Differentially Private High Dimensional Sparse Covariance Matrix Estimation

In this paper, we study the problem of estimating the covariance matrix under differential privacy,where the underlying covariance matrix is assumed to be sparse and of high dimensions. Our approach can be easily extendedto local differential privacy. Experiments on the synthetic datasets show consistent results with our theoretical claims. Keywords: Differential privacy, sparse covariance estimation, high dimensional statistics 1. Introduction Machine Learning and Statistical Estimation have made profound impact in recent years to many applied domains such as social sciences, genomics, and medicine. During theirapplications, a frequently encountered challenge is how to deal with the high dimensionality of the datasets, especially for those in genomics, educational and psychological research.A commonly adopted strategy for dealing with such an issue is to assume that the underlying structures of parameters are sparse.