Differentially private false discovery rate control

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