mlsanityData to 13 Oct 2026

A Finite-Particle Convergence Rate for Stein Variational Gradient Descent

arXiv 2211.09721 ↗First posted 17 Nov 2022cs.LG stat.MLcited by 22

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Abstract (arXiv)

We provide the first finite-particle convergence rate for Stein variational gradient descent (SVGD), a popular algorithm for approximating a probability distribution with a collection of particles. Specifically, whenever the target distribution is sub-Gaussian with a Lipschitz score, SVGD with n particles and an appropriate step size sequence drives the kernel Stein discrepancy to zero at an order 1/sqrt(log log n) rate. We suspect that the dependence on n can be improved, and we hope that our explicit, non-asymptotic proof strategy will serve as a template for future refinements.

Key facts. Cited by 22 papers in the map (data through 13 Oct 2026). Builds on 22 of its 30 references that are in the map. First posted on arXiv 17 Nov 2022.

Builds on

22 of 30 references.

References · 22

  1. 2017Reinforcement Learning with Deep Energy-Based Policiescited by 660
  2. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 502
  3. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  4. 2017Stein Variational Gradient Descent as Gradient Flowcited by 151
  5. 2016A Kernel Test of Goodness of Fitcited by 143
  6. 2017Measuring Sample Quality with Kernelscited by 119
  7. 2015Measuring Sample Quality with Stein's Methodcited by 94
  8. 2019On the geometry of Stein variational gradient descentcited by 82
  9. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  10. 2017Message Passing Stein Variational Gradient Descentcited by 47
  11. 2018Global Non-convex Optimization with Discretized Diffusionscited by 44
  12. 2018Stein Pointscited by 43
10 more
  1. 2017Stein Variational Policy Gradientcited by 42
  2. 2018Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spacescited by 41
  3. 2020Stochastic Stein Discrepanciescited by 30
  4. 2018Random Feature Stein Discrepanciescited by 23
  5. 2016Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learningcited by 21
  6. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  7. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  8. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  9. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  10. 2021Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descentcited by 10

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 6; 2024: 6; 2025: 4; 2026: 6.

22 papers.

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  1. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  2. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 14
  3. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  4. 2023Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Bettingcited by 11
  5. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  6. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  7. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  8. 2026Finite-Particle Rates for Regularized Stein Variational Gradient Descentcited by 5
  9. 2026Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Modelscited by 4
  10. 2023Learning Rate Free Sampling in Constrained Domainscited by 3
  11. 2024Long-time asymptotics of noisy SVGD outside the population limitcited by 3
  12. 2025Stationary MMD Pointscited by 2
10 more
  1. 2025Gradient Flow Sampler-based Distributionally Robust Optimizationcited by 2
  2. 2026Kernel Tests of Equivalencecited by 2
  3. 2024Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herdingcited by 1
  4. 2024ELBOing Stein: Variational Bayes with Stein Mixture Inferencecited by 1
  5. 2026Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensionscited by 1
  6. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 1
  7. 2026Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limitscited by 1
  8. 2024A resource-constrained stochastic scheduling algorithm for homeless street outreach and gleaning edible foodcited by 0
  9. 2025Branching Stein Variational Gradient Descent for sampling multimodal distributionscited by 0
  10. 2025Adaptive Kernel Selection for Stein Variational Gradient Descentcited by 0