数学科学学院学术报告[2024] 099号

(高水平大学建设系列报告979号)

报告题目：Nonlinear Fréchet regression in Metric Spaces: Definition, Learning, Estimation and Theory

报告人：林路 教授（山东大学）

报告时间： 2024年10月18日（周五）下午 3:00—4:00

报告地点：汇星楼514

报告内容: Exploring the regression relationship in a general metric space is still a fundamental and difficult issue in statistics and machine learning. As a famous and special regression relationship in a metric space, the Fréchet regression is actually defined within a linear framework, since the weight function is linearly defined, and the resulting Fréchet regression function is identified to be a linear model when the random object belongs to a Hilbert space. Even for nonparametric and semiparametric Fréchet regressions, the existing methods handle them by local linear (or local polynomial) technique, and the resulting Fréchet regressions are also (locally) linear. We in this work introduce a framework of nonlinear Fréchet regression. As an exploratory work, we first suggest some motivating methods for learning and defining the nonlinearity, and then propose the methods for parameter estimation, and finally establish the asymptotic theories. The proposed framework can be utilized to fit the essentially nonlinear models in a general metric space and uniquely identify the nonlinear structure in a Hilbert space. Particularly, its generalized linear form can return to the standard linear Fréchet regression through a special choice of the weight function. The nonlinear learning methods and favorable theoretical properties, along with the comprehensive simulation studies and real data analysis, demonstrate that the new strategy is easy to use and significantly outperforms the competitors.

报告人简历：林路是山东大学中泰证券金融研究院教授、博士生导师，第一和第二届教育部应用统计专业硕士教育指导委员会成员，山东省教育厅应用统计专业硕士教育指导委员会成员，山东省政府参事。从事大数据、高维统计、非参数和半参数统计以及金融统计等方的研究，在国际统计学、机器学习和相关应用学科顶级期刊（包括Ann. Statist., JMLR, 《中国科学》）和其它重要期刊发表研究论文120余篇；多个金融策略资政报告得到省长的正面批示；主持过多项国家自然科学基金课题、全国统计科学研究重大项目、教育部博士点专项基金课题、教育部新文科课题、山东省自然科学基金重点项目等；获得国家统计局颁发的全国统计优秀研究成果一等和二等奖，山东省优秀教学成果一等奖(均排名第一)。

欢迎师生参加！

报告邀请人：胡宗良

                                                  数学科学学院

                                                2024年 10月 12日