Convex Combination Belief Propagation Algorithms

TL;DR

This paper introduces modified belief propagation algorithms that guarantee convergence to unique solutions on complex graphical models, addressing limitations of traditional methods in loopy graphs.

Contribution

The paper proposes new message passing algorithms that ensure convergence and uniqueness in inference for arbitrary graphical models, even with complex topologies.

Findings

Algorithms converge on complex graphs where standard belief propagation fails.

Modified methods guarantee convergence to a unique solution.

Effective for inference in challenging graphical model structures.

Abstract

We present new message passing algorithms for performing inference with graphical models. Our methods are designed for the most difficult inference problems where loopy belief propagation and other heuristics fail to converge. Belief propagation is guaranteed to converge when the underlying graphical model is acyclic, but can fail to converge and is sensitive to initialization when the underlying graph has complex topology. This paper describes modifications to the standard belief propagation algorithms that lead to methods that converge to unique solutions on graphical models with arbitrary topology and potential functions.