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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Multiple Testing for IR and Recommendation System Experiments
While there has been significant research on statistical techniques for comparing two information retrieval (IR) systems, many IR experiments test more than two systems. This can lead to inflated false discoveries due to the multiple-comparison problem (MCP). A few IR studies have investigated multiple comparison procedures; these studies mostly use TREC data and control the familywise error rate. In this study, we extend their investigation to include recommendation system evaluation data as well as multiple comparison procedures that controls for False Discovery Rate (FDR).
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- Award ID(s):
- 2415042
- PAR ID:
- 10497108
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- ECIR 2024: Advances in Information Retrieval
- Volume:
- 14610
- ISBN:
- 978-3-031-56063-7
- Page Range / eLocation ID:
- 449-457
- Subject(s) / Keyword(s):
- recommender systems evaluation statistical inference multiple comparisons
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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