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.
|Original language||English (US)|
|Title of host publication||2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - Feb 20 2019|