Stochastic Gradient Hamiltonian Monte Carlo with Variance Reduction for Bayesian Inference

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. [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.

arXiv comment25 pages

References in corpus (7)

• Stochastic Gradient Hamiltonian Monte Carlo
• On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators
• Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring
• A Simple Proximal Stochastic Gradient Method for Nonsmooth Nonconvex Optimization
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Cited by in corpus (2)

• Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization
• Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo