Loop Corrected Belief Propagation

We propose a method for improving Belief Propagation (BP) that takes into account the influence of loops in the graphical model. The method is a variation on and generalization of the method recently introduced by Montanari and Rizzo [2005]. It consists of two steps: (i) standard BP is used to calculate cavity distributions for each variable (i.e. probability distributions on the Markov blanket of a variable for a modified graphical model, in which the factors involving that variable have been removed); (ii) all cavity distributions are combined by a messagepassing algorithm to obtain consistent single node marginals. The method is exact if the graphical model contains a single loop. The complexity of the method is exponential in the size of the Markov blankets. The results are very accurate in general: the error is often several orders of magnitude smaller than that of standard BP, as illustrated by numerical experiments.