mlsanityData to 7 Oct 2026

Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scales

arXiv 2607.03367 ↗First posted 3 Jul 2026math.ST stat.ML stat.THcited by 3

Not on the map. Why?

Abstract (arXiv)

Kernel Stein Discrepancy (KSD) compares a sample to a fixed target distribution known only through its score, and is widely used for goodness-of-fit testing, sample quality assessment, and approximate inference. We study the estimation of operatornameKSD(P0,P) from n independent observations and identify the sharp spectral constant governing the minimax risk: it is the Hilbert-Schmidt norm of the Stein covariance operator C_star, giving the minimax scale √|C_star|HS/n. This scale is attained by the positive-part square-root U-statistic, whereas the standard plug-in V-statistic remains at the trace scale √operatornametr(C_star)/n and is therefore suboptimal by the fourth root of the effective rank of C_star; for a Gaussian target with a fixed-bandwidth Gaussian kernel this factor is exponential in the dimension.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 17 of its 26 references that are in the map. First posted on arXiv 3 Jul 2026.

Builds on

17 of 26 references.

References · 17

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  2. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  3. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  4. 2016A Kernel Test of Goodness of Fitcited by 143
  5. 2017Measuring Sample Quality with Kernelscited by 119
  6. 2015Measuring Sample Quality with Stein's Methodcited by 94
  7. 2019Minimum Stein Discrepancy Estimatorscited by 57
  8. 2018Stein Pointscited by 43
  9. 2017A Linear-Time Kernel Goodness-of-Fit Testcited by 41
  10. 2018Random Feature Stein Discrepanciescited by 23
  11. 2019A Kernel Stein Test for Comparing Latent Variable Modelscited by 18
  12. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
5 more
  1. 2024Minimax Optimal Goodness-of-Fit Testing with Kernel Stein Discrepancycited by 9
  2. 2024Nystr"om Kernel Stein Discrepancycited by 4
  3. 2026Probabilistic Inference and Learning with Stein's Methodcited by 3
  4. 2025The Minimax Lower Bound of Kernel Stein Discrepancy Estimationcited by 2
  5. 2026Nystr"om Kernel Stein Discrepancy Testscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  2. 2026Unbounded Characteristic and Universal Kernelscited by 0
  3. 2026Conditional Kernel Stein Discrepancycited by 0