A SPARSE CONDITIONAL GAUSSIAN GRAPHICAL MODEL FORANALYSIS OF GENETICAL GENOMICS DATA

摘要

Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same sub-jects. The gene expression levels are often treated as quantitative traits and are subject to standard genetic analysis in order to identify the gene expression quantitative loci (eQTL). However, the genetic architecture for many gene expressions may be complex, and poorly estimated genetic architecture may compromise the inferences of the dependency structures of the genes at the transcriptional level. In this paper we introduce a sparse conditional Gaus-sian graphical model for studying the conditional independent relationships among a set of gene expressions adjusting for possible genetic effects where the gene expressions are modeled with seemingly unrelated regressions. We present an efficient coordinate descent algorithm to obtain the penalized esti-mation of both the regression coefficients and the sparse concentration matrix. The corresponding graph can be used to determine the conditional indepen-dence among a group of genes while adjusting for shared genetic effects. Sim-ulation experiments and asymptotic convergence rates and sparsistency are used to justify our proposed methods. By sparsistency, we mean the property that all parameters that are zero are actually estimated as zero with probabil-ity tending to one. We apply our methods to the analysis of a yeast eQTL data set and demonstrate that the conditional Gaussian graphical model leads to a more interpretable gene network than a standard Gaussian graphical model based on gene expression data alone.