Loopy Belief Propagation in the Presence of Determinism

It is well known that loopy Belief propagation (LBP) performs poorly on probabilistic graphical models (PGMs) with determinism. In this paper, we propose a new method for remedying this problem. The key idea in our method is finding a reparameterization of the graphical model such that LBP, when run on the reparameterization, is likely to have better convergence properties than LBP on the original graphical model. We propose several schemes for finding such reparameterizations, all of which leverage unique properties of zeros as well as research on LBP convergence done over the last decade. Our experimental evaluation on a variety of PGMs clearly demonstrates the promise of our method – it often yields accuracy and convergence time improvements of an order of magnitude or more over LBP.