L-2,L-1-norm regularized multivariate regression model with applications to genomic prediction

Motivation: Genomic selection (GS) is currently deemed the most effective approach to speed up breeding of agricultural varieties. It has been recognized that consideration of multiple traits in GS can improve accuracy of prediction for traits of low heritability. However, since GS forgoes statistical testing with the idea of improving predictions, it does not facilitate mechanistic understanding of the contribution of particular single nucleotide polymorphisms (SNP). Results: Here, we propose a L-2,L-1-norm regularized multivariate regression model and devise a fast and efficient iterative optimization algorithm, called L-2,L-1-joint, applicable in multi-trait GS. The usage of the L-2,L-1-norm facilitates variable selection in a penalized multivariate regression that considers the relation between individuals, when the number of SNPs is much larger than the number of individuals. The capacity for variable selection allows us to define master regulators that can be used in a multi-trait GS setting to dissect the genetic architecture of the analyzed traits. Our comparative analyses demonstrate that the proposed model is a favorable candidate compared to existing state-of-the-art approaches. Prediction and variable selection with datasets from Brassica napus, wheat and Arabidopsis thaliana diversity panels are conducted to further showcase the performance of the proposed model.