Randomization Tests for Conditional Group Symmetry
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911311830450176 |
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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 |
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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 |