Publication Type

Journal Article

Version

publishedVersion

Publication Date

7-2019

Abstract

Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high variance of noisy stochastic gradients, Dubey et al. (in: Advances in neural information processing systems, pp 1154–1162, 2016) applied the standard variance reduction technique on stochastic gradient Langevin dynamics and obtained both theoretical and experimental improvements. In this paper, we apply the variance reduction tricks on Hamiltonian Monte Carlo and achieve better theoretical convergence results compared with the variance-reduced Langevin dynamics. Moreover, we apply the symmetric splitting scheme in our variance-reduced Hamiltonian Monte Carlo algorithms to further improve the theoretical results. The experimental results are also consistent with the theoretical results. As our experiment shows, variance-reduced Hamiltonian Monte Carlo demonstrates better performance than variance-reduced Langevin dynamics in Bayesian regression and classification tasks on real-world datasets.

Keywords

Hamiltonian Monte Carlo, Variance reduction, Bayesian inference

Discipline

Databases and Information Systems

Research Areas

Data Science and Engineering; Intelligent Systems and Optimization

Publication

Machine Learning

Volume

108

Issue

8-9

First Page

1701

Last Page

1727

ISSN

0885-6125

Identifier

10.1007/s10994-019-05825-y

Publisher

Springer

Additional URL

https://doi.org/10.1007/s10994-019-05825-y

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