Supervised Learning of Bayesian Network Parameters Made Easy

Bayesian network models are widely used for supervised prediction tasks such as classi cation. 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 nd the parameters maximizing the supervised (conditional) likelihood. We show how the supervised learning problem can be solved eciently for a large class of Bayesian network models, including the Naive Bayes (NB) and tree-augmented NB (TAN) classi ers. 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