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 non-private 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.

翻译：近年来，隐私保护数据分析日益普及。本研究针对分布式环境下的符号选择问题，提出了一种分布式群组差分隐私的多数投票机制。为实现这一目标，我们将迭代剥离技术应用于稳定性函数，并采用指数机制恢复符号。为提升适用性，我们进一步研究了分布式系统中均值估计与线性回归问题的隐私符号选择。本方法在恢复支撑集与符号时，能达到与非隐私场景相同的最优信噪比，其性能优于当前隐私变量选择的相关研究。此外，理论保证验证了符号选择的一致性。仿真实验证明了所提方法的有效性。