LORS

LORS models expression quantitative trait loci (eQTL) by jointly estimating a low-rank representation of confounding factors and sparse SNP–gene expression associations to improve detection of true genetic signals.

Key Features:

• Low-Rank Representation: Employs a low-rank representation to model confounding factors such as unobserved covariates, experimental artifacts, and unknown environmental perturbations that influence gene expression.
• Sparse Regression: Utilizes sparse regression to identify significant associations between single-nucleotide polymorphisms (SNPs) and gene expression in high-dimensional genomic settings.
• Unified Framework: Integrates low-rank and sparse components for the joint analysis of SNPs and gene probes to separate genetic effects from non-genetic influences.
• Convex Optimization Problem: Formulates inference as a convex optimization problem enabling computational efficiency and guaranteed convergence of the estimation procedure.

Scientific Applications:

• Accounting for Non-Genetic Effects: Applied in eQTL studies and simulation experiments to account for non-genetic effects and reduce confounding in detected associations.
• Consistency Across Studies: Shown on independent real datasets to improve consistency of detected SNP–expression associations across studies.
• Identification of New Genetic Hotspots: By removing confounding influences, has enabled detection of genetic hotspots affecting gene expression that were previously undetectable.

Methodology:

LORS solves a convex optimization problem estimating a low-rank matrix for confounders and a sparse coefficient matrix for SNP–expression effects using an efficient algorithm with guaranteed convergence.