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20181116 姚方:Intrinsic Riemannian Functional Data Analysis
时间:2018-11-06

报告时间:20181115 15:00-16:00

报告地点:明德主楼1037会议室

报告题目:Intrinsic Riemannian Functional Data Analysis



报告摘要:

In this work we develop a new foundational framework for analyzing Riemannian functional data, including intrinsic Riemannian functional principal component analysis (iRFPCA) and intrinsic Riemannian functional linear regression (iRFLR). The key concept in our development is a novel tensor Hilbert space along a curve on the manifold, based on which Karhunen-Loeve expansion for a Riemannian random process is established for the first time. This framework also features a proper comparison of objects from different tensor Hilbert spaces, which paves the way for asymptotic analysis in Riemannian functional data analysis. Built upon  intrinsic geometric concepts such as vector field, Levi-Civita connection and parallel transport on Riemannian manifolds, the proposed framework embraces full generality of applications and proper handle of intrinsic geometric concepts. We then provide estimation procedures for iRFPCA and iRFLR that are distinct from their traditional and/or extrinsic counterparts, and investigate their asymptotic properties within the intrinsic geometry. Numerical performance is illustrated by simulated and real examples.



报告人简介:

姚方,多伦多大学教授(统计科学系),北京大学博雅讲席教授(数学科学学院概率统计系,统计科学中心),入选中组部“千人计划”。2000取得中国科技大学理学学士学位,2003年获加利福尼亚大学戴维斯分校统计学方向博士学位。2014年获得由加拿大统计学会和数学研究中心联合授予博士毕业15年内在加拿大做出突出贡献统计学者的 CRM-SSC奖,2017年当选国际数理统计学会 (IMS) Fellow,2018年当选为美国统计学会 (ASA) Fellow、国际统计学会(ISI) Elected Member。至今担任9个国际统计学核心期刊的Associate Editor,包括顶级期刊Journal of the American Statistical Association和 Annals of Statistics。主要研究包括函数型数据分析,例如具有复杂结构的函数主因子分析、各类回归与分类问题等。