mlsanityData to 14 Oct 2026

Controlling Moments with Kernel Stein Discrepancies

arXiv 2211.05408 ↗First posted 10 Nov 2022stat.ML cs.LG stat.COcited by 13

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Abstract (arXiv)

Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation and can be computed even when the target density has an intractable normalizing constant. Notable applications include the diagnosis of approximate MCMC samplers and goodness-of-fit tests for unnormalized statistical models. The present work analyzes the convergence control properties of KSDs. We first show that standard KSDs used for weak convergence control fail to control moment convergence. To address this limitation, we next provide sufficient conditions under which alternative diffusion KSDs control both moment and weak convergence. As an immediate consequence we develop, for each q > 0, the first KSDs known to exactly characterize q-Wasserstein convergence.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 20 of its 47 references that are in the map. First posted on arXiv 10 Nov 2022.

Builds on

20 of 47 references.

References · 20

  1. 2016Variational Inference: A Review for Statisticianscited by 1,472
  2. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  4. 2016A Kernel Test of Goodness of Fitcited by 143
  5. 2017Measuring Sample Quality with Kernelscited by 119
  6. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 100
  7. 2015Measuring Sample Quality with Stein's Methodcited by 94
  8. 2016Interpretable Distribution Features with Maximum Testing Powercited by 63
  9. 2014Control functionals for Monte Carlo integrationcited by 59
  10. 2019Minimum Stein Discrepancy Estimatorscited by 57
  11. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  12. 2018Global Non-convex Optimization with Discretized Diffusionscited by 44
8 more
  1. 2018Stein Pointscited by 43
  2. 2017A Linear-Time Kernel Goodness-of-Fit Testcited by 41
  3. 2020Blindness of score-based methods to isolated components and mixing proportionscited by 34
  4. 2021Stein's Method Meets Computational Statistics: A Review of Some Recent Developmentscited by 32
  5. 2020Optimal Thinning of MCMC Outputcited by 26
  6. 2016Measuring Sample Quality with Diffusionscited by 25
  7. 2018Random Feature Stein Discrepanciescited by 23
  8. 2019A Kernel Stein Test for Comparing Latent Variable Modelscited by 18

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 7; 2025: 1; 2026: 3.

13 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. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  4. 2026Sobolev Regularized MMD Gradient Flowcited by 6
  5. 2026Finite-Particle Rates for Regularized Stein Variational Gradient Descentcited by 5
  6. 2023Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancycited by 4
  7. 2024Long-time asymptotics of noisy SVGD outside the population limitcited by 3
  8. 2024The Polynomial Stein Discrepancy for Assessing Moment Convergencecited by 2
  9. 2026Efficient Learning of Stationary Diffusions with Stein-type Discrepanciescited by 2
  10. 2024Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herdingcited by 1
  11. 2024Sequential Kernelized Stein Discrepancycited by 1
  12. 2024Scalable Monte Carlo for Bayesian Learningcited by 0
1 more
  1. 2025Quenched large deviations for Monte Carlo integration with Coulomb gasescited by 0