Fractional Belief Propagation

We consider loopy belief propagation for approximate inference in prob- abilistic graphical models. A limitation of the standard algorithm is that clique marginals are computed as if there were no loops in the graph. To overcome this limitation, we introduce fractional belief propagation. Fractional belief propagation is formulated in terms of a family of ap- proximate free energies, which includes the Bethe free energy and the naive mean-field free as special cases. Using the linear response correc- tion of the clique marginals, the scale parameters can be tuned.