# Self-Guided Belief Propagation -- A Homotopy Continuation Method

## TL;DR

Self-guided belief propagation (SBP) introduces a homotopy continuation approach that gradually incorporates pairwise potentials, leading to more accurate and stable probabilistic inference solutions in graphical models, especially when traditional BP fails to converge.

## Contribution

This work presents SBP, a novel homotopy continuation method for belief propagation that guarantees convergence to a global optimum in certain models and improves accuracy in general.

## Key findings

- SBP outperforms BP in accuracy when BP converges.
- SBP finds unique, stable solutions when BP does not converge.
- SBP converges to the global optimum for attractive models.

## Abstract

Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually. This homotopy continuation method converges to a unique solution and increases the accuracy without increasing the computational burden. We provide a formal analysis to demonstrate that SBP finds the global optimum of the Bethe approximation for attractive models where all variables favor the same state. Moreover, we apply SBP to various graphs with random potentials and empirically show that: (i) SBP is superior in terms of accuracy whenever BP converges, and (ii) SBP obtains a unique, stable, and accurate solution whenever BP does not converge.