基于融合Lasso的非参数加性分位数回归模型

doi:10.16451/j.cnki.issn1003-6059.202401005

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Abstract Additive quantile regression provides a flexible and robust method for modeling non-linear relationships. Methods for fitting the additive quantile models rely on spline functions to approximate components. However, the required prior selection of nodes results in slow computation speed and it renders the methods unsuitable for large-scale data problems. Therefore, a nonparametric additive quantile regression model based on the fused Lasso(AQFL) is proposed in this paper. AQFL leverages a compromise between the fused Lasso penalty and the l₂ penalty for estimating and selecting variables in the additive quantile regression model. The fused Lasso penalty is employed to make the model compute fast and localize adaptively, thereby achieving the prediction for the desired quantile or even extreme quantiles. Additionally, in combination with the l₂ penalty, AQFL compresses the covariate function values with a small impact on the response to zero in high-dimensional data, thereby achieving variable selection. Furthermore, a block coordinate alternating direction method of multipliers(BC-ADMM) algorithm is presented to ensure convergence to the global optimum and demonstrate the prediction consistency of AQFL. Experimental results on synthetic data and ground pork data demonstrate the superiority of AQFL in prediction accuracy and robustness.

Key words： Quantile Regression Additive Model Fused Lasso Penalty l₂ Penalty

Received: 20 October 2023

ZTFLH:

TP181

Fund:Natural Science Basic Research Program of Shaanxi Province(No.2024JC-YBMS-051)

Corresponding Authors: ZHOU Shuisheng,Ph.D.,professor.His research interests include optimization theory and algorithm, pattern recognition and application, intelligent information processing and machine lear-ning.

About author:: FU Manxia,Master student.Her research interests include optimization theory and algorithm, pattern recognition and application.

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Cite this article:

FU Manxia,ZHOU Shuisheng. Nonparametric Additive Quantile Regression Model Based on Fused Lasso[J]. Pattern Recognition and Artificial Intelligence, 2024, 37(1): 58-72.

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http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.202401005 OR http://manu46.magtech.com.cn/Jweb_prai/EN/Y2024/V37/I1/58

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