mlsanityData to 14 Oct 2026

The Minimax Lower Bound of Kernel Stein Discrepancy Estimation

arXiv 2510.15058 ↗First posted 16 Oct 2025stat.ML cs.LG math.STcited by 3

Not on the map. Why?

Abstract (arXiv)

Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve √ n-convergence. In this work, we present two complementary results (with different proof strategies), establishing that the minimax lower bound of KSD estimation is n-1/2 and settling the optimality of these estimators. Our first result focuses on KSD estimation on mathbb Rd with the Langevin-Stein operator; our explicit constant for the Gaussian kernel indicates that the difficulty of KSD estimation may increase exponentially with the dimensionality d. Our second result settles the minimax lower bound for KSD estimation on general domains.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 33 of its 76 references that are in the map. First posted on arXiv 16 Oct 2025.

Builds on

33 of 76 references.

References · 33

  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. 2016A Kernel Test of Goodness of Fitcited by 143
  4. 2017Measuring Sample Quality with Kernelscited by 119
  5. 2015Measuring Sample Quality with Stein's Methodcited by 94
  6. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  7. 2014Control functionals for Monte Carlo integrationcited by 59
  8. 2021Kernel Stein Discrepancy Descentcited by 57
  9. 2018Stein Pointscited by 43
  10. 2017Characteristic and Universal Tensor Product Kernelscited by 41
  11. 2016Kernel-based Tests for Joint Independencecited by 40
  12. 2021Stein's Method Meets Computational Statistics: A Review of Some Recent Developmentscited by 32
21 more
  1. 2019Stein Point Markov Chain Monte Carlocited by 29
  2. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  3. 2019A Kernel Stein Test for Comparing Latent Variable Modelscited by 18
  4. 2018Stein Variational Gradient Descent as Moment Matchingcited by 15
  5. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  6. 2020A Stein Goodness-of-fit Test for Directional Distributionscited by 13
  7. 2013A Kernel Test for Three-Variable Interactionscited by 10
  8. 2018Bayesian posterior approximation via greedy particle optimizationcited by 10
  9. 2020The reproducing Stein kernel approach for post-hoc corrected samplingcited by 10
  10. 2019Kernel Stein Tests for Multiple Model Comparisoncited by 9
  11. 2022A kernel Stein test of goodness of fit for sequential modelscited by 9
  12. 2024Minimax Optimal Goodness-of-Fit Testing with Kernel Stein Discrepancycited by 9
  13. 2024Debiased Distribution Compressioncited by 8
  14. 2021Interpretable Stein Goodness-of-fit Tests on Riemannian Manifoldscited by 7
  15. 2023Kernelized Cumulants: Beyond Kernel Mean Embeddingscited by 5
  16. 2021Handling Hard Affine SDP Shape Constraints in RKHSscited by 4
  17. 2021Stein's method of normal approximation: Some recollections and reflectionscited by 4
  18. 2024Nystr"om Kernel Stein Discrepancycited by 4
  19. 2023Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactionscited by 3
  20. 2024Data-centric Prediction Explanation via Kernelized Stein Discrepancycited by 3
  21. 2024The Minimax Rate of HSIC Estimation for Translation-Invariant Kernelscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scalescited by 3
  2. 2026Nystr"om Kernel Stein Discrepancy Testscited by 2
  3. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2