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

This paper presents a new sampling algorithm for approximating functions of variables representable as undirected graphical models of arbitrary connectivity with pairwise potentials, as well as for estimating the notoriously difficult partition function of the graph. The algorithm fits into the framework of sequential Monte Carlo methods rather than the more widely used MCMC, and relies on constructing a sequence of intermediate distributions which get closer to the desired one. While the idea of using “tempered” proposals is known, we construct a novel sequence of target distributions where, rather than dropping a global temperature 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 partition function for sparse and densely-connected graphs.

[1]  Radford M. Neal.  Annealed importance sampling , 1998, Stat. Comput..

[2]  Peter Carbonetto,et al.  Why can’t José read? The problem of learning semantic associations in a robot environment , 2003, HLT-NAACL 2003.

[3]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[4]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[5]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[6]  James A. Bucklew,et al.  Large Deviation Techniques in Decision, Simulation, and Estimation , 1990 .

[7]  Michael I. Jordan,et al.  An Introduction to Variational Methods for Graphical Models , 1999, Machine-mediated learning.

[8]  Andrew McCallum,et al.  Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data , 2001, ICML.

[9]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[10]  P. Moral,et al.  Sequential Monte Carlo samplers , 2002, cond-mat/0212648.

[11]  Stan Z. Li,et al.  Markov Random Field Modeling in Image Analysis , 2001, Computer Science Workbench.

[12]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[13]  Mark Jerrum,et al.  The Markov chain Monte Carlo method: an approach to approximate counting and integration , 1996 .

[14]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[15]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[16]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[17]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[18]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[19]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[20]  Nando de Freitas,et al.  Diagnosis by a waiter and a Mars explorer , 2004, Proceedings of the IEEE.

[21]  J. Møller,et al.  An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants , 2006 .

[22]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[23]  P. Green,et al.  Hidden Markov Models and Disease Mapping , 2002 .

[24]  Mark Jerrum,et al.  The Swendsen-Wang process does not always mix rapidly , 1997, STOC '97.

[25]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .