Sufficient conditions for convergence of Loopy Belief Propagation

TL;DR

This paper establishes new sufficient conditions guaranteeing the convergence of Loopy Belief Propagation to a unique fixed point, especially sharp for binary variables with ferromagnetic or anti-ferromagnetic interactions.

Contribution

It introduces improved and sharper sufficient conditions for the convergence of Loopy Belief Propagation, advancing theoretical understanding of its behavior.

Findings

Conditions are sharp for binary variables with ferromagnetic interactions.

New conditions improve upon previous convergence criteria.

Results enhance theoretical guarantees for Loopy Belief Propagation.

Abstract

We derive novel sufficient conditions for convergence of Loopy Belief Propagation (also known as the Sum-Product algorithm) to a unique fixed point. Our results improve upon previously known conditions. For binary variables with (anti-)ferromagnetic interactions, our conditions seem to be sharp.