Differentially Private False Discovery Rate Control
This work addresses privacy-preserving statistical analysis for researchers handling sensitive data, representing a novel integration of differential privacy with FDR control rather than an incremental improvement.
The paper tackles the problem of controlling the false discovery rate (FDR) in multiple hypothesis testing under differential privacy constraints, proposing the first differentially private procedure that maintains FDR control up to a small multiplicative factor for arbitrary dependence between test statistics.
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. Moreover, 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.