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A critical problem in genetics is to discover how gene expression isregulated within cells. Two major tasks of regulatory association learning are: (i) identifying SNP-gene relationships, known as eQTL mapping, and (ii)determining gene-gene relationships, known as gene network estimation. To shareinformation between these two tasks, we focus on the unified model for jointestimation of eQTL mapping and gene network, and propose a $L_{1-2}$regularized multi-task graphical lasso, named $L_{1-2}$ GLasso. Numericalexperiments on artificial datasets demonstrate the competitive performance of$L_{1-2}$ GLasso on capturing the true sparse structure of eQTL mapping andgene network. $L_{1-2}$ GLasso is further applied to real dataset of ADNI-1 andexperimental results show that $L_{1 -2}$ GLasso can obtain sparser and moreaccurate solutions than other commonly-used methods.

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