Majority Vote for Distributed Differentially Private Sign Selection

TL;DR

This paper introduces a distributed differentially private majority vote mechanism for sign selection, achieving optimal support recovery and sign consistency in mean estimation and linear regression, outperforming existing private methods.

Contribution

It proposes a novel distributed private sign selection method using iterative peeling and exponential mechanism, with theoretical guarantees and superior performance over prior approaches.

Findings

Recovers support and signs with optimal SNR

Achieves sign selection consistency

Outperforms contemporary private variable selection methods

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 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.