Structured Input-output Lasso

Structured Input-Output Lasso models shared sparse associations between single nucleotide polymorphisms (SNPs) and gene expression to improve discovery in genome-wide association studies (GWAS) and expression quantitative trait loci (eQTL) mapping.

Key Features:

• Multitask Regression Framework: Employs a multitask regression model to jointly analyze multiple genetic variants and multiple expression traits, leveraging interdependencies among them.
• ℓ(1)/ℓ(2) Regularization: Utilizes an ℓ(1)/ℓ(2) norm-based regularization to identify shared sparsity patterns across inputs (SNPs) and outputs (expression levels).
• Shared-Sparsity Estimation: Enables optimal estimation of multiple SNPs that jointly influence various expression traits by enforcing structured sparsity.
• Incorporation of Prior Knowledge: Integrates prior information from genetic interaction networks to construct informative priors that consider additive and epistatic effects.
• Structurally Regularized Polynomial Regression: Extends to structurally regularized polynomial regression to detect epistatic interactions among candidate SNPs with manageable computational complexity.

Scientific Applications:

• GWAS and eQTL mapping: Improves identification of genotype–expression associations in genome-wide association studies and expression quantitative trait loci analyses.
• Causal QTL detection: Enhances detection of causal quantitative trait loci (QTLs) and interpretation of gene regulation influenced by interdependent genome variations.
• Complex disease and expression studies: Supports study of complex disease phenotypes and gene expression patterns arising from perturbations in molecular networks due to genome variation.
• Demonstrations on data: Validated through simulations and real-world datasets such as yeast eQTL data to uncover complex genetic interactions.

Methodology:

Learn a multitask regression model with ℓ(1)/ℓ(2) norm-based structured regularization while incorporating structural priors on inputs (genetic variations) and outputs (expression levels), and optionally extend to structurally regularized polynomial regression to detect epistatic interactions.