Conditional Testing based on Localized Conformal $p$-values
Xiaoyang Wu, Lin Lu, Zhaojun Wang, Changliang Zou
Abstract
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.
BibTeX
@inproceedings{
wu2025conditional,
title={Conditional Testing based on Localized Conformal \$p\$-values},
author={Xiaoyang Wu and Lin Lu and Zhaojun Wang and Changliang Zou},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=Ip6UwB35uT}
}