Median DC for Sign Recovery: Privacy can be Achieved by Deterministic Algorithms
Authors: Jiyuan Tu, Weidong Liu, Xiaojun Mao
Keywords: Median-of-means, divide-and-conquer, privacy, sign recovery
Abstract: Privacy-preserving data analysis becomes prevailing in recent years. It is a common sense in privacy literature that strict differential privacy can only be obtained by imposing additional randomness in the algorithm. In this paper, we study the problem of private sign recovery for sparse mean estimation and sparse linear regression in a distributed setup. By taking a coordinate-wise median among the reported local sign vectors, which can be referred to as a median divide-and-conquer (Med-DC) approach, we can recover the signs of the true parameter with a provable consistency guarantee. Moreover, without adding any extra randomness to the algorithm, our Med-DC method can protect data privacy with high probability. Simulation studies are conducted to demonstrate the effectiveness of our proposed method.