Department of Mathematics - Mathematics Colloquium - Online Nonparametric Estimation for Streaming Data
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Online learning and modeling has attracted considerable interest due to increasingly available data in streaming manner. Nonparametric models, although flexible, have seen limited use in online settings due to their data-driven nature and high computational demands. We introduce an innovative online method for dynamically updating local polynomial regression estimates. Our approach decomposes kernel-type estimates into two sufficient statistics and approximates future optimal bandwidths with a dynamic candidate sequence. This idea extends to general nonlinear optimization problems, where we propose an online smoothing backfitting algorithm for generalized additive models (GAM). We establish asymptotic normality and efficiency lower bounds for online estimation, shedding light on the trade-off between accuracy and computational cost driven by the bandwidth sequence length. For GAM, We also investigate statistical and algorithmic convergence and provide a framework for balancing estimation and computation performance. Our proposed online estimation is also applicable to complex structural data such as functional data. Simulations and real data examples are provided to support the usefulness of the proposed method.
Fang Yao is Chair Professor in School of Mathematical Sciences, Director of Center for Statistical Science at Peking University. 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 Sciences at University of Toronto. His research focuses on complex-structured data analysis, including functional, high-dimensional, manifold 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 dynamic modeling in biomedical studies, human genetics, neuroimaging, engineering, etc. He has received the CRM-SSC Prize and served as the Editor for Canadian Journal of Statistic, and also served as an AE for a number of statistical journals, including Annals of Statistics and JASA.