Validity estimates for loopy belief propagation on binary real-world networks
Joris Mooij and Bert Kappen
In: nips 2004, 13-18 Dec 2004, Vancouver, Canada.
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.