Asymptotic Model Selection for Directed Networks with Hidden Variables
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: Asymptotic Model Selection for Directed Networks with Hidden Variables
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 our 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 naive Bayes model with a hidden root node. 1 Introduction Learning Bayesian networks from data extends their applicability to situations where data is easily obtained and expert knowledge is expensive. Consequently, it has been the subject of much research in recent years (see e.g., Heckerman  and Buntine ). Researchers have pursued two types of approaches ...
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