Loopy Belief Propogation and Gibbs Measures

TL;DR

This paper investigates the convergence of loopy belief propagation (LBP) by linking it to Gibbs measures and their phases, providing new conditions for convergence and insights into the algorithm's mechanics.

Contribution

It introduces easily testable conditions for LBP convergence based on Gibbs measure theory, connecting convergence failure to phase multiplicity.

Findings

Convergence of LBP is related to the existence of a Gibbs measure limit.

Failure of convergence indicates multiple phases in the Gibbs specification.

Provides new insights into the mechanics of LBP.

Abstract

We address the question of convergence in the loopy belief propagation (LBP) algorithm. Specifically, we relate convergence of LBP to the existence of a weak limit for a sequence of Gibbs measures defined on the LBP s associated computation tree.Using tools FROM the theory OF Gibbs measures we develop easily testable sufficient conditions FOR convergence.The failure OF convergence OF LBP implies the existence OF multiple phases FOR the associated Gibbs specification.These results give new insight INTO the mechanics OF the algorithm.