Vol. 15, No. 1, 2020

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A stochastic version of Stein variational gradient descent for efficient sampling

Lei Li, Yingzhou Li, Jian-Guo Liu, Zibu Liu and Jianfeng Lu

Vol. 15 (2020), No. 1, 37–63
Abstract

We propose in this work RBM-SVGD, a stochastic version of the Stein variational gradient descent (SVGD) method for efficiently sampling from a given probability measure, which is thus useful for Bayesian inference. The method is to apply the random batch method (RBM) for interacting particle systems proposed by Jin et al. to the interacting particle systems in SVGD. While keeping the behaviors of SVGD, it reduces the computational cost, especially when the interacting kernel has long range. We prove that the one marginal distribution of the particles generated by this method converges to the one marginal of the interacting particle systems under Wasserstein-2 distance on fixed time interval [0,T]. Numerical examples verify the efficiency of this new version of SVGD.

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Keywords
random batch method, RBM-SVGD, nonparametric variational inference, KL divergence, reproducing kernel Hilbert space, MCMC
Mathematical Subject Classification 2010
Primary: 62D05, 65C35
Milestones
Received: 10 April 2019
Revised: 12 November 2019
Accepted: 14 December 2019
Published: 3 June 2020
Authors
Lei Li
School of Mathematical Sciences
Institute of Natural Sciences
Key Lab of Scientific and Engineering Computing, Ministry of Education
Shanghai Jiao Tong University
Shanghai
China
Yingzhou Li
Department of Mathematics
Duke University
Durham, NC
United States
Jian-Guo Liu
Department of Mathematics
Department of Physics
Duke University
Durham, NC
United States
Zibu Liu
Department of Mathematics
Duke University
Durham, NC
United States
Jianfeng Lu
Department of Mathematics
Department of Physics
Department of Chemistry
Duke University
Durham, NC
United States