Adaptive Sparse Group Lasso Penalized Quantile Regression via Dual ADMM

2026-04-14

AI Summary

This work proposes a novel approach to quantile regression under high-dimensional grouped covariates by introducing, for the first time, an adaptive sparse group Lasso penalty that simultaneously incorporates both within-group and between-group sparsity. By integrating adaptive Lasso and adaptive group Lasso penalties, the method effectively captures the dual sparsity structure while preserving the robustness inherent to quantile regression. To enable efficient computation, the authors develop an alternating direction method of multipliers (ADMM) algorithm based on the dual formulation and rigorously establish its global convergence. Extensive experiments on both simulated and real-world datasets demonstrate that the proposed method substantially outperforms existing alternatives, achieving accurate dual sparsity recovery with superior computational efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• quantile regression
• group sparsity
• variable selection
• high-dimensional data
• sparse modeling

Innovation

• adaptive sparse group lasso
• quantile regression
• dual ADMM
• within- and between-group sparsity
• high-dimensional data