Anytime-Valid Tests of Group Invariance through Conformal Prediction

Tyron Lardy, Muriel F. Pérez-Ortiz
Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications, PMLR 266:645-665, 2025.

Abstract

Many standard statistical hypothesis tests, including those for normality and exchangeability, can be reformulated as tests of invariance under a group of transformations. We develop anytime-valid tests of invariance under the action of general compact groups and show their optimality—in a specific logarithmic-growth sense—against certain alternatives. This is achieved by using the invariant structure of the problem to construct conformal test martingales, a class of objects associated to conformal prediction. We apply our methods to extend recent anytime-valid tests of independence, which leverage exchangeability, to work under general group invariances. Additionally, we show applications to testing for invariance under subgroups of rotations, which corresponds to testing the Gaussian-error assumptions in linear models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v266-lardy25a, title = {Anytime-Valid Tests of Group Invariance through Conformal Prediction}, author = {Lardy, Tyron and P\'{e}rez-Ortiz, Muriel F.}, booktitle = {Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {645--665}, year = {2025}, editor = {Nguyen, Khuong An and Luo, Zhiyuan and Papadopoulos, Harris and Löfström, Tuwe and Carlsson, Lars and Boström, Henrik}, volume = {266}, series = {Proceedings of Machine Learning Research}, month = {10--12 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v266/main/assets/lardy25a/lardy25a.pdf}, url = {https://proceedings.mlr.press/v266/lardy25a.html}, abstract = {Many standard statistical hypothesis tests, including those for normality and exchangeability, can be reformulated as tests of invariance under a group of transformations. We develop anytime-valid tests of invariance under the action of general compact groups and show their optimality—in a specific logarithmic-growth sense—against certain alternatives. This is achieved by using the invariant structure of the problem to construct conformal test martingales, a class of objects associated to conformal prediction. We apply our methods to extend recent anytime-valid tests of independence, which leverage exchangeability, to work under general group invariances. Additionally, we show applications to testing for invariance under subgroups of rotations, which corresponds to testing the Gaussian-error assumptions in linear models.} }
Endnote
%0 Conference Paper %T Anytime-Valid Tests of Group Invariance through Conformal Prediction %A Tyron Lardy %A Muriel F. Pérez-Ortiz %B Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications %C Proceedings of Machine Learning Research %D 2025 %E Khuong An Nguyen %E Zhiyuan Luo %E Harris Papadopoulos %E Tuwe Löfström %E Lars Carlsson %E Henrik Boström %F pmlr-v266-lardy25a %I PMLR %P 645--665 %U https://proceedings.mlr.press/v266/lardy25a.html %V 266 %X Many standard statistical hypothesis tests, including those for normality and exchangeability, can be reformulated as tests of invariance under a group of transformations. We develop anytime-valid tests of invariance under the action of general compact groups and show their optimality—in a specific logarithmic-growth sense—against certain alternatives. This is achieved by using the invariant structure of the problem to construct conformal test martingales, a class of objects associated to conformal prediction. We apply our methods to extend recent anytime-valid tests of independence, which leverage exchangeability, to work under general group invariances. Additionally, we show applications to testing for invariance under subgroups of rotations, which corresponds to testing the Gaussian-error assumptions in linear models.
APA
Lardy, T. & Pérez-Ortiz, M.F.. (2025). Anytime-Valid Tests of Group Invariance through Conformal Prediction. Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 266:645-665 Available from https://proceedings.mlr.press/v266/lardy25a.html.

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