mlsanityData to 14 Oct 2026

Regularized f-Divergence Kernel Tests

arXiv 2601.19755 ↗First posted 27 Jan 2026stat.ML cs.LGcited by 2

On the map: LLM safety and security → Machine unlearning

Abstract (arXiv)

We propose a framework to construct practical kernel-based two-sample tests from the family of f-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we estimate using kernel methods. The proposed test is adaptive over hyperparameters such as the kernel bandwidth and the regularization parameter. We provide theoretical guarantees for statistical test power across our family of f-divergence estimates. While our test covers a variety of f-divergences, we bring particular focus to the Hockey-Stick divergence, motivated by its applications to differential privacy auditing and machine unlearning evaluation. For two-sample testing, experiments demonstrate that different f-divergences are sensitive to different localized differences, illustrating the importance of leveraging diverse statistics. For machine unlearning, we propose a relative test that distinguishes true unlearning failures from safe distributional variations.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in Machine unlearning, one of 12 directions in LLM safety and security. Builds on 35 of its 79 references that are in the map. First posted on arXiv 27 Jan 2026.

Builds on

35 of 79 references.

Closest ancestors · 4

Same direction, newest first

  1. 2025On the Impossibility of Retrain Equivalence in Machine Unlearning18 Oct
  2. 2024Are we making progress in unlearning? Findings from the first NeurIPS unlearning competition13 Jun
  3. 2023Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening15 Aug
  4. 2021Remember What You Want to Forget: Algorithms for Machine Unlearning4 Mar

Other references · 31

  1. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 506
  2. 2020Learning Deep Kernels for Non-Parametric Two-Sample Testscited by 130
  3. 2017Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networkscited by 107
  4. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 100
  5. 2021Optimal Accounting of Differential Privacy via Characteristic Functioncited by 86
  6. 2021MMD Aggregated Two-Sample Testcited by 75
  7. 2020Generalized Energy Based Modelscited by 73
  8. 2020Non-parametric Models for Non-negative Functionscited by 41
  9. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
  10. 2022MAUVE Scores for Generative Models: Theory and Practicecited by 36
  11. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  12. 2014A Wild Bootstrap for Degenerate Kernel Testscited by 29
19 more
  1. 2016Understanding the Sparse Vector Technique for Differential Privacycited by 27
  2. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  3. 2015A Test of Relative Similarity For Model Selection in Generative Modelscited by 25
  4. 2022Learning new physics efficiently with nonparametric methodscited by 21
  5. 2022AutoML Two-Sample Testcited by 20
  6. 2018Property Testing for Differential Privacycited by 16
  7. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  8. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 13
  9. 2023DP-Auditorium: a Large Scale Library for Auditing Differential Privacycited by 11
  10. 2023Goodness of fit by Neyman-Pearson testingcited by 10
  11. 2023Differentially Private Permutation Testscited by 10
  12. 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7
  13. 2024Multiple testing for signal-agnostic searches of new physics with machine learningcited by 7
  14. 2016Analysis of k-Nearest Neighbor Distances with Application to Entropy Estimationcited by 6
  15. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  16. 2025A Unified View of Optimal Kernel Hypothesis Testingcited by 5
  17. 2019Comparing a Large Number of Multivariate Distributionscited by 3
  18. 2022Importance Weighting Approach in Kernel Bayes' Rulecited by 1
  19. 2025Sparse, self-organizing ensembles of local kernels detect rare statistical anomaliescited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Zero-Flow Two-Sample Testscited by 3
  2. 2026Behavioral Guarantees for Proxy-Based Unlearningcited by 0

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  1. 2025A Unified Framework for Diffusion Model Unlearning with f-Divergence
  2. 2025Gaussian Certified Unlearning in High Dimensions: A Hypothesis Testing Approach
  3. 2026Statistical Unlearning of Distributions: A Hypothesis Testing Approach
  4. 2025Leveraging Per-Instance Privacy for Machine Unlearning
  5. 2026The Illusion of Equivalence: Systematic FP16 Divergence in KV-Cached Autoregressive Inference
  6. 2023Kernel-Based Tests for Likelihood-Free Hypothesis Testing
  7. 2025The Measure of Deception: An Analysis of Data Forging in Machine Unlearning
  8. 2026Auditing of Unlearning Algorithms