Bayesian Model Scoring in Markov Random Fields

Scoring structures of undirected graphical models by means of evaluating the marginal likelihood is very hard. The main reason is the presence of the partition functionwhich 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 approximate allremaining intractable quantities using belief propagation and the linear response approximation.