mlsanityData to 14 Oct 2026

Targeted Separation and Convergence with Kernel Discrepancies

arXiv 2209.12835 ↗First posted 26 Sep 2022stat.ML cs.LG math.STcited by 15

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Abstract (arXiv)

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each setting, these kernel-based discrepancy measures are required to (i) separate a target P from other probability measures or even (ii) control weak convergence to P. In this article we derive new sufficient and necessary conditions to ensure (i) and (ii). For MMDs on separable metric spaces, we characterize those kernels that separate Bochner embeddable measures and introduce simple conditions for separating all measures with unbounded kernels and for controlling convergence with bounded kernels. We use these results on ℝd to substantially broaden the known conditions for KSD separation and convergence control and to develop the first KSDs known to exactly metrize weak convergence to P. Along the way, we highlight the implications of our results for hypothesis testing, measuring and improving sample quality, and sampling with Stein variational gradient descent.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 31 of its 96 references that are in the map. First posted on arXiv 26 Sep 2022.

Builds on

31 of 96 references.

References · 31

  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. 2017Stein Variational Gradient Descent as Gradient Flowcited by 152
  4. 2015Training generative neural networks via Maximum Mean Discrepancy optimizationcited 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. 2014Control functionals for Monte Carlo integrationcited by 59
  9. 2019Minimum Stein Discrepancy Estimatorscited by 57
  10. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  11. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 45
  12. 2018Stein Pointscited by 43
19 more
  1. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  2. 2016Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributionscited by 40
  3. 2020Metrizing Weak Convergence with Maximum Mean Discrepanciescited by 36
  4. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
  5. 2021Stein's Method Meets Computational Statistics: A Review of Some Recent Developmentscited by 32
  6. 2020Stochastic Stein Discrepanciescited by 30
  7. 2019Stein Point Markov Chain Monte Carlocited by 29
  8. 2020Optimal Thinning of MCMC Outputcited by 26
  9. 2016Measuring Sample Quality with Diffusionscited by 25
  10. 2017Riemannian Stein Variational Gradient Descent for Bayesian Inferencecited by 24
  11. 2018Random Feature Stein Discrepanciescited by 23
  12. 2022Generalised Bayesian Inference for Discrete Intractable Likelihoodcited by 14
  13. 2016Black-box Importance Samplingcited by 13
  14. 2021Vector-Valued Control Variatescited by 13
  15. 2018Stein Variational Gradient Descent Without Gradientcited by 12
  16. 2018Bayesian posterior approximation via greedy particle optimizationcited by 10
  17. 2020The reproducing Stein kernel approach for post-hoc corrected samplingcited by 10
  18. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  19. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 5; 2025: 6; 2026: 2.

15 papers.

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  1. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  2. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 14
  3. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 13
  4. 2025KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learningcited by 8
  5. 2023Coordinating Distributed Example Orders for Provably Accelerated Trainingcited by 7
  6. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  7. 2025A Unified View of Optimal Kernel Hypothesis Testingcited by 5
  8. 2025The Minimax Lower Bound of Kernel Stein Discrepancy Estimationcited by 3
  9. 2025Stationary MMD Pointscited by 2
  10. 2026Kernel Tests of Equivalencecited by 2
  11. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  12. 2024Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herdingcited by 1
3 more
  1. 2024Sequential Kernelized Stein Discrepancycited by 1
  2. 2025General reproducing properties in RKHS with application to derivative and integral operatorscited by 1
  3. 2024Scalable Monte Carlo for Bayesian Learningcited by 0