On Supervised Learning of Bayesian Network Parameters

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 likelihood maximization, as it has not been clear how to find the parameters maximizing the supervised likelihood or posterior globally. In this paper we show how this supervised learning problem can be solved efficiently for a large class of Bayesian network models, including the Naive Bayes (NB) and Tree-augmented NB (TAN) classifiers. We show that there exists an alternative parameterization of these models in which the supervised likelihood becomes concave. From this result it follows that there can be at most one maximum, easily found by local optimization methods.