Testing Conditional Mean Independence Using Generative Neural Networks
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915126858219520 |
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| author | Zhang, Yi Huang, Linjun Yang, Yun Shao, Xiaofeng |
| author_facet | Zhang, Yi Huang, Linjun Yang, Yun Shao, Xiaofeng |
| contents | Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure that utilizes deep generative neural networks to estimate the conditional mean functions involved in the population measure. The test statistic is thoughtfully constructed to ensure that even slowly decaying nonparametric estimation errors do not affect the asymptotic accuracy of the test. Our approach demonstrates strong empirical performance in scenarios with high-dimensional covariates and response variable, can handle multivariate responses, and maintains nontrivial power against local alternatives outside an $n^{-1/2}$ neighborhood of the null hypothesis. We also use numerical simulations and real-world imaging data applications to highlight the efficacy and versatility of our testing procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Testing Conditional Mean Independence Using Generative Neural Networks Zhang, Yi Huang, Linjun Yang, Yun Shao, Xiaofeng Machine Learning 62H20, 62G10, 62G20 Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure that utilizes deep generative neural networks to estimate the conditional mean functions involved in the population measure. The test statistic is thoughtfully constructed to ensure that even slowly decaying nonparametric estimation errors do not affect the asymptotic accuracy of the test. Our approach demonstrates strong empirical performance in scenarios with high-dimensional covariates and response variable, can handle multivariate responses, and maintains nontrivial power against local alternatives outside an $n^{-1/2}$ neighborhood of the null hypothesis. We also use numerical simulations and real-world imaging data applications to highlight the efficacy and versatility of our testing procedure. |
| title | Testing Conditional Mean Independence Using Generative Neural Networks |
| topic | Machine Learning 62H20, 62G10, 62G20 |
| url | https://arxiv.org/abs/2501.17345 |