mlsanityData to 7 Oct 2026

A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1

arXiv 2106.03076 ↗First posted 6 Jun 2021cs.LG math.OCcited by 21

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Abstract (arXiv)

Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a target density which is known up to a multiplicative constant. Although SVGD is a popular algorithm in practice, its theoretical study is limited to a few recent works. We study the convergence of SVGD in the population limit, (i.e., with an infinite number of particles) to sample from a non-logconcave target distribution satisfying Talagrand's inequality T1. We first establish the convergence of the algorithm. Then, we establish a dimension-dependent complexity bound in terms of the Kernelized Stein Discrepancy (KSD). Unlike existing works, we do not assume that the KSD is bounded along the trajectory of the algorithm. Our approach relies on interpreting SVGD as a gradient descent over a space of probability measures.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 28 of its 44 references that are in the map. First posted on arXiv 6 Jun 2021.

Builds on

28 of 44 references.

References · 28

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  2. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  3. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  4. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  5. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  6. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  7. 2016A Kernel Test of Goodness of Fitcited by 143
  8. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  9. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  10. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  11. 2017Measuring Sample Quality with Kernelscited by 119
  12. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 83
16 more
  1. 2019On the geometry of Stein variational gradient descentcited by 82
  2. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  3. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
  4. 2018Mirrored Langevin Dynamicscited by 61
  5. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  6. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  7. 2017Stein Variational Policy Gradientcited by 42
  8. 2018Scaling limit of the Stein variational gradient descent: the mean field regimecited by 35
  9. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 34
  10. 2020Federated Generalized Bayesian Learning via Distributed Stein Variational Gradient Descentcited by 34
  11. 2020Stochastic Stein Discrepanciescited by 30
  12. 2019Is There an Analog of Nesterov Acceleration for MCMC?cited by 19
  13. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  14. 2017Fractional Langevin Monte Carlo: Exploring L'evy Driven Stochastic Differential Equations for Markov Chain Monte Carlocited by 12
  15. 2019Scalable Thompson Sampling via Optimal Transportcited by 7
  16. 2017Learning Structural Weight Uncertainty for Sequential Decision-Makingcited by 5

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Citing papers per year: 2022: 3; 2023: 8; 2024: 4; 2025: 3; 2026: 3.

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  1. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  2. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  3. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  4. 2022Regularized Stein Variational Gradient Flowcited by 18
  5. 2022Sampling with Mollified Interaction Energy Descentcited by 17
  6. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  7. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
  8. 2023Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Bettingcited by 11
  9. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  10. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  11. 2023Towards a Better Theoretical Understanding of Independent Subnetwork Trainingcited by 6
  12. 2023Learning Rate Free Sampling in Constrained Domainscited by 3
9 more
  1. 2024Bayesian Multi-Task Transfer Learning for Soft Prompt Tuningcited by 3
  2. 2026Finite-Particle Rates for Regularized Stein Variational Gradient Descentcited by 3
  3. 2024Long-time asymptotics of noisy SVGD outside the population limitcited by 2
  4. 2025Gradient Flow Sampler-based Distributionally Robust Optimizationcited by 2
  5. 2026Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flowcited by 1
  6. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 1
  7. 2023Augmented Message Passing Stein Variational Gradient Descentcited by 0
  8. 2025Adaptive Kernel Selection for Stein Variational Gradient Descentcited by 0
  9. 2025Generative Modeling through Koopman Spectral Analysis: An Operator-Theoretic Perspectivecited by 0