mlsanityData to 7 Oct 2026

Finite-Particle Rates for Regularized Stein Variational Gradient Descent

arXiv 2602.05172 ↗First posted 5 Feb 2026stat.ML cs.LG math.STcited by 3

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Abstract (arXiv)

We derive finite-particle rates for the regularized Stein variational gradient descent (R-SVGD) algorithm introduced by He et al. (2024) that corrects the constant-order bias of the SVGD by applying a resolvent-type preconditioner to the kernelized Wasserstein gradient. For the resulting interacting N-particle system, we establish explicit non-asymptotic bounds for time-averaged (annealed) empirical measures, illustrating convergence in the true (non-kernelized) Fisher information and, under a W1I condition on the target, corresponding W1 convergence for a large class of smooth kernels. Our analysis covers both continuous- and discrete-time dynamics and yields principled tuning rules for the regularization parameter, step size, and averaging horizon that quantify the trade-off between approximating the Wasserstein gradient flow and controlling finite-particle estimation error.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 16 of its 30 references that are in the map. First posted on arXiv 5 Feb 2026.

Builds on

16 of 30 references.

References · 16

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  2. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  3. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  4. 2017Measuring Sample Quality with Kernelscited by 119
  5. 2019On the geometry of Stein variational gradient descentcited by 82
  6. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
  7. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  8. 2018Scaling limit of the Stein variational gradient descent: the mean field regimecited by 35
  9. 2020Stochastic Stein Discrepanciescited by 30
  10. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  11. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  12. 2022Regularized Stein Variational Gradient Flowcited by 18
4 more
  1. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  2. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  3. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  4. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Modelscited by 2
  2. 2026Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flowcited by 1
  3. 2026Complexity of Non-Log-Concave Sampling in Fisher Informationcited by 0