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 tree-augmented 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.

In this paper we propose the type of Bayesian networks that we call the hierarchical Bayesian network (HBN) classifiers. We present algorithms for the construction of the HBN classifiers and test them on the Reuters text categorization test collection.