jewel: a novel method for joint node-wise estimation of multiple Gaussian graphical models

Graphical models are well-known mathematical objects for describing conditional dependency relationships between random variables of a complex system. Gaussian graphical models refer to the case of multivariate Gaussian variable for which the graphical model is encoded through the support of corresponding inverse covariance (precision) matrix. We consider a problem of estimating multiple Gaussian graphical models from high- dimensional data sets under the assumption that they share the same conditional independence structure. However, the individual correlation matrices can differ. Such a problem can be motivated by applications where data comes from different sources and can be collected in distinct classes or groups. We propose a joint data estimation that uses a node-wise penalized regression approach. Grouped Lasso penalty simultaneously guarantees the resulting adjacency matrix's symmetry and the joint learning of the graphs. We solve the minimization problem using the group descent algorithm and establish the proposed solution's consistency and sparsity properties. Finally, we show how the regularization parameter can be estimated using cross-validation and BIC. We provide a novel R package jewel with the implementation of the proposed method and illustrate our estimator's performance through simulated and real data examples. We compare the proposed approach with other available alternatives.