Randomization Tests for Conditional Group Symmetry

Fuente: arXiv
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Main Authors: Chiu, Kenny, Sharp, Alex, Bloem-Reddy, Benjamin
Format: Preprint
Published: 2024
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author Chiu, Kenny
Sharp, Alex
Bloem-Reddy, Benjamin
author_facet Chiu, Kenny
Sharp, Alex
Bloem-Reddy, Benjamin
contents Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of equivariance or conditional invariance are absent from the literature. This work initiates the study of nonparametric randomization tests for symmetry (invariance or equivariance) of a conditional distribution under the action of a specified locally compact group. We develop a general framework for randomization tests with finite-sample Type I error control and, using kernel methods, implement tests with finite-sample power lower bounds. We also describe and implement approximate versions of the tests, which are asymptotically consistent. We study their properties empirically using synthetic examples and applications to testing for symmetry in two problems from high-energy particle physics.
format Preprint
id arxiv_https___arxiv_org_abs_2412_14391
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Randomization Tests for Conditional Group Symmetry
Chiu, Kenny
Sharp, Alex
Bloem-Reddy, Benjamin
Methodology
Statistics Theory
Machine Learning
62G10, 62H15, 62H05, 62P35
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of equivariance or conditional invariance are absent from the literature. This work initiates the study of nonparametric randomization tests for symmetry (invariance or equivariance) of a conditional distribution under the action of a specified locally compact group. We develop a general framework for randomization tests with finite-sample Type I error control and, using kernel methods, implement tests with finite-sample power lower bounds. We also describe and implement approximate versions of the tests, which are asymptotically consistent. We study their properties empirically using synthetic examples and applications to testing for symmetry in two problems from high-energy particle physics.
title Randomization Tests for Conditional Group Symmetry
topic Methodology
Statistics Theory
Machine Learning
62G10, 62H15, 62H05, 62P35
url https://arxiv.org/abs/2412.14391