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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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Online control of the false coverage rate and false sign rate
The reproducibility debate has caused a renewed interest in changing how one reports uncertainty, from đť‘ť-value for testing a null hypothesis to a confidence interval (CI) for the corresponding parameter. When CIs for multiple selected parameters are being reported, the analog of the false discovery rate (FDR) is the false coverage rate (FCR), which is the expected ratio of number of reported CIs failing to cover their respective parameters to the total number of reported CIs. Here, we consider the general problem of FCR control in the online setting, where one encounters an infinite sequence of fixed unknown parameters ordered by time. We propose a novel solution to the problem which only requires the scientist to be able to construct marginal CIs. As special cases, our framework yields algorithms for online FDR control and online sign-classification procedures that control the false sign rate (FSR). All of our methodology applies equally well to prediction intervals, having particular implications for selective conformal inference.
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- Award ID(s):
- 1945266
- PAR ID:
- 10251945
- Publisher / Repository:
- PMLR (JMLR W&CP)
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 119
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 10193-10202
- Format(s):
- Medium: X
- Location:
- International Conference on Machine Learning
- Sponsoring Org:
- National Science Foundation
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