Fast proximal gradient optimization of the empirical Bayesian Lasso for multiple quantitative trait locus mapping

Complex quantitative traits are influenced by many factors including the main effects of many quantitative trait loci (QTLs), the epistatic effects involving more than one QTLs, environmental effects and the effects of gene-environment interactions. We recently developed an empirical Bayesian Lasso (EBlasso) method that employs a high-dimensional sparse regression model to infer the QTL effects from a large set of possible effects. Although EBlasso outperformed other state-of-the-art algorithms in terms of power of detection (PD) and false discovery rate (FDR), it was optimized by a greedy coordinate ascent algorithm that limited its capability and efficiency in handling a relatively large number of possible QTLs. In this paper, we developed a fast proximal gradient optimization algorithm for the EBlasso method. The new algorithm inherits the accuracy of our previously developed coordinate ascent algorithm, and achieves much faster computational speed. Simulation results demonstrated that the proximal gradient algorithm provided better PD with the same FDR as the coordinate ascent algorithm, and computational time was reduced by more than 30%. The proximal gradient algorithm enhanced EBlasso will be a useful tool for multiple QTL mappings especially when there are a large number of possible effects. A C/C++ software implementing the proximal gradient algorithm is freely available upon request.