mlsanityData to 7 Oct 2026

Nystr"om Kernel Stein Discrepancy

arXiv 2406.08401 ↗First posted 12 Jun 2024stat.ML cs.LG math.STcited by 4

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Abstract (arXiv)

Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the kernel Stein discrepancy (KSD), which combines Stein's method with the flexibility of kernel techniques, gained considerable attention. Through the Stein operator, KSD allows the construction of powerful goodness-of-fit tests where it is sufficient to know the target distribution up to a multiplicative constant. However, the typical U- and V-statistic-based KSD estimators suffer from a quadratic runtime complexity, which hinders their application in large-scale settings. In this work, we propose a Nystr"om-based KSD acceleration -- with runtime mathcal Oleft(mn+m3right) for n samples and mll n Nystr"om points -- , show its √n-consistency with a classical sub-Gaussian assumption, and demonstrate its applicability for goodness-of-fit testing on a suite of benchmarks. We also show the √ n-consistency of the quadratic-time KSD estimator.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 38 of its 90 references that are in the map. First posted on arXiv 12 Jun 2024.

Builds on

38 of 90 references.

References · 38

  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. 2020Learning Deep Kernels for Non-Parametric Two-Sample Testscited by 129
  6. 2017Measuring Sample Quality with Kernelscited by 119
  7. 2015Measuring Sample Quality with Stein's Methodcited by 94
  8. 2015Less is More: Nystr"om Computational Regularizationcited by 89
  9. 2016Interpretable Distribution Features with Maximum Testing Powercited by 63
  10. 2014Control functionals for Monte Carlo integrationcited by 59
  11. 2015Fast Two-Sample Testing with Analytic Representations of Probability Measurescited by 53
  12. 2018Stein Pointscited by 43
26 more
  1. 2017A Linear-Time Kernel Goodness-of-Fit Testcited by 41
  2. 2015Optimal Rates for Random Fourier Featurescited by 38
  3. 2021Stein's Method Meets Computational Statistics: A Review of Some Recent Developmentscited by 32
  4. 2019Detecting Out-of-Distribution Inputs to Deep Generative Models Using Typicalitycited by 30
  5. 2020Stochastic Stein Discrepanciescited by 30
  6. 2019Stein Point Markov Chain Monte Carlocited by 29
  7. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  8. 2013Austerity in MCMC Land: Cutting the Metropolis-Hastings Budgetcited by 24
  9. 2018Random Feature Stein Discrepanciescited by 23
  10. 2022Nystr"om Kernel Mean Embeddingscited by 21
  11. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  12. 2020Testing Goodness of Fit of Conditional Density Models with Kernelscited by 19
  13. 2022Spectral Regularized Kernel Two-Sample Testscited by 19
  14. 2016An Adaptive Test of Independence with Analytic Kernel Embeddingscited by 13
  15. 2020Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Datacited by 12
  16. 2021Efficient and Generalizable Tuning Strategies for Stochastic Gradient MCMCcited by 11
  17. 2018Bayesian posterior approximation via greedy particle optimizationcited by 10
  18. 2021Statistical Optimality and Computational Efficiency of Nystr"om Kernel PCAcited by 10
  19. 2019Kernel Stein Tests for Multiple Model Comparisoncited by 9
  20. 2022A kernel Stein test of goodness of fit for sequential modelscited by 9
  21. 2024Minimax Optimal Goodness-of-Fit Testing with Kernel Stein Discrepancycited by 9
  22. 2023Counterfactual Density Estimation using Kernel Stein Discrepanciescited by 7
  23. 2023Spectral Regularized Kernel Goodness-of-Fit Testscited by 6
  24. 2023Nystr"om M-Hilbert-Schmidt Independence Criterioncited by 5
  25. 2021Stein's method of normal approximation: Some recollections and reflectionscited by 4
  26. 2024Data-centric Prediction Explanation via Kernelized Stein Discrepancycited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2026Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scalescited by 3
  2. 2025The Minimax Lower Bound of Kernel Stein Discrepancy Estimationcited by 2
  3. 2026DriftXpress: Faster Drifting Models via Projected RKHS Fieldscited by 2
  4. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2