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Differentially Private False Discovery Rate Control. (arXiv:1807.04209v1 [math.ST])
来源于:arXiv
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
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