STATS 375 - Project Proposal

Belief propagation is a message-passing algorithm for performing inference in graphical models that has been implemented in a variety of domains including artificial intelligence, information theory and statistical physics. As we know, BP provides exact results only on a relatively restrictive subclass of problems, when the graphical model is a tree (or more generally if each connected component of the graph is a tree). In all other graphs that contain loops, we are left with what is called Loopy Belief Propagation. This algorithm can actually yield sufficiently accurate approximations in some specific cases [1]; the most prominent example is the near-Shannon limit performance of “Turbo Codes”. However, in the general case the approximate marginals calculated by LBP can have large errors. The motivation, then, for an algorithm that provides accurate results on a wider domain, is obvious. Several such solutions have been suggested. Among others are “Loop Calculus”, (or “Loop Series”) [2, 3] and “Loop Corrected Cavity Method” [4, 5].