Differentially Private Sparse Covariance Matrix Estimation under Lower-Bounded Moment Assumption

Abstract

This paper investigates the problem of sparse covariance matrix estimation while the sampling set contains sensitive information, and both the differentially private algorithm and locally differentially private algorithm are adopted to preserve privacy. It is worth noting that the requirement of the distribution assumption in our work is only the existing bounded 4+ε(ε>0) moment. Meanwhile, we reduce the error bounds by modifying the threshold of the existing differentially private algorithms. Finally, the numerical simulations and results from a real data application are presented to support our theoretical claims.