Differentially private multiple testing procedures can protect the information of individuals used in hypothesis tests while guaranteeing a small fraction of false discoveries. In this paper, we propose a differentially private adaptive FDR control method that can control the classic FDR metric exactly at a user-specified level $\alpha$ with privacy guarantee, which is a non-trivial improvement compared to the differentially private Benjamini-Hochberg method proposed in Dwork et al. (2021). Our analysis is based on two key insights: 1) a novel p-value transformation that preserves both privacy and the mirror conservative property, and 2) a mirror peeling algorithm that allows the construction of the filtration and application of the optimal stopping technique. Numerical studies demonstrate that the proposed DP-AdaPT performs better compared to the existing differentially private FDR control methods. Compared to the non-private AdaPT, it incurs a small accuracy loss but significantly reduces the computation cost.

本文提供了一种不同ially private AdaPT控制方法，它可以在隐私保护下确切地控制经典的FDR指标，同时保证了误发现的小部分，其基于两个关键的insights：1）一种新颖的p值转换方法，可以保护隐私和镜像保守性，2）一种镜像削皮算法，可以构建过滤和应用最优停止技术。

隐私保证的自适应误发现率控制