Counting Belief Propagation

TL;DR

Counting Belief Propagation introduces a new algorithm that exploits symmetries in graphical models to significantly improve inference efficiency, applicable to various AI tasks like relational models and boolean counting.

Contribution

The paper presents counting BP, a simple yet effective method that compresses factor graphs by exploiting symmetries, enabling faster belief propagation inference.

Findings

Counting BP achieves orders of magnitude speedup in inference tasks.

It effectively compresses factor graphs by grouping indistinguishable nodes and factors.

Applicable to dynamic relational models and boolean model counting.

Abstract

A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by efficient inference techniques such as belief propagation (BP). In this paper, we present a new and simple BP algorithm, called counting BP, that exploits such additional symmetries. Starting from a given factor graph, counting BP first constructs a compressed factor graph of clusternodes and clusterfactors, corresponding to sets of nodes and factors that are indistinguishable given the evidence. Then it runs a modified BP algorithm on the compressed graph that is equivalent to running BP on the original factor graph. Our experiments show that counting BP is applicable to a variety of important AI tasks such as (dynamic) relational models and boolean model counting, and that significant efficiency gains are obtainable, often by orders of magnitude.