Stochastic variance-reduced Hamilton Monte Carlo methods

Abstract

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in stochastic optimization. We show that, to achieve e accuracy in 2-Wasserstein distance, our algorithm achieves Õ(n + κ2d1/2/ϵ + κ4/3d1/3n2/3/ϵ2/3) gradient complexity (i.e., number of component gradient evaluations), which outperforms the state-of-the-art HMC and stochastic gradient HMC methods in a wide regime. We also extend our algorithm for sampling from smooth and general log-concave distributions, and prove the corresponding gradient complexity as well. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.