Differentially private false discovery rate control

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Cynthia Dwork
Weijie Su
https://orcid.org/0000-0003-1787-1219
Li Zhang
https://orcid.org/0000-0002-4712-3134

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.

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How to Cite
Dwork, Cynthia, Weijie Su, and Li Zhang. 2021. “Differentially Private False Discovery Rate Control”. Journal of Privacy and Confidentiality 11 (2). https://doi.org/10.29012/jpc.755.
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