Adaptive False Discovery Rate Control with Privacy Guarantee
This addresses the need for privacy-preserving statistical testing in sensitive data analysis, offering an incremental improvement over existing differentially private FDR methods.
The paper tackled the problem of controlling the false discovery rate (FDR) in multiple hypothesis testing while ensuring differential privacy, proposing a method that exactly controls FDR at a user-specified level α with privacy guarantees, improving upon prior work and showing better performance with a small accuracy loss but reduced computation cost compared to non-private methods.
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 $α$ 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.