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.

中文翻译：

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差分私有精度矩阵估计

在本文中，我们研究了当数据集包含敏感信息时的精确矩阵估计问题。在差分隐私框架中，我们通过扰动样本协方差矩阵开发了一个差分私有脊估计器。然后我们通过使用乘法器的交替方向法（ADMM）算法开发了一个差分私有图形套索估计器。还提供了显示所提出方法的实用性的理论结果和实证结果。