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

arXiv: https://arxiv.org/abs/1812.01339 · HTML: https://mlsanity.com/paper/1812.01339/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2018.

## Built on by (most cited first, 4 of 4)

- [Convex Combination Belief Propagation Algorithms](https://mlsanity.com/paper/2105.12815/) (2021)
- [Understanding the Behavior of Belief Propagation](https://mlsanity.com/paper/2209.05464/) (2022)
- [Exact Fractional Inference via Re-Parametrization & Interpolation between Tree-Re-Weighted- and Belief Propagation- Algorithms](https://mlsanity.com/paper/2301.10369/) (2023)
- [Minima and Critical Points of the Bethe Free Energy Are Invariant Under Deformation Retractions of Factor Graphs](https://mlsanity.com/paper/2510.05380/) (2025)

## Abstract (arXiv)

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.