Learning Bayesian networks: The combination of knowledge and statistical data
 David Heckerman,
 Dan Geiger,
 David M. Chickering
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Abstract
We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption oflikelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—aprior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highestscoring network structures in the special case where every node has at mostk=1 parent. For the general case (k>1), which is NPhard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesiannetwork learning algorithms, and apply this approach to a comparison of various approaches.
 Title
 Learning Bayesian networks: The combination of knowledge and statistical data
 Journal

Machine Learning
Volume 20, Issue 3 , pp 197243
 Cover Date
 199509
 DOI
 10.1007/BF00994016
 Print ISSN
 08856125
 Online ISSN
 15730565
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Bayesian networks
 learning
 Dirichlet
 likelihood equivalence
 maximum branching
 heuristic search
 Industry Sectors
 Authors

 David Heckerman ^{(1)}
 Dan Geiger ^{(1)}
 David M. Chickering ^{(1)}
 Author Affiliations

 1. Microsoft Research, 9S, 980526399, Redmond, WA