mlsanityData to 7 Oct 2026

A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks

arXiv 2303.02637 ↗First posted 5 Mar 2023stat.ML cs.LG stat.APcited by 3

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Abstract (arXiv)

A classic inferential statistical problem is the goodness-of-fit (GOF) test. Such a test can be challenging when the hypothesized parametric model has an intractable likelihood and its distributional form is not available. Bayesian methods for GOF can be appealing due to their ability to incorporate expert knowledge through prior distributions. However, standard Bayesian methods for this test often require strong distributional assumptions on the data and their relevant parameters. To address this issue, we propose a semi-Bayesian nonparametric (semi-BNP) procedure in the context of the maximum mean discrepancy (MMD) measure that can be applied to the GOF test. Our method introduces a novel Bayesian estimator for the MMD, enabling the development of a measure-based hypothesis test for intractable models. Through extensive experiments, we demonstrate that our proposed test outperforms frequentist MMD-based methods by achieving a lower false rejection and acceptance rate of the null hypothesis. Furthermore, we showcase the versatility of our approach by embedding the proposed estimator within a generative adversarial network (GAN) framework. It facilitates a robust BNP learning approach as another significant application of our method. With our BNP procedure, this new GAN approach can enhance sample diversity and improve inferential accuracy compared to traditional techniques.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 32 of its 80 references that are in the map. First posted on arXiv 5 Mar 2023.

Builds on

32 of 80 references.

References · 32

  1. 2016Improved Techniques for Training GANscited by 2,938
  2. 2018Demystifying MMD GANscited by 1,268
  3. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  4. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  5. 2018Generative Adversarial Network in Medical Imaging: A Reviewcited by 257
  6. 2015Generative Moment Matching Networkscited by 252
  7. 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 251
  8. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  9. 2015Training generative neural networks via Maximum Mean Discrepancy optimizationcited by 149
  10. 2016Mode Regularized Generative Adversarial Networkscited by 123
  11. 2017PacGAN: The power of two samples in generative adversarial networkscited by 104
  12. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 99
20 more
  1. 2017Deep MR to CT Synthesis using Unpaired Datacited by 86
  2. 2021MMD Aggregated Two-Sample Testcited by 74
  3. 2016Interpretable Distribution Features with Maximum Testing Powercited by 63
  4. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 43
  5. 2016Improving Variational Auto-Encoders using Householder Flowcited by 41
  6. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  7. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
  8. 2017General Bayesian Updating and the Loss-Likelihood Bootstrapcited by 34
  9. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  10. 2017Learning to Draw Samples with Amortized Stein Variational Gradient Descentcited by 26
  11. 2019Finite sample properties of parametric MMD estimation: robustness to misspecification and dependencecited by 24
  12. 2018Nonparametric learning from Bayesian models with randomized objective functionscited by 17
  13. 2019Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior Bootstrapcited by 16
  14. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  15. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  16. 2021Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlocited by 12
  17. 2022Minimum Kernel Discrepancy Estimatorscited by 4
  18. 2020A Test for Independence Via Bayesian Nonparametric Estimation of Mutual Informationcited by 2
  19. 2016Prior based model checkingcited by 1
  20. 2019A Bayesian Semiparametric Gaussian Copula Approach to a Multivariate Normality Testcited by 1

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Cited by year (2026 to 7 Oct)

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

3 papers.

  1. 2023A Bayesian Non-parametric Approach to Generative Models: Integrating Variational Autoencoder and Generative Adversarial Networks using Wasserstein and Maximum Mean Discrepancycited by 1
  2. 2025A Deep Bayesian Nonparametric Framework for Robust Mutual Information Estimationcited by 0
  3. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 0