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September 2010 Variable selection and regression analysis for graph-structured covariates with an application to genomics
Caiyan Li, Hongzhe Li
Ann. Appl. Stat. 4(3): 1498-1516 (September 2010). DOI: 10.1214/10-AOAS332

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.

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Caiyan Li. Hongzhe Li. "Variable selection and regression analysis for graph-structured covariates with an application to genomics." Ann. Appl. Stat. 4 (3) 1498 - 1516, September 2010. https://doi.org/10.1214/10-AOAS332

Information

Published: September 2010
First available in Project Euclid: 18 October 2010

zbMATH: 1202.62157
MathSciNet: MR2758338
Digital Object Identifier: 10.1214/10-AOAS332

Keywords: High-dimensional data , Laplacian matrix , network , regularization , sign consistency

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.4 • No. 3 • September 2010
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