mlsanityData to 14 Oct 2026

MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting

arXiv 2306.08777 ↗First posted 14 Jun 2023stat.ML cs.LG math.STcited by 33

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Abstract (arXiv)

We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining (normalised) MMD values under each of these kernels via a weighted soft maximum. Exponential concentration bounds are proved for our proposed statistics under the null and alternative. We further show how these kernels can be chosen in a data-dependent but permutation-independent way, in a well-calibrated test, avoiding data splitting. This technique applies more broadly to general permutation-based MMD testing, and includes the use of deep kernels with features learnt using unsupervised models such as auto-encoders. We highlight the applicability of our MMD-FUSE test on both synthetic low-dimensional and real-world high-dimensional data, and compare its performance in terms of power against current state-of-the-art kernel tests.

Key facts. Cited by 33 papers in the map (data through 14 Oct 2026). Builds on 58 of its 107 references that are in the map. First posted on arXiv 14 Jun 2023.

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58 of 107 references.

References · 58

  1. 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 12,049
  2. 2019Momentum Contrast for Unsupervised Visual Representation Learningcited by 7,513
  3. 2020Bootstrap your own latent: A new approach to self-supervised Learningcited by 4,750
  4. 2020Exploring Simple Siamese Representation Learningcited by 2,866
  5. 2020Unsupervised Learning of Visual Features by Contrasting Cluster Assignmentscited by 2,857
  6. 2020Improved Baselines with Momentum Contrastive Learningcited by 2,287
  7. 2021Barlow Twins: Self-Supervised Learning via Redundancy Reductioncited by 1,838
  8. 2019Do ImageNet Classifiers Generalize to ImageNet?cited by 1,515
  9. 2020Big Self-Supervised Models are Strong Semi-Supervised Learnerscited by 1,380
  10. 2017Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Datacited by 533
  11. 2016Revisiting Classifier Two-Sample Testscited by 268
  12. 2021User-friendly introduction to PAC-Bayes boundscited by 239
38 more
  1. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  2. 2016A Kernel Test of Goodness of Fitcited by 143
  3. 2019A Primer on PAC-Bayesian Learningcited by 132
  4. 2020Learning Deep Kernels for Non-Parametric Two-Sample Testscited by 130
  5. 2018Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approachcited by 126
  6. 2020Tighter risk certificates for neural networkscited by 112
  7. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 100
  8. 2017Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priorscited by 81
  9. 2021Self-Supervised Learning with Kernel Dependence Maximizationcited by 77
  10. 2021MMD Aggregated Two-Sample Testcited by 75
  11. 2016Interpretable Distribution Features with Maximum Testing Powercited by 63
  12. 2015Fast Two-Sample Testing with Analytic Representations of Probability Measurescited by 53
  13. 2021Kernel Thinningcited by 47
  14. 2021Galaxy Zoo DECaLS: Detailed Visual Morphology Measurements from Volunteers and Deep Learning for 314,000 Galaxiescited by 41
  15. 2020Second Order PAC-Bayesian Bounds for the Weighted Majority Votecited by 34
  16. 2014A Wild Bootstrap for Degenerate Kernel Testscited by 29
  17. 2020Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networkscited by 29
  18. 2019Two-sample Testing Using Deep Learningcited by 27
  19. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  20. 2023A unified recipe for deriving (time-uniform) PAC-Bayes boundscited by 25
  21. 2022PAC-Bayes Generalisation Bounds for Heavy-Tailed Losses through Supermartingalescited by 24
  22. 2021A Witness Two-Sample Testcited by 23
  23. 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networkscited by 22
  24. 2022Online PAC-Bayes Learningcited by 22
  25. 2019On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternativescited by 21
  26. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  27. 2022A Permutation-free Kernel Two-Sample Testcited by 21
  28. 2022AutoML Two-Sample Testcited by 20
  29. 2022Spectral Regularized Kernel Two-Sample Testscited by 20
  30. 2020Learning Kernel Tests Without Data Splittingcited by 19
  31. 2021On Margins and Derandomisation in PAC-Bayescited by 19
  32. 2021Meta Two-Sample Testing: Learning Kernels for Testing with Limited Datacited by 18
  33. 2014FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Testcited by 17
  34. 2019Function-Space Distributions over Kernelscited by 17
  35. 2021Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Boundcited by 16
  36. 2020Dimension-agnostic inference using cross U-statisticscited by 14
  37. 2023Compress Then Test: Powerful Kernel Testing in Near-linear Timecited by 14
  38. 2021Chebyshev-Cantelli PAC-Bayes-Bennett Inequality for the Weighted Majority Votecited by 13

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Citing papers per year: 2024: 8; 2025: 15; 2026: 10.

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  1. 2024Practical Kernel Tests of Conditional Independencecited by 15
  2. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  3. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 13
  4. 2024Neural-Kernel Conditional Mean Embeddingscited by 7
  5. 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7
  6. 2024Particle Semi-Implicit Variational Inferencecited by 7
  7. 2024Multiple testing for signal-agnostic searches of new physics with machine learningcited by 7
  8. 2024A Unified Data Representation Learning for Non-parametric Two-sample Testingcited by 6
  9. 2025A Scalable Nystrom-Based Kernel Two-Sample Test with Permutationscited by 6
  10. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  11. 2025A Unified View of Optimal Kernel Hypothesis Testingcited by 5
  12. 2025Knowledge Distillation Detection for Open-weights Modelscited by 4
21 more
  1. 2026Model-Agnostic Signal Discovery with Machine Learning: Bridging the Gap Between Theory and Practicecited by 3
  2. 2026Zero-Flow Two-Sample Testscited by 3
  3. 2024Learning Representations for Independence Testingcited by 2
  4. 2025AutoSciDACT: Automated Scientific Discovery through Contrastive Embedding and Hypothesis Testingcited by 2
  5. 2026Regularized f-Divergence Kernel Testscited by 2
  6. 2025KAIROS: Scalable Model-Agnostic Data Valuationcited by 1
  7. 2025Conformal C2ST: Turning weak classifiers into strong two-sample testscited by 1
  8. 2025Anchor-based Maximum Discrepancy for Relative Similarity Testingcited by 1
  9. 2025Minimax-Optimal Two-Sample Test with Sliced Wassersteincited by 1
  10. 2025Sparse, self-organizing ensembles of local kernels detect rare statistical anomaliescited by 1
  11. 2026LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetrycited by 1
  12. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 1
  13. 2025Kernel Quantile Embeddings and Associated Probability Metricscited by 0
  14. 2025Weakly Supervised Object Segmentation by Background Conditional Divergencecited by 0
  15. 2025Are Two Datasets Close Enough With Statistical Significance? A Kernel Distributional Closeness Testing Approachcited by 0
  16. 2025Classical and quantum kernel fusion for two-sample testingcited by 0
  17. 2026Learning to Test: Latent Representation Learning for Dynamic Instability Detectioncited by 0
  18. 2026Kernel Selection is Model Selection: A Unified Complexity-Penalized Approach for MMD Two-Sample Testscited by 0
  19. 2026Nonparametric Deconvolution and Denoising using Simulation Based Inferencecited by 0
  20. 2026USAD: Uncertainty-aware Statistical Adversarial Detectioncited by 0
  21. 2026Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributionscited by 0