Parallelizable Sampling of Markov Random Fields

13th International Conference on Artificial Intelligence and Statistics

计算机科学;数学科学

James Martens Ilya Sutskever

PID  :  119746

来源: CEUR

【 摘 要 】

Markov Random Fields (MRFs) are an im portant class of probabilistic models which are used for density estimation, classifica tion, denoising, and for constructing Deep Belief Networks. Every application of an MRF requires addressing its inference prob lem, which can be done using deterministic inference methods or using stochastic Markov Chain Monte Carlo methods. In this paper we introduce a new Markov Chain transition operator that updates all the variables of a pairwise MRF in parallel by using auxiliary Gaussian variables. The proposed MCMC operator is extremely simple to implement and to parallelize. This is achieved by a formal equivalence result between arbitrary pairwise MRFs and a particular type of Re stricted Boltzmann Machine. This result also implies that the later can be learned in place of the former without any loss of modeling power, a possibility we explore in experi