Title: Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models,
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.