Hot Coupling: A Particle Approach to Inference and Normalization on Pairwise Undirected Graphs

Abstract

This paper presents a new sampling algorithm for approximating func- tions of variables representable as undirected graphical models of arbi- trary connectivity with pairwise potentials, as well as for estimating the notoriously dif(cid:2)cult partition function of the graph. The algorithm (cid:2)ts into the framework of sequential Monte Carlo methods rather than the more widely used MCMC, and relies on constructing a sequence of in- termediate distributions which get closer to the desired one. While the idea of using (cid:147)tempered(cid:148) proposals is known, we construct a novel se- quence of target distributions where, rather than dropping a global tem- perature parameter, we sequentially couple individual pairs of variables that are, initially, sampled exactly from a spanning tree of the variables. We present experimental results on inference and estimation of the parti- tion function for sparse and densely-connected graphs.