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Journal of Machine Learning Research, Volume 1
Leslie Pack Kaelbling, Editor

Learning with Mixtures of Trees

Marina Meila
Department of Statistics
University of Washington
Seattle, WA 98195-4322, USA

Michael I. Jordan
Division of Computer Science and Department of Statistics
University of California
Berkeley, CA 94720-1776, USA


This paper describes the mixtures-of-trees model, a probabilistic model for discrete multidimensional domains. Mixtures-of-trees generalize the probabilistic trees of [Chow, Liu 1968] in a different and complementary direction to that of Bayesian networks. We present efficient algorithms for learning mixtures-of-trees models in maximum likelihood and Bayesian frameworks. We also discuss additional efficiencies that can be obtained when data are ``sparse,'' and we present data structures and algorithms that exploit such sparseness. Experimental results demonstrate the performance of the model for both density estimation and classification. We also discuss the sense in which tree-based classifiers perform an implicit form of feature selection, and demonstrate a resulting insensitivity to irrelevant attributes.

Journal of Machine Learning Research 2000-10-19