主题：Online Learning of Functional Principal Component Analysis
主讲人：加拿大温哥华西蒙弗雷泽大学曹际国教授
主持人：统计与数据科学学院林华珍教授
时间：2026年9月18日（周五）下午4:00-5:00
地点：柳林校区弘远楼408会议室
主办单位：统计与数据科学学院和统计研究中心 国际交流与合作处 科研处
主讲人简介：
曹际国博士, 加拿大温哥华西蒙弗雷泽大学(Simon Fraser University)统计与精算系教授，加拿大数据科学国家特聘教授(Canada Research Chair in Data Science)，现担任Statistics in Medicine等国际统计期刊副主编。曹际国2006年获得加拿大麦吉尔大学(McGill University) 博士，2007年美国耶鲁大学博士后出站，长期从事人工智能，机器学习，函数型数据分析(functional data analysis) 和估计微分方程的研究。曹际国2021年获得加拿大统计协会(Statistical Society of Canada)和国家数学研究中心(Centre de recherches mathématiques)联合评比的最高奖之一：加拿大国家杰出青年统计学家奖(CRM-SSC award)。曹际国近些年来在国际优秀期刊中发表超过150篇文章。
内容提要：
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and scalable modeling of such data. Our method represents functional principal components using tensor product splines, enforcing smoothness and orthonormality through a penalized framework on a Stiefel manifold. We develop an efficient Riemannian stochastic gradient descent algorithm and a Riemannian adaptive gradient (AdaGrad) variant, both utilizing iterative averaging techniques to stabilize the estimation and accelerate convergence. Additionally, a dynamic tuning strategy for smoothing parameter selection is developed based on a rolling averaged block validation score that adapts to the streaming nature of the data. Furthermore, we derive the asymptotic normality of the estimators and construct pointwise confidence intervals to quantify the uncertainty of the estimated functional principal components. Extensive simulations and real-world applications demonstrate the flexibility and effectiveness of this framework for analyzing multidimensional functional data.
