A Simple Insight into Iterative Belief Propagation's Success

TL;DR

This paper reveals that iterative belief propagation in non-ergodic networks is equivalent to arc-consistency algorithms for zero-belief queries, establishing its soundness and limitations in inference.

Contribution

It demonstrates the equivalence between iterative belief propagation and arc-consistency, clarifying the inference power and limitations of loopy belief propagation and its extensions.

Findings

Belief propagation's zero-belief conclusions are sound and convergent.

Its inference power is comparable to arc-consistency algorithms.

The results apply to generalized belief propagation methods.

Abstract

In Non - ergodic belief networks the posterior belief OF many queries given evidence may become zero.The paper shows that WHEN belief propagation IS applied iteratively OVER arbitrary networks(the so called, iterative OR loopy belief propagation(IBP)) it IS identical TO an arc - consistency algorithm relative TO zero - belief queries(namely assessing zero posterior probabilities). This implies that zero - belief conclusions derived BY belief propagation converge AND are sound.More importantly it suggests that the inference power OF IBP IS AS strong AND AS weak, AS that OF arc - consistency.This allows the synthesis OF belief networks FOR which belief propagation IS useless ON one hand, AND focuses the investigation OF classes OF belief network FOR which belief propagation may be zero - complete.Finally, ALL the above conclusions apply also TO Generalized belief propagation algorithms that extend loopy belief propagation AND allow a crisper understanding OF their power.