationally expensive when there are many datapoints and many continuous variables with complex nonlinear relationships, particularly when no good ways of decomposing the joint distribution are known a priori. In such situations, previous research has generally focused on the use of discretization techniques in which each continuous variable has a single discretization that is used throughout the entire network. In this paper, we present and compare a wide variety of treebased algorithms for learning and evaluating conditional density estimates over continuous variables. These trees can be thought of as discretizations that vary according to the particular interactions being modeled; however, the density within a given leaf of the tree need not be assumed constant, and we show that such nonuniform leaf densities lead to more accurate density estimation. We have developed Bayesian network structurelearning algorithms that employ these treebased conditional density representations, and we show that they can be used to practically learn complex joint probability models over dozens of continuous variables from thousands of datapoints. We focus on nding models that are simultaneously accurate, fast to learn, and fast to evaluate once they are learned.