Inferring High-Dimensional Dynamic Networks Changing with Multiple Covariates

TL;DR

This paper introduces a new graphical model framework called covariate-varying networks (CVN) that can capture dynamic relationships in high-dimensional data as they change with multiple external factors, using a novel sparsity and similarity modeling approach.

Contribution

The paper proposes a novel CVN model that handles multiple covariates and enforces similarity via a meta-graph, solved with ADMM, and demonstrates its effectiveness through simulations and real gene expression data.

Findings

Successfully models networks changing with multiple covariates.

Demonstrates improved estimation accuracy over static models.

Applicable to real-world gene expression data.

Abstract

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 $L_1$-penalty to the precision matrices of $m \geq 2$ 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