本期报告具体信息如下：

时间：2022年10月26日 10:00—11:00

Lecture 7   Overview and Outlook for Functional Data Analysis

函数型数据分析综述与展望

姚方

Speaker Bio

Fang Yao is Chair Professor in School of Mathematical Sciences at Peking University, Director of Center for Statistical Science, and Head of Department of Probability & Statistics. He is a Fellow of IMS and ASA, and an elected member of ISI. He received his B.S. degree in 2000 from University of Science & Technology in China, and his Ph.D. degree in Statistics in 2003 at UC Davis. He was a tenured Full Professor in Statistical Science at University of Toronto, and has been selected into the National Talents Program of China. Dr. Yao’s research focuses on complex-structured data analysis, including functional, high-dimensional, manifold and non-Euclidean data objects; incorporating machine/deep learning and partial/ordinary differential equations to establish scalable statistical modeling and inference; conducting applications involving functional, high-dimensional and differential dynamics in biomedical studies, human genetics, neuroimaging, finance and economics, engineering etc. In 2014, he received the CRM-SSC Prize that recognizes a statistical scientist’s professional accomplishments in research primarily conducted in Canada during the first 15 years after receiving a doctorate. He has served as the Editor for Canadian Journal of Statistics, and is/was on editorial boards for a numebr of statistical journals, including the Annals of Statistics and Journal of the American Statistical Association.

姚方，北京大学讲席教授，国家高层次人才，北大统计科学中心主任，概率统计系主任。数理统计学会与美国统计学会会士。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。主要研究方向为复杂结构数据分析，包括函数型数据、高维数据、流形和非欧数据等；融合机器/深度学习的方法理论、微分方程等机理模型建立可拓展的统计学习与推断；涉及函数型、高维数据与微分动力系统等在生物医学、人类基因组学、神经影像学、金融和经济学、工程学等领域的应用。由于在函数型数据分析领域所做出的奠基性和开创性的贡献，2014年获得由加拿大统计学会和数学研究中心联合颁发的授予博士毕业15年内做出突出贡献的统计学家的 CRM-SSC奖。曾任《加拿大统计学期刊》主编，担任多个统计学期刊的编委，包括统计学顶级期刊《统计年刊》和《北美统计学会会刊》。 

Abstract

Functional data analysis (FDA) has received substantial attention in the field of Statistics and data science, as such data varying with time or space are ubiquitous in the big data era nowadays, with applications arising from various disciplines, such as medical studies, public health, engineering, finance and economics, and so on. In general, the FDA approaches focus on nonparametrically modeling underlying random functions, which treats the data as observed or sampled from realizations of stochastic processes satisfying some regularity conditions, e.g., smoothness constraints. The estimation and inference procedures usually do not depend on a finite number of parameters, which contrasts with parametric models, and exploit techniques, such as smoothing methods and dimension reduction, that allow data to speak for themselves. In this talk, I will give an overview and discuss some potential outlook for FDA and related topics.

近年来，函数型数据分析在统计与数据科学领域受到广泛关注，尤其是这类随时间或空间时化的数据在大数据时代越来越普遍，并且在医学研究、公共卫生、工程、经济金融等领域有着大量应用。一般来讲，函数型数据分析的方法聚焦于随机函数的非参数建模，其数据被认为来自于有一定正则化条件（例如光滑型等）约束的随机过程的带有误差的重复观测或采样。函数型数据中估计和推断的方法通常无法用有限个（不依赖于样本量）的参数来描述和刻画，这和统计学中经典的参数化方法有着本质的区别。因此函数型数据分析中常用的包括光滑化去燥和数据降维等典型的数据驱动的非参数方法允许数据为自己“讲话”。在此报告中，我们会回顾与展望函数型数据分析的重要问题以及相关应用。