  In this paper, we study the problem of precision matrix estimation when the
dataset contains sensitive information. In the differential privacy framework,
we develop a differentially private ridge estimator by perturbing the sample
covariance matrix. Then we develop a differentially private graphical lasso
estimator by using the alternating direction method of multipliers (ADMM)
algorithm. The theoretical results and empirical results that show the utility
of the proposed methods are also provided.
