Motivated by the analysis of genetical genomic data, we consider the problem of estimating high-dimensional sparse precision matrix adjusting for possibly a large number of covariates, where the covariates can affect the mean value of the random vector. We develop a two-stage estimation procedure to first identify the relevant covariates that affect the means by a joint ℓ1 penalization. The estimated regression coefficients are then used to estimate the mean values in a multivariate sub-Gaussian model in order to estimate the sparse precision matrix through a ℓ1-penalized log-determinant Bregman divergence. Under the multivariate normal assumption, the precision matrix has the interpretation of a conditional Gaussian graphical model. We show that under some regularity conditions, the estimates of the regression coefficients are consistent in element-wise ℓ∞ norm, Frobenius norm and also spectral norm even when p ≫ n and q ≫ n. We also show that with probability converging to one, the estimate of the precision matrix correctly specifies the zero pattern of the true precision matrix. We illustrate our theoretical results via simulations and demonstrate that the method can lead to improved estimate of the precision matrix. We apply the method to an analysis of a yeast genetical genomic data.
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| Evidence ID | Analyze ID | Gene/Complex | Systematic Name/Complex Accession | Qualifier | Gene Ontology Term ID | Gene Ontology Term | Aspect | Annotation Extension | Evidence | Method | Source | Assigned On | Reference |
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| Evidence ID | Analyze ID | Gene | Gene Systematic Name | Phenotype | Experiment Type | Experiment Type Category | Mutant Information | Strain Background | Chemical | Details | Reference |
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| Evidence ID | Analyze ID | Gene | Gene Systematic Name | Disease Ontology Term | Disease Ontology Term ID | Qualifier | Evidence | Method | Source | Assigned On | Reference |
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| Evidence ID | Analyze ID | Regulator | Regulator Systematic Name | Target | Target Systematic Name | Direction | Regulation of | Happens During | Regulator Type | Direction | Regulation Of | Happens During | Method | Evidence | Strain Background | Reference |
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| Site | Modification | Modifier | Source | Reference |
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| Evidence ID | Analyze ID | Interactor | Interactor Systematic Name | Interactor | Interactor Systematic Name | Allele | Assay | Annotation | Action | Phenotype | SGA score | P-value | Source | Reference | Note |
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| Evidence ID | Analyze ID | Interactor | Interactor Systematic Name | Interactor | Interactor Systematic Name | Assay | Annotation | Action | Modification | Source | Reference | Note |
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| Complement ID | Locus ID | Gene | Species | Gene ID | Strain background | Direction | Details | Source | Reference |
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| Evidence ID | Analyze ID | Dataset | Description | Keywords | Number of Conditions | Reference |
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