DIFFERENTIALLY PRIVATE SPARSE INVERSE COVARIANCE ESTIMATION

Abstract

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.