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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 |
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Vol. 15 (2020), No. 1, 37–63
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Abstract |
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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. |
Keywords
random batch method, RBM-SVGD, nonparametric variational
inference, KL divergence, reproducing kernel Hilbert space,
MCMC
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Mathematical Subject Classification 2010
Primary: 62D05, 65C35
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Milestones
Received: 10 April 2019
Revised: 12 November 2019
Accepted: 14 December 2019
Published: 3 June 2020
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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 |
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| Yingzhou Li | |
| Department of Mathematics Duke University Durham, NC United States |
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| Jian-Guo Liu | |
| Department of Mathematics Department of Physics Duke University Durham, NC United States |
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| Zibu Liu | |
| Department of Mathematics Duke University Durham, NC United States |
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| Jianfeng Lu | |
| Department of Mathematics Department of Physics Department of Chemistry Duke University Durham, NC United States |
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