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.

翻译：本文通过共形推断框架解决条件检验问题。我们通过逆推预测区间定义局部化共形p值，并证明其理论性质。随后将这些定义的p值应用于多个条件检验问题以展示其实用性。首先，我们提出条件异常值检测程序，用于检验条件分布中的异常值，并在有限样本下控制错误发现率（FDR）。我们还引入新颖的条件标签筛选问题，旨在筛选多元响应变量，并提出控制族错误率（FWER）的筛选程序。最后，我们考虑双样本条件分布检验，通过聚合局部化p值定义加权U统计量。数值模拟与真实数据案例验证了我们所提出策略的优越性能。