Differentially Private Precision Matrix Estimation

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. Keywords differential privacy, graphical model, ADMM algorithm 1 Introduction Precision matrix plays a fundamental role in many statistical inference problems. For example, in discriminant analysis, the precision matrix needs to be estimated to compute the classification rules[1]. In graphical models, the structure exploration of gaussian graphical model is equivalent to recover the support of the precision matrix[2]. Moreover, the precision matrix is useful for a wide range of applications including portfolio optimization, genomics and single processing, among many others. Therefore, it is of great importance to estimate the precision matrix.