Abstract
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.
Funding Statement
Weidong Liu’s research is supported by NSFC Grant No. 11825104.
Jiyuan Tu’s research is supported by “the Fundamental Research Funds for the Central Universities.”
Xiaojun Mao’s research is supported by NSFC Grant No. 12371273, Shanghai Rising-Star Program 23QA1404600 and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001).
Acknowledgments
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Xiaojun Mao and Xi Chen are the co-corresponding authors.
Citation
Weidong Liu. Jiyuan Tu. Xiaojun Mao. Xi Chen. "Majority vote for distributed differentially private sign selection." Ann. Statist. 52 (4) 1671 - 1690, August 2024. https://doi.org/10.1214/24-AOS2411
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