Covariate-adjusted precision matrix estimation with an application in genetical genomics

• 成果类型: Article
• 署名作者: Cai, T. Tony; Li, Hongzhe; Liu, Weidong; Xie, Jichun
• 署名单位: University of Pennsylvania; University of Pennsylvania; Shanghai Jiao Tong University; Shanghai Jiao Tong University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass058
• 发表日期: 2013
• 页码: 139156
• 关键词: sparse; regression; selection; regularization; networks; graphs; models

摘要

Motivated by analysis of genetical genomics data, we introduce a sparse high-dimensional multivariate regression model for studying conditional independence relationships among a set of genes adjusting for possible genetic effects. The precision matrix in the model specifies a covariate-adjusted Gaussian graph, which presents the conditional dependence structure of gene expression after the confounding genetic effects on gene expression are taken into account. We present a covariate-adjusted precision matrix estimation method using a constrained l(1) minimization, which can be easily implemented by linear programming. Asymptotic convergence rates in various matrix norms and sign consistency are established for the estimators of the regression coefficients and the precision matrix, allowing both the number of genes and the number of the genetic variants to diverge. Simulation shows that the proposed method results in significant improvements in both precision matrix estimation and graphical structure selection when compared to the standard Gaussian graphical model assuming constant means. The proposed method is applied to yeast genetical genomics data for the identification of the gene network among a set of genes in the mitogen-activated protein kinase pathway.