Covariate Adjusted Precision Matrix Estimation with an Application in Genetical GenomicsTony Cai, Hongzhe Li, Weidong Liu, and Jichun Xie
Covariate Adjusted Precision Matrix Estimation with an Application in Genetical GenomicsTony Cai, Hongzhe Li, Weidong Liu, and Jichun Xie
- Abstract: Motivated by the analysis of eQTL data, we introduce a sparse high dimensional multivariate regression model for studying the conditional independent relationships among a set of genes adjusting for possible genetic effects, as well as the genetic architecture that influences the gene expressions. The precision matrix in the model specifies a covariate-adjusted Gaussian graph, which presents the conditional dependency structure of gene expression after the confounding genetic effects on gene expressions are taken into account. We present a covariate-adjusted precision matrix estimation (CAPME) method using constrained l1 minimization, which can be easily implemented by linear programming. Asymptotic convergence rates 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. Numerical performance of the estimators is investigated using both simulated and real data sets. Simulation results show that CAPME results in significant improvements in both precision matrix estimation and in graphical structure selection when compared to the standard Gaussian graphical model assuming constant means. CAPME is also applied to analyze a yeast eQTL data for the identification of the gene network among a set of genes in the Mitogen-activated protein kinase (MAPK) pathway.
- Paper: pdf file.
- Other related papers:
- Cai, T. & Zhou, H. (2010).
Optimal rates of convergence for sparse covariance matrix estimation.
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