mlsanityData to 7 Oct 2026

A Kernel Test of Goodness of Fit

arXiv 1602.02964 ↗First posted 9 Feb 2016stat.MLcited by 143

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Abstract (arXiv)

We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence constructed via Stein's method using functions from a Reproducing Kernel Hilbert Space. Our test statistic is based on an empirical estimate of this divergence, taking the form of a V-statistic in terms of the log gradients of the target density and the kernel. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, where we estimate the null distribution quantiles using a wild bootstrap procedure. We apply our test to quantifying convergence of approximate Markov Chain Monte Carlo methods, statistical model criticism, and evaluating quality of fit vs model complexity in nonparametric density estimation.

Key facts. Cited by 143 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Feb 2016.

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Citing papers per year: 2021: 27; 2022: 33; 2023: 17; 2024: 18; 2025: 26; 2026: 22.

143 papers.

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  1. 2025LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristicscited by 227
  2. 2021Benchmarking Simulation-Based Inferencecited by 160
  3. 2021MMD Aggregated Two-Sample Testcited by 74
  4. 2021Kernel Stein Discrepancy Descentcited by 57
  5. 2023CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problemscited by 54
  6. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  7. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  8. 2021Generalized Kernel Thinningcited by 29
  9. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  10. 2021A Survey of Monte Carlo Methods for Parameter Estimationcited by 23
  11. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  12. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
38 more
  1. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  2. 2022Particle-based Variational Inference with Preconditioned Functional Gradient Flowcited by 20
  3. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 19
  4. 2022Regularized Stein Variational Gradient Flowcited by 18
  5. 2021Sampling with Mirrored Stein Operatorscited by 17
  6. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  7. 2022Amortized Variational Inference: A Systematic Reviewcited by 16
  8. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  9. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  10. 2022Towards Healing the Blindness of Score Matchingcited by 13
  11. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  12. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  13. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
  14. 2022Grassmann Stein Variational Gradient Descentcited by 12
  15. 2024Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operatorcited by 12
  16. 2021Efficient and Generalizable Tuning Strategies for Stochastic Gradient MCMCcited by 11
  17. 2022MixFlows: principled variational inference via mixed flowscited by 11
  18. 2024Stein transport for Bayesian inferencecited by 11
  19. 2021A Computationally Efficient Method for Learning Exponential Family Distributionscited by 10
  20. 2021Interpreting diffusion score matching using normalizing flowcited by 9
  21. 2022A kernel Stein test of goodness of fit for sequential modelscited by 9
  22. 2023Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularizationcited by 9
  23. 2023Energy Discrepancies: A Score-Independent Loss for Energy-Based Modelscited by 9
  24. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 9
  25. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  26. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  27. 2021On Energy-Based Models with Overparametrized Shallow Neural Networkscited by 8
  28. 2022Are you using test log-likelihood correctly?cited by 8
  29. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  30. 2023A Bias-Variance-Covariance Decomposition of Kernel Scores for Generative Modelscited by 8
  31. 2024Kernel Semi-Implicit Variational Inferencecited by 8
  32. 2024Path-Guided Particle-based Samplingcited by 8
  33. 2021Kernel Two-Sample Tests for Manifold Datacited by 7
  34. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  35. 2024Kernel Approximation of Fisher-Rao Gradient Flowscited by 7
  36. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  37. 2021Stein ICP for Uncertainty Estimation in Point Cloud Matchingcited by 6
  38. 2021Detecting Anomalous Event Sequences with Temporal Point Processescited by 6

50 most cited of 143 All 143 (JSON)