Learning Bayesian Networks: The Combination of Knowledge and Statistical Data

David Heckerman, Dan Geiger, and David M. Chickering

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure, statistical data, and a user’s prior knowledge, and returns a score proportional to the posterior probability of the network structure given the data. The search procedure generates networks for evaluation by the scoring metric. Our contributions are threefold. First, we identify two important properties of metrics, which we call score equivalence and parameter modu. iarity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user’s prior knowledge. In particular, a user can express his knowledge--for the most part--as a single prior Bayesian network for the domain. Second, we describe greedy hill-climbing and annealing search algorithms to be used in conjunction with scoring metrics. In the spec. is] case where each node has at most one parent, we show that heuristic search can be replaced with a polynomial algorithm to identify the networks with the highest score. Third, we describe a methodology for evaluating Bayesian-network learning algorithms. We apply this approach to a comparison of our metrics and search procedures.

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