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In this paper, we study the problem of estimating the covariance matrix underdifferential privacy, where the underlying covariance matrix is assumed to besparse and of high dimensions. We propose a new method, called DP-Thresholding,to achieve a non-trivial $\ell_2$-norm based error bound, which issignificantly better than the existing ones from adding noise directly to theempirical covariance matrix. We also extend the $\ell_2$-norm based error boundto a general $\ell_w$-norm based one for any $1\leq w\leq \infty$, and showthat they share the same upper bound asymptotically. Our approach can be easilyextended to local differential privacy. Experiments on the synthetic datasetsshow consistent results with our theoretical claims.

Differentially Private High Dimensional Sparse Covariance Matrix Estimation