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
.
Numerical examples verify the efficiency of this new version of SVGD.
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School of Mathematical
Sciences
Institute of Natural Sciences
Key Lab of Scientific and Engineering Computing, Ministry of
Education
Shanghai Jiao Tong University
Shanghai
China