mlsanityData to 7 Oct 2026

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

arXiv 1805.04035 ↗First posted 10 May 2018math.AP stat.ME stat.MLcited by 35

Not on the map. Why?

Abstract (arXiv)

We study an interacting particle system in Rd 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 of the particle system converges to a solution of a non-local and nonlinear PDE. We also prove 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 long time limit.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 May 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 9; 2023: 8; 2024: 6; 2025: 3; 2026: 4.

35 papers.

Sort:

By area:

  1. 2022Probability flow solution of the Fokker-Planck equationcited by 46
  2. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  3. 2023A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methodscited by 31
  4. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  5. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  6. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  7. 2022Regularized Stein Variational Gradient Flowcited by 18
  8. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  9. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  10. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  11. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  12. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
23 more
  1. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
  2. 2022Grassmann Stein Variational Gradient Descentcited by 12
  3. 2024Stein transport for Bayesian inferencecited by 11
  4. 2023Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemescited by 10
  5. 2021Ensemble Inference Methods for Models With Noisy and Expensive Likelihoodscited by 8
  6. 2022Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce datacited by 8
  7. 2022A blob method for inhomogeneous diffusion with applications to multi-agent control and samplingcited by 6
  8. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  9. 2021Relative Entropy Gradient Sampler for Unnormalized Distributionscited by 5
  10. 2022A Note on the Convergence of Mirrored Stein Variational Gradient Descent under (L0,L1)-Smoothness Conditioncited by 4
  11. 2023Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networkscited by 4
  12. 2024Ensemble-Based Annealed Importance Samplingcited by 4
  13. 2026Finite-Particle Rates for Regularized Stein Variational Gradient Descentcited by 3
  14. 2021Low-rank variational Bayes correction to the Laplace methodcited by 2
  15. 2024Stein Boltzmann Sampling: A Variational Approach for Global Optimizationcited by 2
  16. 2024Long-time asymptotics of noisy SVGD outside the population limitcited by 2
  17. 2024ELBOing Stein: Variational Bayes with Stein Mixture Inferencecited by 1
  18. 2026Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensionscited by 1
  19. 2026Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flowcited by 1
  20. 2022Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice modelscited by 0
  21. 2025Boosting Statistic Learning with Synthetic Data from Pretrained Large Modelscited by 0
  22. 2025Adaptive Kernel Selection for Stein Variational Gradient Descentcited by 0
  23. 2026Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limitscited by 0