mlsanityData to 14 Oct 2026

Learning Deep Kernels for Non-Parametric Two-Sample Tests

arXiv 2002.09116 ↗First posted 21 Feb 2020stat.ML cs.LG stat.MEcited by 130

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Abstract (arXiv)

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two sample tests is available at https://github.com/fengliu90/DK-for-TST.

Key facts. Cited by 130 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Feb 2020.

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Citing papers per year: 2021: 20; 2022: 27; 2023: 20; 2024: 19; 2025: 25; 2026: 19.

130 papers.

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  1. 2021Benchmarking Simulation-Based Inferencecited by 162
  2. 2022Federated Class-Incremental Learningcited by 127
  3. 2021MMD Aggregated Two-Sample Testcited by 75
  4. 2022M3Care: Learning with Missing Modalities in Multimodal Healthcare Datacited by 72
  5. 2021Neural Mean Discrepancy for Efficient Out-of-Distribution Detectioncited by 42
  6. 2025Beyond Reward Hacking: Causal Rewards for Large Language Model Alignmentcited by 42
  7. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  8. 2021Meta Discovery: Learning to Discover Novel Classes given Very Limited Datacited by 31
  9. 2022Evaluating generative models in high energy physicscited by 31
  10. 2022Bilateral Dependency Optimization: Defending Against Model-inversion Attackscited by 30
  11. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 30
  12. 2021Learning Bounds for Open-Set Learningcited by 27
38 more
  1. 2021Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processescited by 27
  2. 2021A Witness Two-Sample Testcited by 23
  3. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  4. 2023Sequential Predictive Two-Sample and Independence Testingcited by 21
  5. 2022AutoML Two-Sample Testcited by 20
  6. 2023Detecting Adversarial Data by Probing Multiple Perturbations Using Expected Perturbation Scorecited by 20
  7. 2024Detecting Machine-Generated Texts by Multi-Population Aware Optimization for Maximum Mean Discrepancycited by 20
  8. 2022A Learning Based Hypothesis Test for Harmful Covariate Shiftcited by 19
  9. 2021Isometric Propagation Network for Generalized Zero-shot Learningcited by 18
  10. 2021Meta Two-Sample Testing: Learning Kernels for Testing with Limited Datacited by 18
  11. 2021On the benefits of representation regularization in invariance based domain generalizationcited by 17
  12. 2021TOHAN: A One-step Approach towards Few-shot Hypothesis Adaptationcited by 17
  13. 2025Understanding Multimodal LLMs Under Distribution Shifts: An Information-Theoretic Approachcited by 16
  14. 2021Neural Tangent Kernel Maximum Mean Discrepancycited by 15
  15. 2023Differentially Private Neural Tangent Kernels for Privacy-Preserving Data Generationcited by 15
  16. 2024Practical Kernel Tests of Conditional Independencecited by 15
  17. 2022Model-agnostic out-of-distribution detection using combined statistical testscited by 14
  18. 2022DC-Check: A Data-Centric AI checklist to guide the development of reliable machine learning systemscited by 14
  19. 2023Compress Then Test: Powerful Kernel Testing in Near-linear Timecited by 14
  20. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  21. 2022MMD-B-Fair: Learning Fair Representations with Statistical Testingcited by 13
  22. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 13
  23. 2024Online Drift Detection with Maximum Concept Discrepancycited by 12
  24. 2022How Robust is Your Fairness? Evaluating and Sustaining Fairness under Unseen Distribution Shiftscited by 11
  25. 2022CADet: Fully Self-Supervised Out-Of-Distribution Detection With Contrastive Learningcited by 11
  26. 2022Evaluating Aleatoric Uncertainty via Conditional Generative Modelscited by 10
  27. 2022E-Valuating Classifier Two-Sample Testscited by 10
  28. 2023Boosting the Power of Kernel Two-Sample Testscited by 10
  29. 2022Context-Aware Drift Detectioncited by 9
  30. 2023The Representation Jensen-Shannon Divergencecited by 9
  31. 2023A Bias-Variance-Covariance Decomposition of Kernel Scores for Generative Modelscited by 8
  32. 2023Variable Selection for Kernel Two-Sample Testscited by 7
  33. 2025Low-Rank Thinningcited by 7
  34. 2025On the Hardness of Conditional Independence Testing In Practicecited by 7
  35. 2024A Unified Data Representation Learning for Non-parametric Two-sample Testingcited by 6
  36. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  37. 2022A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networkscited by 5
  38. 2022Evaluating Graph Generative Models with Contrastively Learned Featurescited by 5

50 most cited of 130 All 130 (JSON)