A Bayesian approach to learning Bayesian networks with local structure

Recently several researchers have investi-gated techniques for using data to learn Bayesian networks containing compact rep-resentations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, researchers typi-cally apply non-Bayesian (or asymptotically Bayesian) scoring functions such as MDL to evaluate the goodness-of-t of networks to the data. In this paper we investigate a Bayesian ap-proach to learning Bayesian networks that contain the more general decision-graph rep-resentations of the CPDs. First, we describe how to evaluate the posterior probability| that is, the Bayesian score|of such a net-work, given a database of observed cases. Second, we describe various search spaces that can be used, in conjunction with a scor-ing function and a search procedure, to iden-tify one or more high-scoring networks. Fi-nally, we present an experimental evaluation of the search spaces, using a greedy algorithm and a Bayesian scoring function.