FDR Control via Neural Networks under Covariate-Dependent Symmetric Nulls

Abstract

In modern multiple hypothesis testing, the availability of covariate information alongside the primary test statistics has motivated the development of more powerful and adaptive inference methods. However, most existing approaches rely on p-values that are precomputed under the assumption that their null distributions are independent of the covariates. In this paper, we propose a framework that derives covariate-adaptive p-values from the assumption of a symmetric null distribution of the primary variable given the covariates, without imposing any parametric assumptions. Building on these data-driven p-values, we employ a neural network model to learn a covariate-adaptive rejection threshold via the mirror estimation principle, optimizing the number of discoveries while maintaining valid false discovery rate control. Furthermore, our estimation of the conditional null distribution enables the computation of p-values directly from the raw data. The proposed method provides a principled way to derive covariate-adjusted p-values from raw data and allows seamless integration with previously established p-value based procedures. Simulation studies show that the proposed method outperforms existing approaches in terms of power. We further illustrate its applicability through two real data analyses: age-specific blood pressure data and U.S. air pollution data.