Adaptive False Discovery Rate Control with Privacy Guarantee
Xintao Xia, Zhanrui Cai; 24(252):1−35, 2023.
Abstract
This paper introduces a novel method for adaptively controlling the False Discovery Rate (FDR) with privacy guarantees in multiple testing procedures. By applying differential privacy techniques, our method ensures the protection of individuals’ information while maintaining a low rate of false discoveries. We improve upon the differentially private Benjamini-Hochberg method proposed by Dwork et al. (2021) by precisely controlling the classic FDR metric at a user-specified level α. Our approach is based on two key insights: (1) a new transformation of p-values that preserves privacy and the mirror conservative property, and (2) a mirror peeling algorithm that enables the construction of the filtration and the application of optimal stopping techniques. Numerical studies demonstrate the superiority of our proposed DP-AdaPT method compared to existing differentially private FDR control methods. Although there is a slight loss in accuracy compared to the non-private AdaPT method, our approach significantly reduces computation costs.
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