MAJORITY VOTE FOR DISTRIBUTED DIFFERENTIALLY PRIVATE SIGN SELECTION

• 成果类型: Article
• 署名作者: Liu, Weidong; Tu, Jiyuan; Mao, Xiaojun; Chen, Xi
• 署名单位: Shanghai Jiao Tong University; Shanghai University of Finance & Economics; New York University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2411
• 发表日期: 2024
• 页码: 1671-1690
• 关键词: VARIABLE SELECTION

摘要

Privacy-preserving data analysis has become more prevalent in recent years. In this study, we propose a distributed group differentially private Majority Vote mechanism, for the sign selection problem in a distributed setup. To achieve this, we apply the iterative peeling to the stability function and use the exponential mechanism to recover the signs. For enhanced applicability, we study the private sign selection for mean estimation and linear regression problems, in distributed systems. Our method recovers the support and signs with the optimal signal-to-noise ratio as in the nonprivate scenario, which is better than contemporary works of private variable selections. Moreover, the sign selection consistency is justified by theoretical guarantees. Simulation studies are conducted to demonstrate the effectiveness of the proposed method.