When discriminative learning of Bayesian network parameters is easy

Authors:
Hannes Wettig;Peter Grunwald;Teemu Roos;Petri Myllymaki;Henry Tirri
Affiliations:
Complex Systems Computation Group, Helsinki Institute for Information Technology, University of Helsinki & Helsinki University of Technology, Finland;Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands;Complex Systems Computation Group, Helsinki Institute for Information Technology, University of Helsinki & Helsinki University of Technology, Finland;Complex Systems Computation Group, Helsinki Institute for Information Technology, University of Helsinki & Helsinki University of Technology, Finland;Complex Systems Computation Group, Helsinki Institute for Information Technology, University of Helsinki & Helsinki University of Technology, Finland
Venue:
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Year:
2003

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Abstract

Bayesian network models are widely used for discriminative prediction tasks such as classification. Usually their parameters are determined using 'unsupervised' methods such as maximization of the joint likelihood. The reason is often that it is unclear how to find the parameters maximizing the conditional (supervised) likelihood. We show how the discriminative learning problem can be solved efficiently for a large class of Bayesian network models, including the Naive Bayes (NB) and tree-augmented Naive Bayes (TAN) models. We do this by showing that under a certain general condition on the network structure, the discriminative learning problem is exactly equivalent to logistic regression with unconstrained convex parameter spaces. Hitherto this was known only for Naive Bayes models. Since logistic regression models have a concave log-likelihood surface, the global maximum can be easily found by local optimization methods.