Sparse group LASSO (SGL) is a penalization technique used in regression problems where the covariates have a natural grouped structure and provides solutions that are both between and within group sparse. In this paper the SGL is introduced to the quantile regression (QR) framework, and a more flexible version, the adaptive sparse group LASSO (ASGL), is proposed. This proposal adds weights to the penalization improving prediction accuracy. Usually, adaptive weights are taken as a function of the original non-penalized solution model. This approach is only feasible in the n > p framework. In this work, a solution that allows using adaptive weights in high-dimensional scenarios is proposed. The benefits of this proposal are studied both in synthetic and real datasets.In this research we have made use of Uranus, a supercomputer cluster located
at University Carlos III of Madrid and funded jointly by EU-FEDER funds
and by the Spanish Government via the National Projects No. UNC313-4E-
2361, No. ENE2009-12213- C03-03, No. ENE2012-33219 and No. ENE2015-
68265-P. This research was partially supported by research grants and Project
ECO2015-66593-P from Ministerio de Economía, Industria y Competitividad,
Project MTM2017-88708-P from Ministerio de Economía y Competi-
tividad, FEDER funds and Project IJCI-2017-34038 from Agencia Estatal
de Investigación, Ministerio de Ciencia, Innovación y Universidades
