Validity Estimates for Loopy Belief Propagation on Binary Real-world Networks

A computationally efficient method is introduced to estimate the validity of the BP method as a function of graph topology, the connectivity strength, frustration and network size and it is found that BP always performs better than MF.

Abstract

We introduce a computationally efficient method to estimate the validity of the BP method as a function of graph topology, the connectivity strength, frustration and network size. We present numerical results that demonstrate the correctness of our estimates for the uniform random model and for a real-world network (“C. Elegans”). Although the method is restricted to pair-wise interactions, no local evidence (zero “biases”) and binary variables, we believe that its predictions correctly capture the limitations of BP for inference and MAP estimation on arbitrary graphical models. Using this approach, we find that BP always performs better than MF. Especially for large networks with broad degree distributions (such as scale-free networks) BP turns out to significantly outperform MF. 1