A Simple Insight into Iterative Belief Propagation's Success
This provides theoretical insight into the limitations and applicability of belief propagation algorithms for probabilistic inference in belief networks, but it is incremental as it builds on existing arc-consistency concepts.
The paper shows that iterative belief propagation (IBP) is equivalent to an arc-consistency algorithm for zero-belief queries, implying that zero-belief conclusions from IBP converge and are sound, and that IBP's inference power matches that of arc-consistency.
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.