<i>Jewel</i>: A Novel Method for Joint Estimation of Gaussian Graphical Models

• Main Authors: Claudia Angelini, Daniela De Canditiis, Anna Plaksienko
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Mathematics
• Subjects: Gaussian Graphical Model; group Lasso; joint estimation; network estimation
• Online Access: https://www.mdpi.com/2227-7390/9/17/2105

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose <i>jewel</i>, a joint data estimation method that uses a node-wise penalized regression approach. In particular, <i>jewel</i> uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix’s symmetry and the graphs’ joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator’s consistency property. Finally, we illustrate our estimator’s performance through simulated and real data examples on gene regulatory networks.