Differentially Private False Discovery Rate Control

Abstract

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.

To appear in The Journal of Privacy and Confidentiality

References in corpus (8)

• Deep Learning with Differential Privacy
• An adaptive step-down procedure with proven FDR control under independence
• Robustness of multiple testing procedures against dependence
• Gaussian Differential Privacy
• On the false discovery rate and an asymptotically optimal rejection curve
• On a generalized false discovery rate
• Testing hypotheses on a tree: new error rates and controlling strategies
• The FDR-Linking Theorem

Cited by in corpus (9)

• The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy
• Simultaneous high-probability bounds on the false discovery proportion in structured, regression, and online settings
• The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds
• Aggregating Votes with Local Differential Privacy: Usefulness, Soundness vs. Indistinguishability
• The FDR-Linking Theorem
• PAPRIKA: Private Online False Discovery Rate Control
• High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guarantees
• Oneshot Differentially Private Top-k Selection
• Differentially Private Variable Selection via the Knockoff Filter