Stochastic Variance-Reduced Hamilton Monte Carlo Methods

02/13/2018 ∙ by Difan Zou, et al. ∙ 0

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 ϵ accuracy in 2-Wasserstein distance, our algorithm achieves Õ(n+κ^2d^1/2/ϵ+κ^4/3d^1/3n^2/3/ϵ^2/3) 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.

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