Projecting Markov Random Field Parameters for Fast Mixing
This work addresses the practical issue of slow MCMC convergence for researchers and practitioners in machine learning and statistics, offering a method to accelerate sampling in MRFs.
The paper tackles the slow convergence of Gibbs sampling in Markov Random Fields by providing conditions to guarantee fast mixing and an algorithm to project parameters onto this set, demonstrating improved sampling efficiency compared to variational methods and original Gibbs sampling.
Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univariate Gibbs sampling on Markov Random Fields (MRFs) will be fast mixing, in a precise sense. Further, an algorithm is given to project onto this set of fast-mixing parameters in the Euclidean norm. Following recent work, we give an example use of this to project in various divergence measures, comparing univariate marginals obtained by sampling after projection to common variational methods and Gibbs sampling on the original parameters.