Differentially Private Precision Matrix Estimation

TL;DR

This paper introduces differentially private methods for estimating precision matrices, including a ridge estimator and a graphical lasso, ensuring privacy while maintaining utility through theoretical and empirical validation.

Contribution

It proposes novel differentially private estimators for precision matrices using covariance perturbation and ADMM, advancing privacy-preserving statistical inference.

Findings

The private ridge estimator performs well in utility tests.

The private graphical lasso effectively recovers sparse precision matrices.

The methods are validated through theoretical analysis and empirical experiments.

Abstract

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.