摘要
在高维数据分析中,惩罚分位数回归是进行变量选择和参数估计的有效方法.在实际应用中,变量常以分组形式呈现,为同时实现组间稀疏性和组内稀疏性,本文研究了带稀疏Group Lasso惩罚的分位数回归模型.为解决目标函数的非光滑性带来的计算挑战,利用分位数Huber函数近似分位数损失函数,得到稀疏Group Lasso惩罚分位数Huber回归模型(SGLQHR).基于Groupwise Majorization Descent(GMD)算法提出了一种快速、有效算法求解该模型,并建立算法收敛性.数值实验和实例分析验证了该算法的有效性.
In high-dimensional data analysis,penalized quantile regression is an effective tool for variable selection and parameter estimation.In many real applications,variables are structured into groups.In order to achieve the desired effect of sparsity within and between groups,we study the sparse group lasso penalized quantile regression model that combines lasso and group Lasso.To solve computational challenges caused by non-smoothness of object function,we approximate the quantile loss function using quantile Huber function,and the quantile Huber regression with sparse group Lasso penalty(SGLQHR)is obtained.We introduce Groupwise Majorization Descent(GMD)algorithm for computing the proposed model.Numerical examples and real data analysis demonstrate the competitive performance of our algorithm.
作者
张蕊
阎爱玲
Zhang Rui;Yan Ailing(College of Science,Hebei University of Technology,Tianjin 300401,China)
出处
《数值计算与计算机应用》
2024年第2期174-188,共15页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金(12271022)
河北自然科学基金(A2023202038)资助
