mlsanityData to 14 Oct 2026

Regularized Stein Variational Gradient Flow

arXiv 2211.07861 ↗First posted 15 Nov 2022stat.ML cs.LG cs.NAcited by 19

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Abstract (arXiv)

The Stein Variational Gradient Descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient Flow) only provides a constant-order approximation to the Wasserstein Gradient Flow corresponding to the KL-divergence minimization. In this work, we propose the Regularized Stein Variational Gradient Flow, which interpolates between the Stein Variational Gradient Flow and the Wasserstein Gradient Flow. We establish various theoretical properties of the Regularized Stein Variational Gradient Flow (and its time-discretization) including convergence to equilibrium, existence and uniqueness of weak solutions, and stability of the solutions. We provide preliminary numerical evidence of the improved performance offered by the regularization.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 22 of its 53 references that are in the map. First posted on arXiv 15 Nov 2022.

Builds on

22 of 53 references.

References · 22

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 507
  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 227
  4. 2016Generalization Properties of Learning with Random Featurescited by 164
  5. 2017Stein Variational Gradient Descent as Gradient Flowcited by 152
  6. 2016A Kernel Test of Goodness of Fitcited by 143
  7. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  8. 2017Measuring Sample Quality with Kernelscited by 119
  9. 2019On the geometry of Stein variational gradient descentcited by 82
  10. 2020Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHScited by 74
  11. 2022Improved analysis for a proximal algorithm for samplingcited by 73
  12. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
10 more
  1. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  2. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  3. 2017Stein Variational Policy Gradientcited by 44
  4. 2020Metrizing Weak Convergence with Maximum Mean Discrepanciescited by 36
  5. 2018Scaling limit of the Stein variational gradient descent: the mean field regimecited by 35
  6. 2019Stein Variational Gradient Descent With Matrix-Valued Kernelscited by 32
  7. 2015Randomized sketches for kernels: Fast and optimal non-parametric regressioncited by 31
  8. 2016Measuring Sample Quality with Diffusionscited by 25
  9. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  10. 2017On the Optimality of Kernel-Embedding Based Goodness-of-Fit Testscited by 19

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 2; 2024: 6; 2025: 2; 2026: 8.

19 papers.

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  1. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  2. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  3. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 14
  4. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  5. 2024Stein transport for Bayesian inferencecited by 11
  6. 2024Kernel Approximation of Fisher-Rao Gradient Flowscited by 7
  7. 2026Sobolev Regularized MMD Gradient Flowcited by 6
  8. 2026Finite-Particle Rates for Regularized Stein Variational Gradient Descentcited by 5
  9. 2024Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learningcited by 4
  10. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  11. 2025Stationary MMD Pointscited by 2
  12. 2025Hessian-guided Perturbed Wasserstein Gradient Flows for Escaping Saddle Pointscited by 2
7 more
  1. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 2
  2. 2026Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensionscited by 1
  3. 2022Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversioncited by 0
  4. 2026Complexity of Non-Log-Concave Sampling in Fisher Informationcited by 0
  5. 2026Stability of Finite-Batch Particle Mean-Field Variational Inference Beyond Strong Convexitycited by 0
  6. 2026A Distributional Optimisation Perspective on Combining Models in Deep Learningcited by 0
  7. 2026Markov Chain Convergence in Kernel-Induced Geometrycited by 0