A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces  

作　　者：Hongzhi Tong Michael Ng 

机构地区：[1]School of Statistics,University of International Business and Economics,Beijing 100029,China [2]Institute of Data Science and Department of Mathematics,The University of Hong Kong,Pokfulam,Hong Kong,China

出　　处：《Annals of Applied Mathematics》2022年第3期280-295,共16页应用数学年刊（英文版）

基　　金：supported in part by National Natural Science Foundation of China(Grant No.11871438);supported in part by the HKRGC GRF Nos.12300218,12300519,17201020,17300021,C1013-21GF,C7004-21GF;Joint NSFC-RGC N-HKU76921。

摘　　要：We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces.In the algorithm,we use an early stopping technique,instead of the classical Tikhonov regularization,to prevent the iteration from an overfitting function.Under mild conditions,we obtain upper bounds,essentially matching the known minimax lower bounds,for excess prediction risk.An almost sure convergence is also established for the proposed algorithm.

关 键 词：Gradient iteration algorithm functional linear regression reproducing kernel Hilbert space early stopping convergence rates 

分 类 号：O177.1[理学—数学]