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Functional Regression with Unknown Manifold Structures
时间  Datetime
2017-04-27 15:00 — 16:00 
地点  Venue
Large Conference Room
报告人  Speaker
Prof. Fang Yao
单位  Affiliation
多伦多大学、北京大学
邀请人  Host
统计系
报告摘要  Abstract

Abstract: Statistical methods that adapt to unknown population structures are attractive due to both practical and theoretical advantages over their non-adaptive counterparts. We contribute to adaptive modelling of functional regression, where challenges arise from the infinite dimensionality of functional predictor in the underlying space. We are interested in the scenario that the predictor process lies in a potentially nonlinear manifold that is intrinsically finite-dimensional and embedded in an infinite-dimensional functional space. By a novel functional regression approach built upon local linear manifold smoothing, we achieve a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the level of noise/sampling contamination with a phase transition phenomenon depending on their interplay, which is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We demonstrate that the proposed method enjoys favourable finite sample performance relative to commonly used methods via simulated and real data examples.

嘉宾介绍:  姚方,多伦多大学统计科学系教授,北京大学概率统计系和统计科学中心讲席教授,国家“千人计划”入选专家。2000取得中国科技大学理学学士学位,2002和2003年分别取得加利福尼亚大学戴维斯分校统计学方向硕士和博士学位。

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年内在加拿大做出突出贡献的统计学家的 CRM-SSC奖,2012年获加拿大自然与工程科研基金颁发给统计学科唯一的 Discovery Accelerator Supplement奖(类似于美国NSF的Career奖)。其研究成果在国际上被广泛引用,至今为止担任10个国际统计学核心期刊的副主编,包括顶级期刊Journal of the American Statistical Association和 Annals of Statistics等。