Poisson-Minibatching for Gibbs Sampling with Convergence Rate Guarantees

TL;DR

This paper introduces Poisson-minibatching Gibbs, a new unbiased minibatched Gibbs sampling method with proven convergence guarantees, suitable for large-scale graphical models and continuous or discrete state spaces.

Contribution

The paper proposes a novel auxiliary-variable minibatched Gibbs sampling algorithm with theoretical convergence guarantees and broad applicability to continuous and discrete models.

Findings

Supports fast sampling from continuous state spaces

Avoids Metropolis-Hastings correction for discrete spaces

Demonstrates improved efficiency over previous methods

Abstract

Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale to large graphical models by reducing its computational cost. In this paper, we propose a new auxiliary-variable minibatched Gibbs sampling method, {\it Poisson-minibatching Gibbs}, which both produces unbiased samples and has a theoretical guarantee on its convergence rate. In comparison to previous minibatched Gibbs algorithms, Poisson-minibatching Gibbs supports fast sampling from continuous state spaces and avoids the need for a Metropolis-Hastings correction on discrete state spaces. We demonstrate the effectiveness of our method on multiple applications and in comparison with both plain Gibbs and previous minibatched methods.