Asymptotic Model Selection for Directed Networks with Hidden Variables

Dan Geiger, David Heckerman, and Christopher Meek

Abstract

We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as out extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian network with hidden variables is the rank of the Jacobian matrix of the transformation between the parameters of the network and the parameters of the observable variables. We compute the dimensions of several networks including the naïve Bayes model with a hidden root node.

Details

Publication typeTechReport
URLhttp://www.mkp.com/
NumberMSR-TR-96-07
Pages17
InstitutionMicrosoft Research
PublisherMorgan Kaufmann Publishers
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