Parallel MCMC with Generalized Elliptical Slice Sampling

TL;DR

This paper introduces a parallel MCMC algorithm that leverages multi-core computing and elliptical slice sampling to efficiently sample from complex distributions, improving mixing speed without gradient computations.

Contribution

It presents a novel parallel MCMC method combining Gaussian scale-mixture approximation with elliptical slice sampling for faster, gradient-free inference.

Findings

Supports hundreds of cores for scalable inference

Achieves rapid mixing without gradient or curvature calculations

Builds Gaussian mixture approximation for efficient sampling

Abstract

Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate inference is often performed using Markov chain Monte Carlo (MCMC). To achieve the best possible results from MCMC, we want to efficiently simulate many steps of a rapidly mixing Markov chain which leaves the target distribution invariant. Of particular interest in this regard is how to take advantage of multi-core computing to speed up MCMC-based inference, both to improve mixing and to distribute the computational load. In this paper, we present a parallelizable Markov chain Monte Carlo algorithm for efficiently sampling from continuous probability distributions that can take advantage of hundreds of cores. This method shares information between parallel Markov chains to build a scale-mixture of Gaussians approximation to the density function of the target distribution. We combine this approximation with a recent method known as elliptical slice sampling to create a Markov chain with no step-size parameters that can mix rapidly without requiring gradient or curvature computations.