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  1. Free, publicly-accessible full text available May 1, 2025
  2. Abstract

    This paper presents a conformal inference method for out-of-distribution testing that leverages side information from labelled outliers, which are commonly underutilized or even discarded by conventional conformal p-values. This solution is practical and blends inductive and transductive inference strategies to adaptively weight conformal p-values, while also automatically leveraging the most powerful model from a collection of one-class and binary classifiers. Further, this approach leads to rigorous false discovery rate control in multiple testing when combined with a conditional calibration strategy. Extensive numerical simulations show that the proposed method outperforms existing approaches.

     
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  3. Abstract

    Adaptive multiple testing with covariates is an important research direction that has gained major attention in recent years. It has been widely recognised that leveraging side information provided by auxiliary covariates can improve the power of false discovery rate (FDR) procedures. Currently, most such procedures are devised with p-values as their main statistics. However, for two-sided hypotheses, the usual data processing step that transforms the primary statistics, known as p-values, into p-values not only leads to a loss of information carried by the main statistics, but can also undermine the ability of the covariates to assist with the FDR inference. We develop a p-value based covariate-adaptive (ZAP) methodology that operates on the intact structural information encoded jointly by the p-values and covariates. It seeks to emulate the oracle p-value procedure via a working model, and its rejection regions significantly depart from those of the p-value adaptive testing approaches. The key strength of ZAP is that the FDR control is guaranteed with minimal assumptions, even when the working model is misspecified. We demonstrate the state-of-the-art performance of ZAP using both simulated and real data, which shows that the efficiency gain can be substantial in comparison with p-value-based methods. Our methodology is implemented in the R package zap.

     
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