Variable selection and regression analysis for graph-structured covariates with an application to genomics

TL;DR

This paper introduces a graph-constrained regularization method for regression analysis that leverages biological network structures to improve variable selection and prediction accuracy.

Contribution

It develops a novel regularization approach incorporating graph Laplacian smoothness, with theoretical guarantees and demonstrated advantages over existing methods.

Findings

Improves variable selection accuracy in genomics data

Provides theoretical consistency results for the proposed method

Outperforms existing methods that ignore graph structure

Abstract

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks. This kind of a priori use of graphs is a useful supplement to the standard numerical data such as microarray gene expression data. In this paper we consider the problem of regression analysis and variable selection when the covariates are linked on a graph. We study a graph-constrained regularization procedure and its theoretical properties for regression analysis to take into account the neighborhood information of the variables measured on a graph. This procedure involves a smoothness penalty on the coefficients that is defined as a quadratic form of the Laplacian matrix associated with the graph. We establish estimation and model selection consistency results and provide estimation bounds for both fixed and diverging numbers of parameters in regression models. We demonstrate by simulations and a real data set that the proposed procedure can lead to better variable selection and prediction than existing methods that ignore the graph information associated with the covariates.