Differentially Private High Dimensional Sparse Covariance Matrix Estimation
This addresses privacy-preserving statistical estimation for high-dimensional data, offering incremental improvements over prior methods.
The paper tackles the problem of estimating high-dimensional sparse covariance matrices under differential privacy, proposing DP-Thresholding to achieve significantly better error bounds than existing methods, with experiments validating theoretical results.
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 $\ell_2$-norm based error bound, which is significantly better than the existing ones from adding noise directly to the empirical covariance matrix. We also extend the $\ell_2$-norm based error bound to a general $\ell_w$-norm based one for any $1\leq w\leq \infty$, and show that they share the same upper bound asymptotically. Our approach can be easily extended to local differential privacy. Experiments on the synthetic datasets show consistent results with our theoretical claims.