Conditional Testing based on Localized Conformal p-values
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916410900348928 |
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| author | Wu, Xiaoyang Lu, Lin Wang, Zhaojun Zou, Changliang |
| author_facet | Wu, Xiaoyang Lu, Lin Wang, Zhaojun Zou, Changliang |
| contents | In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conditional Testing based on Localized Conformal p-values Wu, Xiaoyang Lu, Lin Wang, Zhaojun Zou, Changliang Methodology Machine Learning In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies. |
| title | Conditional Testing based on Localized Conformal p-values |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2409.16829 |