题   目：Semi-proximal ADMM for Fused Lasso Penalized Least Absolute Deviation in Partially Linear Regression Model

报告人：尚有林 教授

单   位：河南科技大学

时   间：2024年12月30日 14:00

地   点：龙子湖校区九章学堂南组团C座209报告厅

摘要：The partially linear regression model is a type of semiparametric regression model characterized by unknown linear regression coefficients, an unknown nonparametric function, and random errors. This model is particularly useful when the relationship between the dependent variable and some predictors is not strictly linear, allowing for more flexibility in capturing complex relationships in the data. In this paper, we propose a novel variable selection model using fused lasso penalized least absolute deviation in partially linear regression, which is noted as PLM-RFlasso, while simultaneously estimating both parametric and nonparametric components. The proposed model exhibits superior robustness and applicability compared to the least squares model. It is capable of handling high-dimensional data with correlated adjacent variables and with outliers or containing variables with heavy tailed distributions. Then we design a semi-proximal alternating direction method of multipliers (sPADMM) to solve the dual problem of PLM-RFlasso, and give its convergence guarantees. Finally, numerical experiments on simulated and real datasets illustrate the robustness of the proposed model the effectiveness of the proposed algorithm.

报告人简介：尚有林，二级教授，博士生导师，河南省政府特殊津贴专家，曾任河南科技大学数学与统计学院院长，现任河南科技大学运筹与大数据研究院院长，河南省大数据智能分析与优化创新实验室主任，洛阳市城市交通运筹与优化重点实验室主任，中国运筹学会常务理事，中国运筹学会数学规划分会常务理事，河南省运筹学会理事长。2005年上海大学运筹学与控制论专业博士毕业，2005年10月-2007年10月同济大学应用数学博士后流动站研究。一直从事最优化理论、算法及其应用研究。在非线性规划、全局优化、系统工程等领域取得多项研究成果，国内外期刊发表论文150多篇。先后到美国、巴西、智利等进行学术访问交流。主持国家自然科学基金面上项目4项、河南省自然科学基金项目、国际合作项目多项。出版专著1部，主编教材4部。