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【北航数学论坛(6月12日,姚方教授)】Functional Regression on Manifold with Contamination
ag平台网址:2019-06-05  浏览量:


题目: Functional Regression on Manifold with Contamination

报告人:姚方  教授(北京大学)



摘要:We propose a new perspective on functional regression with a predictor process via the concept of manifold that is intrinsically finite-dimensional and embedded in an infinite-dimensional functional space, where the predictor is contaminated with discrete/noisy measurements.  By a novel method of  functional local linear manifold smoothing, we achieve a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the level of sampling/noise contamination with a phase transition phenomenon depending on their interplay. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We demonstrate that the proposed method enjoys favorable finite sample performance relative to commonly used methods via simulated and real data examples.

报告人概况:姚方,北京大学讲席教授(ag平台网址概率统计系,统计科学中心),国家高层次人才专家。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年获得授予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) Fellow2018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其中包括顶级期刊Journal of the American Statistical Association Annals of Statistics。主要研究方向包括函数型数据分析,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。


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