mlsanityData to 7 Oct 2026

A Unified View of Optimal Kernel Hypothesis Testing

arXiv 2503.07084 ↗First posted 10 Mar 2025stat.ML cs.LG stat.MEcited by 4

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Abstract (arXiv)

This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and L2 metrics are presented, with two adaptive kernel selection methods (kernel pooling and aggregation), and under various testing constraints: computational efficiency, differential privacy, and robustness to data corruption. Intuition behind the derivation of the power results is provided in a unified way across the three frameworks, and open problems are highlighted.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 23 of its 49 references that are in the map. First posted on arXiv 10 Mar 2025.

Builds on

23 of 49 references.

References · 23

  1. 2014RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Responsecited by 262
  2. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  3. 2017Collecting Telemetry Data Privatelycited by 147
  4. 2016A Kernel Test of Goodness of Fitcited by 143
  5. 2017Measuring Sample Quality with Kernelscited by 119
  6. 2021MMD Aggregated Two-Sample Testcited by 74
  7. 2015Fast Two-Sample Testing with Analytic Representations of Probability Measurescited by 53
  8. 2021Kernel Thinningcited by 47
  9. 2020Blindness of score-based methods to isolated components and mixing proportionscited by 33
  10. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  11. 2016Large-Scale Kernel Methods for Independence Testingcited by 32
  12. 2014A Wild Bootstrap for Degenerate Kernel Testscited by 28
11 more
  1. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  2. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  3. 2014FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Testcited by 17
  4. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  5. 2023Compress Then Test: Powerful Kernel Testing in Near-linear Timecited by 14
  6. 2022Towards Healing the Blindness of Score Matchingcited by 13
  7. 2024Practical Kernel Tests of Conditional Independencecited by 13
  8. 2023Differentially Private Permutation Testscited by 10
  9. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 9
  10. 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7
  11. 2015Goodness of fit tests for high-dimensional linear modelscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  2. 2025Amortized Linear-time Exact Shapley Value for Product-Kernel Methodscited by 3
  3. 2026Regularized f-Divergence Kernel Testscited by 2
  4. 2025Kernel Quantile Embeddings and Associated Probability Metricscited by 0