Learning Bayesian Networks: The Combination of Knowledge and Statistical Data

We describe algorithms for learning Bayesian networks from a combination of\nuser knowledge and statistical data. The algorithms have two components: a\nscoring metric and a search procedure. The scoring metric takes a network\nstructure, statistical data, and a user's prior knowledge, and returns a score\nproportional to the posterior probability of the network structure given the\ndata. The search procedure generates networks for evaluation by the scoring\nmetric. Our contributions are threefold. First, we identify two important\nproperties of metrics, which we call event equivalence and parameter\nmodularity. These properties have been mostly ignored, but when combined,\ngreatly simplify the encoding of a user's prior knowledge. In particular, a\nuser can express her knowledge-for the most part-as a single prior Bayesian\nnetwork for the domain. Second, we describe local search and annealing\nalgorithms to be used in conjunction with scoring metrics. In the special case\nwhere each node has at most one parent, we show that heuristic search can be\nreplaced with a polynomial algorithm to identify the networks with the highest\nscore. Third, we describe a methodology for evaluating Bayesian-network\nlearning algorithms. We apply this approach to a comparison of metrics and\nsearch procedures.\n

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