The Linearized Alternating Direction Method Of Multipliers For Sparse Group LAD Model

While the least absolute shrinkage and selection operator(LASSO)became a pop-ular model due to its wide applications in high dimensional settings,some generalized LASSO models were developed.The sparse group LASSO is one of the important lasso-type methods,which aims to solve the linear regression problems with grouped covariates and tends to produce a solution with sparse effects both on a group and with-in group level.At the same time,we know that the least absolute deviation(LAD)is a useful and robust model when the noise distribution may be heavy-tailed or heteroge-neous.In this paper,we combine these two classical ideas together to develop sparse group LAD model.We shows that the sparse group LAD estimator achieves near or-acle performance under certain conditions,i.e.,with high probability,the L2 norm of the estimation error is of order O(?klogp/n).Moreover,with the help of the lineariza-tion technique we generalise the linearized alternating direction method of multipliers to solve the sparse group LAD estimator and establish its convergence.Numerical ex-periments are reported to illustrate the efficiency of the proposed algorithm.