Applications of Gibbs measure theory to Loopy BP algorithm

Abstract

In this paper, we pursue application of Gibbs measure theory to LBP in two ways. First, we show this theory can be applied directly to LBP for factor graphs, where one can use higher-order potentials. Consequently, we show beliefs are just marginal probabilities for a certain Gibbs measure on a computation tree. We also give a convergence criterion using this tree. Second, to see the usefulness of this approach, we apply a well-known general condition and a special condition, which are developed in Gibbs measure theory, to LBP. We compare these two criteria and another criterion derived by the best present result. Consequently, we show that the special condition is better than the others and also show the general condition is better than the best present result when the influence of one-body potentials is sufficiently large. These results surely encourage the use of Gibbs measure theory in this area.