Adaptive Sparse Group Lasso Penalized Quantile Regression via Dual ADMM

TL;DR

This paper introduces an adaptive sparse group lasso penalized quantile regression method optimized with ADMM, effectively achieving dual sparsity in high-dimensional data with proven convergence and efficiency.

Contribution

It develops a novel adaptive penalization approach for quantile regression that ensures sparsity within and between groups, with a proven convergent optimization algorithm.

Findings

Effective in achieving within- and between-group sparsity

Demonstrates computational efficiency over existing methods

Validated through simulations and real data analysis

Abstract

Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and between groups is essential. However, existing quantile regression methods often fail to meet this dual objective. To address this gap, we introduce the adaptive sparse group lasso penalized quantile regression, which integrates adaptive lasso and adaptive group lasso penalties. We optimize the model parameters via the alternating direction method of multipliers (ADMM) applied to the dual problem, and establish global convergence. Through extensive simulation studies and real data analyses, we demonstrate (i) the efficacy of the proposed method in achieving simultaneous within- and between-group sparsity, and (ii) the computational efficiency of our algorithm relative to existing alternatives.