Loop corrected belief propagation ## AbstractWe 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 message-passing 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.
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