An efficient algorithm for structured sparse quantile regression

TL;DR

This paper introduces an efficient algorithm for structured sparse quantile regression using a mixed norm penalty, enabling the calculation of the entire solution path and demonstrating practical applications.

Contribution

It develops a novel algorithm to compute the piece-wise linear solution path for structured sparse quantile regression with a mixed norm penalty.

Findings

Algorithm efficiently computes the solution path.

Matlab implementation provided for practical use.

Applications demonstrate effectiveness of the method.

Abstract

Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-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.