Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models

TL;DR

This paper proves that the Swendsen-Wang sampler mixes rapidly in certain attractive graphical models, overcoming slow mixing issues of the Gibbs sampler, and demonstrates its superior performance in learning tasks.

Contribution

It establishes O(log n) mixing time for the Swendsen-Wang sampler in stochastic partitioned attractive models, including low temperature regimes.

Findings

Swendsen-Wang mixes rapidly in stochastic partitioned attractive models.

The sampler outperforms Gibbs in learning parameters of attractive GMs.

Experimental results confirm theoretical improvements.

Abstract

The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Markov chain designed to overcome bottlenecks that impede the Gibbs sampler. We prove O(\log n) mixing time for attractive binary pairwise GMs (i.e., ferromagnetic Ising models) on stochastic partitioned graphs having n vertices, under some mild conditions, including low temperature regions where the Gibbs sampler provably mixes exponentially slow. Our experiments also confirm that the Swendsen-Wang sampler significantly outperforms the Gibbs sampler when they are used for learning parameters of attractive GMs.