报告题目：Fréchet Regression with Semi-supervised Learning and Ensemble Learning
主讲人：邱锐博士（北京大学）
时间：2026年1月15日（周四）10:00 a.m.
形式：线上讲座
腾讯会议：449794702
主办单位：统计与数学学院
摘要：
This talk studies Fréchet regression in general metric spaces, motivated by the high cost of acquiring non-Euclidean labels and the need for scalable, theoretically grounded methods. We develop semi-supervised Fréchet regression procedures, which leverage graph distances constructed from both labeled and unlabeled data. We establish convergence rates under regimes with few labeled samples, abundant unlabeled data, and low-dimensional manifold structure, and demonstrate improved performance over supervised methods in simulations and real applications. We further investigate ensemble learning for Fréchet regression by deriving non-asymptotic risk bounds for Fréchet Mondrian forests. Under suitable regularity and smoothness conditions, these forests achieve convergence rates comparable to Euclidean counterparts and outperform individual Fréchet trees, providing a theoretical justification for ensemble benefits in non-Euclidean regression.
主讲人简介：
邱锐，北京大学统计科学中心博雅博士后，电话13476036353。研究方向包括统计机器学习，充分降维以及非欧数据分析。研究工作发表于《Annals of Statistics》，《Journal of the Royal Statistical Society: Series B》，《Journal of Machine Learning Research》等期刊或会议上。2025年“博新计划”入选者，目前正主持国自然青年基金和博士后面上基金，担任《Journal of the American Statistical Association》、《Journal of Machine Learning Research》等多个期刊审稿人。
