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Divergence measures and message passing

This paper presents a unifying view of messagepassing algorithms, as methods to approximate a complex Bayesian network by a simpler network with minimum information divergence. In this view, the difference between mean-field methods and belief propagation is not the amount of structure they model, but only the measure of loss they minimize (‘exclusive’ versus ‘inclusive’ Kullback-Leibler divergence). In each case, message-passing arises by minimizing a localized version of the divergence, local to each factor. By examining these divergence measures, we can intuit the types of solution they prefer (symmetry-breaking, for example) and their suitability for different tasks. Furthermore, by considering a wider variety of divergence measures (such as alpha-divergences), we can achieve different complexity and performance goals.