Bayesian Model Scoring in Markov Random Fields

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Sridevi Parise, Max Welling


Scoring structures of undirected graphical models by means of evaluating the marginal likelihood is very hard. The main reason is the presence of the parti- tion function which is intractable to evaluate, let alone integrate over. We propose to approximate the marginal likelihood by employing two levels of approximation: we assume normality of the posterior (the Laplace approximation) and approxi- mate all remaining intractable quantities using belief propagation and the linear response approximation. This results in a fast procedure for model scoring. Em- pirically, we find that our procedure has about two orders of magnitude better accuracy than standard BIC methods for small datasets, but deteriorates when the size of the dataset grows.