深圳大学四十周年校庆暨数学学科四十周年庆

荔园学者Colloquium第五十期

讲座题目:Online Nonparametric Estimation for Streaming Data

主讲人：姚方讲席教授（北京大学）

讲座时间：2023年11月8日16：00-17:00

讲座地点：深圳大学粤海校区汇星楼一楼三号教室

内容概述：Online learning and modeling has attracted considerable interest due to increasingly available data in streaming manner. Nonparametric models, although flexible, have seen limited use in online settings due to their data-driven nature and high computational demands. We introduce an innovative online method for dynamically updating local polynomial regression estimates. Our approach decomposes kernel-type estimates into two sufficient statistics and approximates future optimal bandwidths with a dynamic candidate sequence. This idea extends to general nonlinear optimization problems, where we propose an online smoothing backfittingalgorithmfor generalized additive models(GAM).We establish asymptotic normality and efficiency lower bounds for online estimation, shedding light on the trade-off between accuracy and computational cost driven by the bandwidth sequence length.For GAM,Wealsoinvestigate statistical and algorithmic convergence and provide a framework for balancing estimation and computation performance. Ourproposed online estimationis alsoapplicableto complex structural data such as functional data. Simulations and real data examples are provided to support the usefulness of the proposed method.

主讲人简介：姚方，北京大学讲席教授、入选国家高层次人才计划，北大统计科学中心主任、概率统计系主任。国际数理统计学会（IMS）Fellow与理事会理事，美国统计学会（ASA）Fellow。2000年本科毕业于中国科技大学统计专业，2003获得加利福尼亚大学戴维斯分校统计学博士学位，曾任职于多伦多大学统计科学系长聘正教授。至今担任9个国际统计学核心期刊的主编或编委，包括《加拿大统计学期刊》主编，顶级期刊《Journal of the American Statistical Association》和《Annals of Statistics》编委等。

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2023年11月2日