mlsanityData to 7 Oct 2026

Robust Kernel Hypothesis Testing under Data Corruption

arXiv 2405.19912 ↗First posted 30 May 2024stat.ML cs.LGcited by 7

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Abstract (arXiv)

We propose a general method for constructing robust permutation tests under data corruption. The proposed tests effectively control the non-asymptotic type I error under data corruption, and we prove their consistency in power under minimal conditions. This contributes to the practical deployment of hypothesis tests for real-world applications with potential adversarial attacks. For the two-sample and independence settings, we show that our kernel robust tests are minimax optimal, in the sense that they are guaranteed to be non-asymptotically powerful against alternatives uniformly separated from the null in the kernel MMD and HSIC metrics at some optimal rate (tight with matching lower bound). We point out that existing differentially private tests can be adapted to be robust to data corruption, and we demonstrate in experiments that our proposed tests achieve much higher power than these private tests. Finally, we provide publicly available implementations and empirically illustrate the practicality of our robust tests.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 39 of its 83 references that are in the map. First posted on arXiv 30 May 2024.

Builds on

39 of 83 references.

References · 39

  1. 2016Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixturescited by 114
  2. 2019Recent Advances in Algorithmic High-Dimensional Robust Statisticscited by 100
  3. 2021MMD Aggregated Two-Sample Testcited by 74
  4. 2020Differentially Private Assouad, Fano, and Le Camcited by 54
  5. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 43
  6. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  7. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
  8. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  9. 2018Robust Hypothesis Testing Using Wasserstein Uncertainty Setscited by 28
  10. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  11. 2019Finite sample properties of parametric MMD estimation: robustness to misspecification and dependencecited by 24
  12. 2019On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternativescited by 21
27 more
  1. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  2. 2022A Permutation-free Kernel Two-Sample Testcited by 21
  3. 2022Spectral Regularized Kernel Two-Sample Testscited by 19
  4. 2014FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Testcited by 17
  5. 2022On robustness and local differential privacycited by 15
  6. 2023Compress Then Test: Powerful Kernel Testing in Near-linear Timecited by 14
  7. 2018Test without Trust: Optimal Locally Private Distribution Testingcited by 13
  8. 2019Differentially Private Nonparametric Hypothesis Testingcited by 12
  9. 2018Post Selection Inference with Incomplete Maximum Mean Discrepancy Estimatorcited by 11
  10. 2022A Permutation-Free Kernel Independence Testcited by 11
  11. 2017Priv'IT: Private and Sample Efficient Identity Testingcited by 10
  12. 2023Boosting the Power of Kernel Two-Sample Testscited by 10
  13. 2023Differentially Private Permutation Testscited by 10
  14. 2022A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Setscited by 9
  15. 2023The Test of Tests: A Framework For Differentially Private Hypothesis Testingcited by 9
  16. 2015A simpler condition for consistency of a kernel independence testcited by 8
  17. 2023The Full Landscape of Robust Mean Testing: Sharp Separations between Oblivious and Adaptive Contaminationcited by 8
  18. 2022Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanismcited by 7
  19. 2022Kernel Robust Hypothesis Testingcited by 6
  20. 2020The Sample Complexity of Robust Covariance Testingcited by 5
  21. 2021Robust Testing and Estimation under Manipulation Attackscited by 5
  22. 2017Differentially Private ANOVA Testingcited by 4
  23. 2019Comparing a Large Number of Multivariate Distributionscited by 3
  24. 2022Concentration of discrepancy-based approximate Bayesian computation via Rademacher complexitycited by 3
  25. 2017Differentially Private Identity and Closeness Testing of Discrete Distributionscited by 2
  26. 2018A Differentially Private Kernel Two-Sample Testcited by 1
  27. 2022Robust Testing in High-Dimensional Sparse Modelscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 2.

7 papers.

  1. 2025Integral Imprecise Probability Metricscited by 11
  2. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 9
  3. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  4. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  5. 2025A Unified View of Optimal Kernel Hypothesis Testingcited by 4
  6. 2026Regularized f-Divergence Kernel Testscited by 2
  7. 2026Kernel Tests of Equivalencecited by 2