Self-Guided Belief Propagation -- A Homotopy Continuation Method

We propose self-guided belief propagation (SBP) that modifies belief propagation (BP) by incorporating the pairwise potentials only gradually. This homotopy continuation method converges to a unique solution and increases the accuracy without increasing the computational burden. We apply SBP to grid graphs, complete graphs, and random graphs with random Ising potentials and show that: (i) SBP is superior in terms of accuracy whenever BP converges, and (ii) SBP obtains a unique, stable, and accurate solution whenever BP does not converge. We further provide a formal analysis to demonstrate that SBP obtains the global optimum of the Bethe approximation for attractive models with unidirectional fields.