Wessel N. van Wieringen

Carel F. W. Peeters, Anders Ellern Bilgrau, Wessel N. van Wieringen

A graphical model is an undirected network representing the conditional independence properties between random variables. Graphical modeling has become part and parcel of systems or network approaches to multivariate data, in particular when the variable dimension exceeds the observation dimension. rags2ridges is an R package for graphical modeling of high-dimensional precision matrices. It provides a modular framework for the extraction, visualization, and analysis of Gaussian graphical models from high-dimensional data. Moreover, it can handle the incorporation of prior information as well as multiple heterogeneous data classes. As such, it provides a one-stop-shop for graphical modeling of high-dimensional precision matrices. The functionality of the package is illustrated with an example dataset pertaining to blood-based metabolite measurements in persons suffering from Alzheimer's Disease.

Carel F. W. Peeters, Mark A. van de Wiel, Wessel N. van Wieringen

Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample covariance matrix. These estimators depend on a penalty parameter and choosing its value can be hard, in terms of being computationally unfeasible or tenable only for a restricted set of ridge-type estimators. Here we introduce a simple graphical tool, the spectral condition number plot, for informed heuristic penalty parameter selection. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators.

Anders Ellern Bilgrau, Carel F. W. Peeters, Poul Svante Eriksen et al.

We consider the problem of jointly estimating multiple inverse covariance matrices from high-dimensional data consisting of distinct classes. An $\ell_2$-penalized maximum likelihood approach is employed. The suggested approach is flexible and generic, incorporating several other $\ell_2$-penalized estimators as special cases. In addition, the approach allows specification of target matrices through which prior knowledge may be incorporated and which can stabilize the estimation procedure in high-dimensional settings. The result is a targeted fused ridge estimator that is of use when the precision matrices of the constituent classes are believed to chiefly share the same structure while potentially differing in a number of locations of interest. It has many applications in (multi)factorial study designs. We focus on the graphical interpretation of precision matrices with the proposed estimator then serving as a basis for integrative or meta-analytic Gaussian graphical modeling. Situations are considered in which the classes are defined by data sets and subtypes of diseases. The performance of the proposed estimator in the graphical modeling setting is assessed through extensive simulation experiments. Its practical usability is illustrated by the differential network modeling of 12 large-scale gene expression data sets of diffuse large B-cell lymphoma subtypes. The estimator and its related procedures are incorporated into the R-package rags2ridges.