Volume 38, Issue 3
A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces

Hongzhi Tong & Michael Ng

Ann. Appl. Math., 38 (2022), pp. 280-295.

Published online: 2022-08

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  • Abstract

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.

  • AMS Subject Headings

60K35, 62J05

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COPYRIGHT: © Global Science Press

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@Article{AAM-38-280, author = {Tong , Hongzhi and Ng , Michael}, title = {A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {38}, number = {3}, pages = {280--295}, abstract = {

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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2021-0016}, url = {http://global-sci.org/intro/article_detail/aam/20879.html} }
TY - JOUR T1 - A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces AU - Tong , Hongzhi AU - Ng , Michael JO - Annals of Applied Mathematics VL - 3 SP - 280 EP - 295 PY - 2022 DA - 2022/08 SN - 38 DO - http://doi.org/10.4208/aam.OA-2021-0016 UR - https://global-sci.org/intro/article_detail/aam/20879.html KW - Gradient iteration algorithm, functional linear regression, reproducing kernel Hilbert space, early stopping, convergence rates. AB -

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.

Hongzhi Tong & Michael Ng. (2022). A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces. Annals of Applied Mathematics. 38 (3). 280-295. doi:10.4208/aam.OA-2021-0016
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