Differential privacy provides a rigorous framework for privacy-preserving data analysis. This paper proposes the first differentially private procedure for controlling the false discovery rate (FDR) in multiple hypothesis testing. Inspired by the Benjamini- Hochberg procedure (BHq), our approach is to first repeatedly add noise to the logarithms of the p-values to ensure differential privacy and to select an approximately smallest p-value serving as a promising candidate at each iteration; the selected p-values are further supplied to the BHq and our private procedure releases only the rejected ones. Apart from the privacy considerations, we develop a new technique that is based on a backward submartingale for proving FDR control of a broad class of multiple testing procedures, including our private procedure, and both the BHq step-up and step-down procedures. As a novel aspect, the proof works for arbitrary dependence between the true null and false null test statistics, while FDR control is maintained up to a small multiplicative factor. This theoretical guarantee is the first in the FDR literature to explain the empirical validity of the BHq procedure in three simulation studies.

该论文提出了第一个控制多重假设检验中的假阳性发现率的差分隐私程序，该程序基于Benjamini-Hochberg程序，并开发了一种新技术来证明一类多重检验过程的FDR控制。

差分隐私假发现率控制