$l_{1-2}$ GLasso: $L_{1-2}$ Regularized Multi-task Graphical Lasso for Joint Estimation of eQTL Mapping and Gene Network

Developments in sequencing technology allow us to obtain more and more genomic data since the publication of the first human genome sequence. Computational techniques can help us to mine meaningful information from raw data and understand how gene expression is regulated in cells. In general, these problems include identifying cancer gene co-expression (co-expression: simultaneous expression of two or more genes) modules, determining SNP-gene relationships through eQTL (expression quantitative trait locus) mapping and determining gene-gene relationships by estimating gene network structure, etc (Rockman and Kruglyak, 2006; Gardner and Faith, 2005). Given a dataset containing single nucleotide polymorphisms (SNPs) and mRNA expression, the problem is to understand the SNP-gene and gene-gene relationships.