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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 domainâ€™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.
Fast Factored Density Estimation and Compression with Bayesian Networks
, 2002
"... my family especially my father, Donald. iv Abstract Many important data analysis tasks can be addressed by formulating them as probability estimation problems. For example, a popular general approach to automatic classification problems is to learn a probabilistic model of each class from data in ..."
Abstract

Cited by 3 (1 self)
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my family especially my father, Donald. iv Abstract Many important data analysis tasks can be addressed by formulating them as probability estimation problems. For example, a popular general approach to automatic classification problems is to learn a probabilistic model of each class from data in which the classes are known, and then use Bayes's rule with these models to predict the correct classes of other data for which they are not known. Anomaly detection and scientific discovery tasks can often be addressed by learning probability models over possible events and then looking for events to which these models assign low probabilities. Many data compression algorithms such as Huffman coding and arithmetic coding rely on probabilistic models of the data stream in order achieve high compression rates.