Differentially Private Precision Matrix Estimation
This addresses privacy concerns in statistical analysis for domains like healthcare or finance, though it appears incremental as it adapts existing methods to differential privacy.
The paper tackles the problem of estimating precision matrices from sensitive datasets while preserving differential privacy, developing both ridge and graphical lasso estimators with theoretical and empirical validation of their utility.
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.