Stochastic Gradient Monomial Gamma Sampler

TL;DR

This paper introduces a generalized Hamiltonian Monte Carlo framework that enhances stochastic gradient MCMC methods, significantly improving exploration of complex multimodal posterior distributions in large datasets.

Contribution

It proposes a novel generalized kinetic function for stochastic gradient MCMC, improving mixing and exploration of multimodal distributions, with practical techniques to address implementation challenges.

Findings

Better exploration of multimodal posteriors demonstrated on multiple applications.

Outperforms existing stochastic gradient MCMC methods in mixing efficiency.

Provides practical solutions for issues arising from the generalized kinetic function.

Abstract

Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is often poor. This results in inadequate exploration of the posterior distribution. A framework is proposed to improve the sampling efficiency of stochastic gradient MCMC, based on Hamiltonian Monte Carlo. A generalized kinetic function is leveraged, delivering superior stationary mixing, especially for multimodal distributions. Techniques are also discussed to overcome the practical issues introduced by this generalization. It is shown that the proposed approach is better at exploring complex multimodal posterior distributions, as demonstrated on multiple applications and in comparison with other stochastic gradient MCMC methods.