Optimal Differentially Private Ranking from Pairwise Comparisons

• 成果类型: Article; Early Access
• 署名作者: Cai, T. Tony; Chakraborty, Abhinav; Wang, Yichen
• 署名单位: University of Pennsylvania; Columbia University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2612773
• 发表日期: 2026-05-20
• 关键词: Bradley-Terry-Luce model; Differential privacy; Minimax Optimality; ranking

摘要

Data privacy is a central concern in many applications involving ranking from incomplete and noisy pairwise comparisons, such as recommendation systems, educational assessments, and opinion surveys on sensitive topics. In this work, we propose differentially private algorithms for ranking based on pairwise comparisons. Specifically, we develop and analyze ranking methods under two privacy notions: edge differential privacy, which protects the confidentiality of individual comparison outcomes, and individual differential privacy, which safeguards potentially many comparisons contributed by a single individual. Our algorithms-including a perturbed maximum likelihood estimator and a noisy count-based method-are shown to achieve minimax optimal rates of convergence under the respective privacy constraints. We further demonstrate the practical effectiveness of our methods through experiments on both simulated and real-world data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.