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

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

Year:    2022

Author:    Hongzhi Tong, Michael Ng

Annals of Applied Mathematics, Vol. 38 (2022), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aam.OA-2021-0016

Annals of Applied Mathematics, Vol. 38 (2022), Iss. 3 : pp. 280–295

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Gradient iteration algorithm functional linear regression reproducing kernel Hilbert space early stopping convergence rates.

Author Details

Hongzhi Tong

Michael Ng

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