Anytime Belief Propagation Using Sparse Domains

TL;DR

This paper introduces an anytime belief propagation algorithm that operates on sparse domains, offering faster inference with consistent marginals and improved accuracy when stopped early, especially on large-scale problems.

Contribution

It presents a novel message passing method that incrementally grows sparse domains and converges to BP fixed points, enabling anytime inference with speedups.

Findings

Up to 25x speedup on grid models

Up to 6x speedup on NLP tasks

Provides local anytime consistency and fast convergence

Abstract

Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but lacks important anytime properties such as: 1) providing accurate and consistent marginals when stopped early, 2) improving the approximation when run longer, and 3) converging to the fixed point of BP. To this end, we propose a message passing algorithm that works on sparse (partially instantiated) domains, and converges to consistent marginals using dynamic message scheduling. The algorithm grows the sparse domains incrementally, selecting the next value to add using prioritization schemes based on the gradients of the marginal inference objective. Our experiments demonstrate local anytime consistency and fast convergence, providing significant speedups over BP to obtain low-error marginals: up to 25 times on grid models, and up to 6 times on a real-world natural language processing task.