Estimating Sparse Covariance Matrix Under Differential Privacy via Thresholding

Abstract

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. We propose a new method, called DP-Thresholding, to achieve a non-trivial $l_{2}$-norm based error bound, which is significantly better than the existing ones from adding noise directly to the empirical covariance matrix. Experiments on the synthetic datasets show consistent results with our theoretical claims.