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.
Cite
Text
Park et al. "Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models." International Conference on Artificial Intelligence and Statistics, 2017.Markdown
[Park et al. "Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models." International Conference on Artificial Intelligence and Statistics, 2017.](https://mlanthology.org/aistats/2017/park2017aistats-rapid/)BibTeX
@inproceedings{park2017aistats-rapid,
title = {{Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models}},
author = {Park, Sejun and Jang, Yunhun and Galanis, Andreas and Shin, Jinwoo and Stefankovic, Daniel and Vigoda, Eric},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2017},
pages = {440-449},
url = {https://mlanthology.org/aistats/2017/park2017aistats-rapid/}
}