# Adaptive sparse group LASSO in quantile regression

arXiv: https://arxiv.org/abs/1911.01081 · HTML: https://mlsanity.com/paper/1911.01081/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Loss-guided Stability Selection](https://mlsanity.com/paper/2202.04956/) (2022)
- [Sparse-group boosting -- Unbiased group and variable selection](https://mlsanity.com/paper/2206.06344/) (2022)
- [A unified consensus-based parallel ADMM algorithm for high-dimensional regression with combined regularizations](https://mlsanity.com/paper/2311.12319/) (2023)
- [Carbon Price Forecasting with Quantile Regression and Feature Selection](https://mlsanity.com/paper/2305.03224/) (2023)
- [Dual Feature Reduction for the Sparse-group Lasso and its Adaptive Variant](https://mlsanity.com/paper/2405.17094/) (2024)

## Abstract (arXiv)

This paper studies the introduction of sparse group LASSO (SGL) to the quantile regression framework. Additionally, a more flexible version, an adaptive SGL is proposed based on the adaptive idea, this is, the usage of adaptive weights in the penalization. Adaptive estimators are usually focused on the study of the oracle property under asymptotic and double asymptotic frameworks. A key step on the demonstration of this property is to consider adaptive weights based on a initial √n-consistent estimator. In practice this implies the usage of a non penalized estimator that limits the adaptive solutions to low dimensional scenarios. In this work, several solutions, based on dimension reduction techniques PCA and PLS, are studied for the calculation of these weights in high dimensional frameworks. The benefits of this proposal are studied both in synthetic and real datasets.