报告题目：The optimal weighted Fréchet random forest for metric-space-valued responses with Euclidean predictors

报告人：于渊

时间：10月25日 16：30-17：30

地点：疯av 106会议室

报告摘要：The Fréchet random forest (FRF) has emerged as a powerful method for modeling complex regression relationships between Euclidean predictors and metric-space-valued responses. FRF offers significant advantages by preserving the flexibility and accuracy of classical random forests while circumventing the curse of dimensionality of Fréchet regression. However, current implementations typically employ equal-weight aggregation of Fréchet trees, though the inherent randomness in bootstrap aggregation and variable selection may induce significant heterogeneity in predictive performance across individual trees. In this paper, we address the optimal weighted problem for the Fréchet random forest (wFRFopt) by proposing a Jackknife optimal weighting algorithm that determines Fréchet tree weights through cross-validation criterion minimization. Under some regularity conditions, we show the asymptotic optimality of the proposed algorithm by demonstrating that its metric squared prediction error asymptotically matches that of the infeasible but best possible weighted FRF. Through comprehensive simulation studies with various response types including probability distributions, symmetric positive definite matrices, and spherical data, we provide evidence for the superiority of wFRFopt over both equal-weight FRF and alternative Fréchet regression methods. The practical advantages of our approach are further validated by using New York taxi data.

报告人简介：于渊，副教授，硕士生导师，山东财经大学统计与数学学院数据科学系主任兼任学院人事秘书、外事干事。上海财经大学统计学博士研究生毕业，博士期间受国家留学生基金委员会资助分别在美国北卡罗来纳大学教堂山分校和德州大学M.D.安德森癌症研究中心进行访学。主持山东省社会科学基金项目与山东省自然科学基金项目，参与多项国家自然科学基金项目，在《SCIENCE CHINA Mathematics》、《Journal of Statistical Planning and Inference》、《Metrika》、《Statistics and Its Interface》等期刊发表论文多篇。《Annals of Applied Statistics》、《Statistics and Its Interface》、《Economic Analysis and Policy》等期刊匿名审稿人。兼任中国现场统计研究会资源与环境统计分会、中国优选法统筹法与经济数学研究会数据科学分会、全国工业统计学教学研究会金融科技与大数据技术分会、山东省统计学会、山东省工业与应用数学学会理事。指导学生参加全国大学生数学建模、全国大学生统计建模、正大杯市场调查、国家级创新创业等比赛并多次获奖，主持并参与多项省级教学项目。