An efficient algorithm for structured sparse quantile regression

An efficient algorithm is derived for solving the quantile regression problem combined with a group sparsity promoting penalty. The group sparsity of the regression parameters is achieved by using a \(\ell _{1,\infty }\) -norm penalty (or constraint) on the regression parameters. The algorithm is efficient in the sense that it obtains the regression parameters for a wide range of penalty parameters, thus enabling easy application of a model selection criteria afterwards. A Matlab implementation of the proposed algorithm is provided and some applications of the methods are studied.