Multi-block alternating direction method of multipliers for ultrahigh dimensional quantile fused regression

Xiaofei Wu, Hao Ming, Zhimin Zhang and Zhenyu Cui

Computational Statistics & Data Analysis, 2024, vol. 192, issue C

Abstract: In this paper, we consider a quantile fused LASSO regression model that combines quantile regression loss with the fused LASSO penalty. Intuitively, this model offers robustness to outliers, thanks to the quantile regression, while also effectively recovering sparse and block coefficients through the fused LASSO penalty. To adapt our proposed method for ultrahigh dimensional datasets, we introduce an iterative algorithm based on the multi-block alternating direction method of multipliers (ADMM). Moreover, we demonstrate the global convergence of the algorithm and derive comparable convergence rates. Importantly, our ADMM algorithm can be easily applied to solve various existing fused LASSO models. In terms of theoretical analysis, we establish that the quantile fused LASSO can achieve near oracle properties with a practical penalty parameter, and additionally, it possesses a sure screening property under a wide class of error distributions. The numerical experimental results support our claims, showing that the quantile fused LASSO outperforms existing fused regression models in robustness, particularly under heavy-tailed distributions.

Keywords: Fused LASSO; Multi-block ADMM; Oracle properties; Quantile regression (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002128

DOI: 10.1016/j.csda.2023.107901

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