mlsanityData to 13 Oct 2026

Interpretable Distribution Features with Maximum Testing Power

arXiv 1605.06796 ↗First posted 22 May 2016stat.ML cs.LGcited by 63

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Abstract (arXiv)

Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the distinguishability of the distributions, by optimizing a lower bound on test power for a statistical test using these features. The result is a parsimonious and interpretable indication of how and where two distributions differ locally. An empirical estimate of the test power criterion converges with increasing sample size, ensuring the quality of the returned features. In real-world benchmarks on high-dimensional text and image data, linear-time tests using the proposed semimetrics achieve comparable performance to the state-of-the-art quadratic-time maximum mean discrepancy test, while returning human-interpretable features that explain the test results.

Key facts. Cited by 63 papers in the map (data through 13 Oct 2026). First posted on arXiv 22 May 2016.

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Citing papers per year: 2021: 12; 2022: 14; 2023: 13; 2024: 9; 2025: 10; 2026: 5.

63 papers.

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  1. 2021MMD Aggregated Two-Sample Testcited by 74
  2. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  3. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  4. 2021PEARL: Data Synthesis via Private Embeddings and Adversarial Reconstruction Learningcited by 23
  5. 2021A Witness Two-Sample Testcited by 22
  6. 2022Nystr"om Kernel Mean Embeddingscited by 21
  7. 2022A Permutation-free Kernel Two-Sample Testcited by 21
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  9. 2023Sequential Predictive Two-Sample and Independence Testingcited by 20
  10. 2022AutoML Two-Sample Testcited by 19
  11. 2021Meta Two-Sample Testing: Learning Kernels for Testing with Limited Datacited by 18
  12. 2021Neural Tangent Kernel Maximum Mean Discrepancycited by 15
38 more
  1. 2022DC-Check: A Data-Centric AI checklist to guide the development of reliable machine learning systemscited by 14
  2. 2023Compress Then Test: Powerful Kernel Testing in Near-linear Timecited by 14
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  4. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  5. 2021An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddingscited by 12
  6. 2022CADet: Fully Self-Supervised Out-Of-Distribution Detection With Contrastive Learningcited by 11
  7. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 11
  8. 2022E-Valuating Classifier Two-Sample Testscited by 10
  9. 2022Context-Aware Drift Detectioncited by 9
  10. 2023The Representation Jensen-Shannon Divergencecited by 9
  11. 2021Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samplescited by 8
  12. 2021Kernel Two-Sample Tests for Manifold Datacited by 7
  13. 2023Variable Selection for Kernel Two-Sample Testscited by 7
  14. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  15. 2025On the Hardness of Conditional Independence Testing In Practicecited by 6
  16. 2023Nystr"om M-Hilbert-Schmidt Independence Criterioncited by 5
  17. 2023Variable Selection in Maximum Mean Discrepancy for Interpretable Distribution Comparisoncited by 5
  18. 2024A Unified Data Representation Learning for Non-parametric Two-sample Testingcited by 5
  19. 2025PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transportcited by 5
  20. 2021Human-in-the-loop Handling of Knowledge Driftcited by 4
  21. 2024Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distancescited by 4
  22. 2024MOKD: Cross-domain Finetuning for Few-shot Classification via Maximizing Optimized Kernel Dependencecited by 4
  23. 2024Nystr"om Kernel Stein Discrepancycited by 4
  24. 2025A Scalable Nystrom-Based Kernel Two-Sample Test with Permutationscited by 4
  25. 2022AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generatorscited by 3
  26. 2022Kernel Biclustering algorithm in Hilbert Spacescited by 3
  27. 2023A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networkscited by 3
  28. 2023MLOps Spanning Whole Machine Learning Life Cycle: A Surveycited by 3
  29. 2023Understanding Deep Generative Models with Generalized Empirical Likelihoodscited by 3
  30. 2024A Sinkhorn-type Algorithm for Constrained Optimal Transportcited by 3
  31. 2026Zero-Flow Two-Sample Testscited by 3
  32. 2022Adversarial Attack and Defense for Non-Parametric Two-Sample Testscited by 2
  33. 2023MLHOps: Machine Learning for Healthcare Operationscited by 2
  34. 2024Learning Representations for Independence Testingcited by 2
  35. 2024Recurrent Neural Goodness-of-Fit Test for Time Seriescited by 2
  36. 2021Kernel distance measures for time series, random fields and other structured datacited by 1
  37. 2021A fast and effective kernel two-sample test for large-scale datacited by 1
  38. 2022A Kernelised Stein Statistic for Assessing Implicit Generative Modelscited by 1

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