  Recently several researchers have investigated techniques for using data to
learn Bayesian networks containing compact representations 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 typically apply non-Bayesian (or asymptotically Bayesian)
scoring functions such as MDL to evaluate the goodness-of-fit of networks to
the data. In this paper we investigate a Bayesian approach to learning Bayesian
networks that contain the more general decision-graph representations of the
CPDs. First, we describe how to evaluate the posterior probability that is, the
Bayesian score of such a network, given a database of observed cases. Second,
we describe various search spaces that can be used, in conjunction with a
scoring function and a search procedure, to identify one or more high-scoring
networks. Finally, we present an experimental evaluation of the search spaces,
using a greedy algorithm and a Bayesian scoring function.
