Inferring High-Dimensional Dynamic Networks Changing with Multiple Covariates

High-dimensional networks play a key role in understanding complex relationships. These relationships are often dynamic in nature and can change with multiple external factors (e. g. , time and groups). Methods for estimating graphical models are often restricted to static graphs or graphs that can change with a single covariate (e. g. , time). We propose a novel class of graphical models, the covariate-varying network (CVN), that can change with multiple external covariates. In order to introduce sparsity, we apply a L₁-penalty to the precision matrices of m 2 graphs we want to estimate. These graphs often show a level of similarity. In order to model this 'smoothness', we introduce the concept of a 'meta-graph' where each node in the meta-graph corresponds to an individual graph in the CVN. The (weighted) adjacency matrix of the meta-graph represents the strength with which similarity is enforced between the m graphs. The resulting optimization problem is solved by employing an alternating direction method of multipliers. We test our method using a simulation study and we show its applicability by applying it to a real-world data set, the gene expression networks from the study 'German Cancer in childhood and molecular-epidemiology' (KiKme). An implementation of the algorithm in R is publicly available under https: //github. com/bips-hb/cvn