# Differentially Private Precision Matrix Estimation

arXiv: https://arxiv.org/abs/1909.02750 · HTML: https://mlsanity.com/paper/1909.02750/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [Graph Structure Learning with Privacy Guarantees for Open Graph Data](https://mlsanity.com/paper/2507.19116/) (2025)

## Abstract (arXiv)

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.