mlsanityData to 7 Oct 2026

Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy

arXiv 1611.04488 ↗First posted 14 Nov 2016stat.ML cs.AI cs.LGcited by 99

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Abstract (arXiv)

We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD is applied to the setting of unsupervised learning by generative adversarial networks (GAN), in which a model attempts to generate realistic samples, and a discriminator attempts to tell these apart from data samples. In this context, the MMD may be used in two roles: first, as a discriminator, either directly on the samples, or on features of the samples. Second, the MMD can be used to evaluate the performance of a generative model, by testing the model's samples against a reference data set. In the latter role, the optimized MMD is particularly helpful, as it gives an interpretable indication of how the model and data distributions differ, even in cases where individual model samples are not easily distinguished either by eye or by classifier.

Key facts. Cited by 99 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Nov 2016.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 20; 2022: 20; 2023: 17; 2024: 11; 2025: 16; 2026: 14.

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  1. 2021How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Modelscited by 193
  2. 2021Benchmarking Simulation-Based Inferencecited by 160
  3. 2021MMD Aggregated Two-Sample Testcited by 74
  4. 2021Generating Synthetic Mixed-type Longitudinal Electronic Health Records for Artificial Intelligent Applicationscited by 47
  5. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  6. 2022Normalizing flow neural networks by JKO schemecited by 39
  7. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 38
  8. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  9. 2023A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Materialcited by 34
  10. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  11. 2023Can You Rely on Your Model Evaluation? Improving Model Evaluation with Synthetic Test Datacited by 31
  12. 2021Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processescited by 27
38 more
  1. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  2. 2022Nystr"om Kernel Mean Embeddingscited by 21
  3. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  4. 2021A Witness Two-Sample Testcited by 20
  5. 2021Generative adversarial networks in time series: A survey and taxonomycited by 20
  6. 2022PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equationscited by 20
  7. 2022Controllable Data Generation by Deep Learning: A Reviewcited by 20
  8. 2023Sequential Predictive Two-Sample and Independence Testingcited by 20
  9. 2022AutoML Two-Sample Testcited by 19
  10. 2021Meta Two-Sample Testing: Learning Kernels for Testing with Limited Datacited by 18
  11. 2023SurvivalGAN: Generating Time-to-Event Data for Survival Analysiscited by 17
  12. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  13. 2021Neural Tangent Kernel Maximum Mean Discrepancycited by 15
  14. 2023Differentially Private Neural Tangent Kernels for Privacy-Preserving Data Generationcited by 15
  15. 2023Compress Then Test: Powerful Kernel Testing in Near-linear Timecited by 14
  16. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  17. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  18. 2022MMD-B-Fair: Learning Fair Representations with Statistical Testingcited by 13
  19. 2021Maximum Mean Discrepancy for Generalization in the Presence of Distribution and Missingness Shiftcited by 11
  20. 2022How Robust is Your Fairness? Evaluating and Sustaining Fairness under Unseen Distribution Shiftscited by 11
  21. 2022CADet: Fully Self-Supervised Out-Of-Distribution Detection With Contrastive Learningcited by 11
  22. 2025Scale-wise Distillation of Diffusion Modelscited by 11
  23. 2023Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Samplingcited by 10
  24. 2021Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimizationcited by 9
  25. 2023The Representation Jensen-Shannon Divergencecited by 9
  26. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 9
  27. 2023Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimationcited by 8
  28. 2021Kernel Two-Sample Tests for Manifold Datacited by 7
  29. 2021Statistical and Topological Properties of Gaussian Smoothed Sliced Probability Divergencescited by 7
  30. 2023Variable Selection for Kernel Two-Sample Testscited by 7
  31. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 7
  32. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  33. 2022Kernel Robust Hypothesis Testingcited by 6
  34. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  35. 2025On the Hardness of Conditional Independence Testing In Practicecited by 6
  36. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  37. 2023Variable Selection in Maximum Mean Discrepancy for Interpretable Distribution Comparisoncited by 5
  38. 2024A Unified Data Representation Learning for Non-parametric Two-sample Testingcited by 5

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