Asymptotic model selection for naive Bayesian networks

Authors:
Dmitry Rusakov;Dan Geiger
Affiliations:
Computer Science Department, Technion - Israel Institute of Technology, Haifa, Israel;Computer Science Department, Technion - Israel Institute of Technology, Haifa, Israel
Venue:
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Year:
2002

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Abstract

We develop a closed form asymptotic formula to compute the marginal likelihood of data given a naive Bayesian network model with two hidden states and binary features. This formula deviates from the standard BIC score. Our work provides a concrete example that the BIC score is generally not valid for statistical models that belong to a stratified exponential family. This stands in contrast to linear and curved exponential families, where the BIC score has been proven to provide a correct approximation for the marginal likelihood.