An efficient algorithm for structured sparse quantile regression

Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed ${\mathrm{\ell }}_{1,\mathrm{\infty }}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression problem. An algorithm is derived to calculate the piece-wise linear solution path of the corresponding minimization problem. A Matlab implementation of the proposed algorithm is provided and some applications of the methods are also studied.