mlsanityData to 14 Oct 2026

Composite Goodness-of-fit Tests with Kernels

arXiv 2111.10275 ↗First posted 19 Nov 2021stat.ML cs.LG stat.MEcited by 16

Not on the map. Why?

Abstract (arXiv)

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more involved methods are required will depend on whether the model is really misspecified, and there is a lack of generally applicable methods to answer this question. In this paper, we propose one such method. More precisely, we propose kernel-based hypothesis tests for the challenging composite testing problem, where we are interested in whether the data comes from any distribution in some parametric family. Our tests make use of minimum distance estimators based on the maximum mean discrepancy and the kernel Stein discrepancy. They are widely applicable, including whenever the density of the parametric model is known up to normalisation constant, or if the model takes the form of a simulator. As our main result, we show that we are able to estimate the parameter and conduct our test on the same data (without data splitting), while maintaining a correct test level. Our approach is illustrated on a range of problems, including testing for goodness-of-fit of an unnormalised non-parametric density model, and an intractable generative model of a biological cellular network.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 35 of its 85 references that are in the map. First posted on arXiv 19 Nov 2021.

Builds on

35 of 85 references.

References · 35

  1. 2019The frontier of simulation-based inferencecited by 502
  2. 2015Generative Moment Matching Networkscited by 257
  3. 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 254
  4. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  5. 2015Training generative neural networks via Maximum Mean Discrepancy optimizationcited by 151
  6. 2016A Kernel Test of Goodness of Fitcited by 143
  7. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 100
  8. 2015Measuring Sample Quality with Stein's Methodcited by 94
  9. 2021MMD Aggregated Two-Sample Testcited by 75
  10. 2014Control functionals for Monte Carlo integrationcited by 59
  11. 2019Minimum Stein Discrepancy Estimatorscited by 57
  12. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
23 more
  1. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 45
  2. 2018Learning deep kernels for exponential family densitiescited by 36
  3. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
  4. 2019Approximate Bayesian computation with the Wasserstein distancecited by 34
  5. 2020Blindness of score-based methods to isolated components and mixing proportionscited by 34
  6. 2021Stein's Method Meets Computational Statistics: A Review of Some Recent Developmentscited by 32
  7. 2014A Wild Bootstrap for Degenerate Kernel Testscited by 29
  8. 2015A Test of Relative Similarity For Model Selection in Generative Modelscited by 25
  9. 2019Finite sample properties of parametric MMD estimation: robustness to misspecification and dependencecited by 25
  10. 2016Conditional Generative Moment-Matching Networkscited by 24
  11. 2020Sliced Kernelized Stein Discrepancycited by 23
  12. 2020Testing Goodness of Fit of Conditional Density Models with Kernelscited by 19
  13. 2019A Kernel Stein Test for Comparing Latent Variable Modelscited by 18
  14. 2020A Stein Goodness-of-fit Test for Directional Distributionscited by 13
  15. 2020Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Datacited by 12
  16. 2021Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlocited by 12
  17. 2018A maximum-mean-discrepancy goodness-of-fit test for censored datacited by 9
  18. 2018Informative Features for Model Comparisoncited by 9
  19. 2019Kernel Stein Tests for Multiple Model Comparisoncited by 9
  20. 2020A General Method for Calibrating Stochastic Radio Channel Models with Kernelscited by 9
  21. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  22. 2021A Stein Goodness of fit Test for Exponential Random Graph Modelscited by 2
  23. 2019Minimum Lq-distance estimators for non-normalized parametric modelscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 4; 2025: 3; 2026: 4.

16 papers.

Sort:

By area:

  1. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  2. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  3. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  4. 2024Practical Kernel Tests of Conditional Independencecited by 15
  5. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  6. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  7. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  8. 2024Cost-aware simulation-based inferencecited by 6
  9. 2025Multilevel neural simulation-based inferencecited by 5
  10. 2023A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networkscited by 3
  11. 2026Minimum Distance Summaries for Robust Neural Posterior Estimationcited by 3
  12. 2026Regularized f-Divergence Kernel Testscited by 2
4 more
  1. 2026Kernel Tests of Equivalencecited by 2
  2. 2024Sequential Kernelized Stein Discrepancycited by 1
  3. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 1
  4. 2025Stein Discrepancy for Unsupervised Domain Adaptationcited by 0