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

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.

Published in at http://dx.doi.org/10.1214/10-AOAS332 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Cited by in corpus (13)

• Variable selection and regression analysis for graph-structured covariates with an application to genomics
• The sparse Laplacian shrinkage estimator for high-dimensional regression
• Rare Feature Selection in High Dimensions
• Prediction models for network-linked data
• Network-Guided Biomarker Discovery
• Structured Regularization for conditional Gaussian Graphical Models
• High-dimensional Precision Matrix Estimation with a Known Graphical Structure
• Joint Estimation of Precision Matrices in Heterogeneous Populations
• Discriminative Subnetworks with Regularized Spectral Learning for Global-state Network Data
• Network inference and community detection, based on covariance matrices, correlations and test statistics from arbitrary distributions
• Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems
• Gene-gene interaction analysis incorporating network information via a structured Bayesian approach
• High-dimensional Gaussian graphical model for network-linked data