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

Journal Article

© 2019 Society for Industrial and Applied Mathematics We study an interacting particle system in Rd motivated by Stein variational gradient descent [Q. Liu and D. Wang, Proceedings of NIPS, 2016], a deterministic algorithm for approximating a given probability density with unknown normalization based on particles. We prove that in the large particle limit the empirical measure of the particle system converges to a solution of a nonlocal and nonlinear PDE. We also prove the global existence, uniqueness, and regularity of the solution to the limiting PDE. Finally, we prove that the solution to the PDE converges to the unique invariant solution in a long time limit.

Full Text

Duke Authors

Cited Authors

  • Lu, J; Lu, Y; Nolen, J

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 51 / 2

Start / End Page

  • 648 - 671

Electronic International Standard Serial Number (EISSN)

  • 1095-7154

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/18M1187611

Citation Source

  • Scopus