Fused Ridge Estimation of Multiple Inverse Class Covariance Matrices from High-Dimensional Data

In the recent years of emerging high-dimensional datasets and applications the fundamental problem of estimating the precision matrix, has been devoted considerable effort. To this end, the l1-penalized graphical lasso and its sparse solutions has for a decade been a popular estimator, while some focus lately has shifted to the more stable l2-penalised alternatives.

However, these estimators consider only a single class of data. We consider the l2-penalized maximum likelihood problem of jointly estimating multiple high-dimensional precision matrices where a number of related but heterogeneous classes of data are available.

This so-called fused ridge estimate is applicable where the precision matrices of each class is believed to chiefly share the same relational structure while potentially differing in a number of places of interest. Hence, it shares statistical power between classes allowing for stable class precision estimates of common relational structures. By the interpretation of precision matrices, it thus provides a basis for both integrative and differential network analysis of Gaussian models where the classes are e.g. datasets and diseases.

The suggested fused penalty is quite general containing many other proposed l2-penalized estimations. The fused ridge estimate has applications in multifactorial study designs such as meta or integrative analysis of partial correlation networks and Gaussian graphical models.

The estimation procedures are incorporated into the R-package rags2ridges and applied to a meta analysis study of network structures in 11 large-scale diffuse large B-cell lymphoma gene expression datasets.