Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing

TL;DR

Residual Belief Propagation (RBP) is an informed, asynchronous message scheduling algorithm that accelerates convergence in belief propagation, outperforming existing methods on synthetic and real-world probabilistic graphical models.

Contribution

The paper introduces RBP, a novel asynchronous message scheduling method that improves convergence speed and reliability in belief propagation for probabilistic inference.

Findings

RBP converges more often than state-of-the-art methods.

RBP reduces running time until convergence.

RBP outperforms existing methods on various problems.

Abstract

Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, real-life inference tasks. While it is widely recognized that the scheduling of messages in these algorithms may have significant consequences, this issue remains largely unexplored. In this work, we address the question of how to schedule messages for asynchronous propagation so that a fixed point is reached faster and more often. We first show that any reasonable asynchronous BP converges to a unique fixed point under conditions similar to those that guarantee convergence of synchronous BP. In addition, we show that the convergence rate of a simple round-robin schedule is at least as good as that of synchronous propagation. We then propose residual belief propagation (RBP), a novel, easy-to-implement, asynchronous propagation algorithm that schedules messages in an informed way, that pushes down a bound on the distance from the fixed point. Finally, we demonstrate the superiority of RBP over state-of-the-art methods for a variety of challenging synthetic and real-life problems: RBP converges significantly more often than other methods; and it significantly reduces running time until convergence, even when other methods converge.