Optimizing Reweighted Belief Propagation for Distributed Likelihood Fusion Problems

TL;DR

This paper enhances belief propagation for distributed likelihood fusion by analyzing reweighted BP, deriving convergence conditions, and demonstrating faster convergence compared to standard belief consensus.

Contribution

It introduces a linear formulation of reweighted BP for likelihood fusion, providing analytical convergence conditions and optimization of convergence speed.

Findings

Reweighted BP converges faster than standard belief consensus.

Analytical convergence conditions are derived for specific graph types.

Optimized reweighting improves distributed inference efficiency.

Abstract

Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for certain types of problems are convergence properties understood. We extend this knowledge by investigating the use of reweighted BP for distributed likelihood fusion problems, which are characterized by equality constraints along possibly short cycles. Through a linear formulation of BP, we are able to analytically derive convergence conditions for certain types of graphs and optimize the convergence speed. We compare with standard belief consensus and observe significantly faster convergence.