Scaling limit of the Stein variational gradient descent part I: the mean field regime

05/10/2018

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by   Jianfeng Lu, et al.

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We study an interacting particle system in R^d motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization. We prove that in the large particle limit the empirical measure converges to a solution of a non-local and nonlinear PDE. We also prove global well-posedness and uniqueness of the solution to the limiting PDE. Finally, we prove that the solution to the PDE converges to the unique invariant solution in large time limit.