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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\ell _{1,\infty }$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>∞</mi> </mrow> </msub> </math> </EquationSource> </InlineEquation>-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. Copyright Springer-Verlag Berlin Heidelberg 2014