Regularized $f$-Divergence Kernel Tests

Mónica Ribero, Antonin Schrab, Arthur Gretton
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4249-4257, 2026.

Abstract

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. Aggregation is used to adapt the test over hyperparameters such as the kernel bandwidth and the regularization parameter. 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. We provide theoretical guarantees for statistical test power across our family of $f$-divergence estimates. 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-ribero26a, title = { Regularized $f$-Divergence Kernel Tests }, author = {Ribero, M{\'o}nica and Schrab, Antonin and Gretton, Arthur}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4249--4257}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/ribero26a/ribero26a.pdf}, url = {https://proceedings.mlr.press/v300/ribero26a.html}, abstract = { 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. Aggregation is used to adapt the test over hyperparameters such as the kernel bandwidth and the regularization parameter. 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. We provide theoretical guarantees for statistical test power across our family of $f$-divergence estimates. 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. } }
Endnote
%0 Conference Paper %T Regularized $f$-Divergence Kernel Tests %A Mónica Ribero %A Antonin Schrab %A Arthur Gretton %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-ribero26a %I PMLR %P 4249--4257 %U https://proceedings.mlr.press/v300/ribero26a.html %V 300 %X 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. Aggregation is used to adapt the test over hyperparameters such as the kernel bandwidth and the regularization parameter. 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. We provide theoretical guarantees for statistical test power across our family of $f$-divergence estimates. 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.
APA
Ribero, M., Schrab, A. & Gretton, A.. (2026). Regularized $f$-Divergence Kernel Tests . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4249-4257 Available from https://proceedings.mlr.press/v300/ribero26a.html.

Related Material