Adaptive False Discovery Rate Control with Privacy Guarantee

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 a privacy guarantee, which is a non-trivial improvement compared to the differentially private Benjamini-Hochb erg 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.

Automated summary

This paper proposes a differentially private adaptive FDR control method that can protect individual information and precisely control the FDR metric. By using a novel p-value transformation and a mirror peeling algorithm, privacy protection and optimal stopping technique are achieved. Empirical studies demonstrate that this method can better control FDR while reducing computation cost.