@MISC{Chickering96learningbayesian, author = {David Maxwell Chickering}, title = {Learning Bayesian Networks is NP-Complete}, year = {1996} }

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Algorithms for learning Bayesian networks from data havetwo components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodness-of-fit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et al. (1995) introduce a Bayesian metric, called the BDe metric, that computes the relative posterior probabilityofanetwork structure given data. In this paper, we show that the search problem of identifying a Bayesian network---among those where each node has at most K parents---that has a relative posterior probability greater than a given constant is NP-complete, when the BDe metric is used. 12.1