A Unified Framework for Statistical Testing of Invariance

MCML Authors

Stefanie Jegelka

Prof. Dr.

Core PI

Foundations of Deep Neural Networks

Abstract

While invariances naturally arise in almost any type of real-world data, no efficient and robust test exists for detecting them in observational data under arbitrarily given group actions. We tackle this problem by studying discrepancy-based measures of invariance that can capture even subtle distributional asymmetries. Our first contribution is to show that, while detecting worst-case asymmetries can be emph{computationally intractable}, a randomized method can estimate closeness measures to invariance within emph{universal constant factors}. This provides a general framework for statistical testing of invariance under compact group actions. Despite the extensive and well-established literature on group-based testing, our methodology, to the best of our knowledge, is the emph{first} to provide statistical tests for general group invariances with emph{finite-sample guarantees on Type II errors} against worst-case alternatives. We instantiate the framework for common probability discrepancies, including total variation, Wasserstein distances, integral probability metrics, energy distance, and maximum mean discrepancy, obtaining explicit sample-complexity guarantees from empirical convergence rates.

inproceedings STJ+26a

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Testing @ICML 2026

Workshop on Hypothesis Testing at the 43rd International Conference on Machine Learning. Seoul, South Korea, Jul 06-11, 2026.

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Authors

A. Soleymani • B. Tahmasebi • P. Jaillet • S. Jegelka

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Links

URL

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Research Area

 A3 | Computational Models