Quantile regression: a penalization approach

TL;DR

This paper introduces a penalization approach combining sparse group LASSO with quantile regression, including an adaptive version suitable for high-dimensional data, improving prediction accuracy in complex models.

Contribution

It extends sparse group LASSO to quantile regression and proposes an adaptive method that works in high-dimensional settings, enhancing model flexibility and accuracy.

Findings

Improved prediction accuracy with adaptive weights.

Effective in high-dimensional scenarios.

Validated on synthetic and real datasets.

Abstract

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 nonpenalized 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.