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.

翻译：差分隐私多重检验程序能够在保护假设检验中个体信息的同时，确保错误发现的比例控制在较小范围内。本文提出了一种具有差分隐私的自适应FDR控制方法，该方法能在隐私保证下精确地将经典FDR指标控制在用户指定的水平$\alpha$，相较于Dwork等人(2021)提出的差分隐私Benjamini-Hochberg方法，实现了非平凡改进。我们的分析基于两个关键洞见：1)一种新颖的p值变换方法，既能保护隐私又能保持镜像保守性质；2)一种镜像剥离算法，可构建滤过结构并应用最优停止技术。数值实验表明，所提出的DP-AdaPT方法优于现有差分隐私FDR控制方法。与非隐私保护的AdaPT相比，该方法仅造成轻微精度损失，但显著降低了计算成本。