Belief-Propagation Guided Monte-Carlo Sampling

TL;DR

This paper introduces a Monte-Carlo sampling method guided by Belief Propagation, effectively sampling from discrete models, especially on locally tree-like graphs, and demonstrates its superior performance on spin-glass models.

Contribution

It combines Belief Propagation with a heat bath approach to improve Monte-Carlo sampling efficiency on complex graph models.

Findings

Effective on locally tree-like graphs

State-of-the-art results on spin-glass models

Combines Belief Propagation with detailed-balanced sampling

Abstract

A Monte-Carlo algorithm for discrete statistical models that combines the full power of the Belief Propagation algorithm with the advantages of a detailed-balanced heat bath approach is presented. A sub-tree inside the factor graph is first extracted randomly; Belief Propagation is then used as a perfect sampler to generate a configuration on the tree given the boundary conditions and the procedure is iterated. This appoach is best adapted for locally tree like graphs, it is therefore tested on the hard cases of spin-glass models for random graphs demonstrating its state-of-the art status in those cases.