mlsanityData to 14 Oct 2026

Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit

arXiv 2106.12105 ↗First posted 23 Jun 2021stat.ME stat.MLcited by 4

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Abstract (arXiv)

Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works focused on studying kernel choices to boost test performances. However, the choices of (non-unique) Stein operators also have considerable effect on the test performances. Inspired by the standardisation technique that was originally developed to better derive approximation properties for normal distributions, we present a unifying framework, called standardisation-function kernel Stein discrepancy (Sf-KSD), to study different Stein operators in KSD-based tests for goodness-of-fit. We derive explicitly how the proposed framework relates to existing KSD-based tests and show that Sf-KSD can be used as a guide to develop novel kernel-based non-parametric tests on complex data scenarios, e.g. truncated distributions or compositional data. Experimental results demonstrate that the proposed tests control type-I error well and achieve higher test power than existing approaches.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 32 of its 84 references that are in the map. First posted on arXiv 23 Jun 2021.

Builds on

32 of 84 references.

References · 32

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 507
  2. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 364
  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 130
  6. 2017Measuring Sample Quality with Kernelscited by 119
  7. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 100
  8. 2015Measuring Sample Quality with Stein's Methodcited by 94
  9. 2019Minimum Stein Discrepancy Estimatorscited by 57
  10. 2018Stein Pointscited by 43
  11. 2017A Linear-Time Kernel Goodness-of-Fit Testcited by 41
  12. 2020Stochastic Stein Discrepanciescited by 30
20 more
  1. 2014A Wild Bootstrap for Degenerate Kernel Testscited by 29
  2. 2019Stein Point Markov Chain Monte Carlocited by 29
  3. 2016Measuring Sample Quality with Diffusionscited by 25
  4. 2017Riemannian Stein Variational Gradient Descent for Bayesian Inferencecited by 24
  5. 2018Random Feature Stein Discrepanciescited by 23
  6. 2017On the Optimality of Kernel-Embedding Based Goodness-of-Fit Testscited by 19
  7. 2020Testing Goodness of Fit of Conditional Density Models with Kernelscited by 19
  8. 2020Learning Kernel Tests Without Data Splittingcited by 19
  9. 2019A Kernel Stein Test for Comparing Latent Variable Modelscited by 18
  10. 2020Stein Variational Inference for Discrete Distributionscited by 16
  11. 2020A Stein Goodness-of-fit Test for Directional Distributionscited by 13
  12. 2020Generalized Score Matching for General Domainscited by 13
  13. 2020Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Datacited by 12
  14. 2018A maximum-mean-discrepancy goodness-of-fit test for censored datacited by 9
  15. 2019Kernel Stein Tests for Multiple Model Comparisoncited by 9
  16. 2020Measure Transport with Kernel Stein Discrepancycited by 8
  17. 2021Interpretable Stein Goodness-of-fit Tests on Riemannian Manifoldscited by 7
  18. 2018Graphical Models for Non-Negative Data Using Generalized Score Matchingcited by 6
  19. 2020Score matching for compositional distributionscited by 5
  20. 2020A diffusion approach to Stein's method on Riemannian manifoldscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 1; 2024: 0; 2025: 0; 2026: 1.

4 papers.

  1. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  2. 2022A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spacescited by 3
  3. 2023Approximate Stein Classes for Truncated Density Estimationcited by 1
  4. 2026Event Generation with Parallel Langevin Sampling and Learned Stein Diagnosticscited by 0