Differentially private sparse inverse covariance estimation

In this paper, we present the first results on the sparse inverse covariance estimation problem under the differential privacy model. We first gave an ϵ-differentially private algorithm using output perturbation strategy, which is based on the sensitivity of the optimization problem and the Wishart mechanism. To further improve this result, we then introduce a general covariance perturbation method to achieve both ϵ-differential privacy and (ϵ, δ)-differential privacy. For ϵ-differential privacy, we analyze the performance of Laplacian and Wishart mechanisms, and for (ϵ, δ)-differential privacy, we examine the performance of Gaussian and Wishart mechanisms. Experiments on both synthetic and benchmark datasets confirm our theoretical analysis.