Learning Rate of Regularized Regression Associated with Zonal Translation Networks

Xuexue Ran, Baohuai Sheng () and Shuhua Wang
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Xuexue Ran: School of Mathematical Physics and Information, Shaoxing University, Shaoxing 312000, China
Baohuai Sheng: Department of Economic Statistics, School of International Business, Zhejiang Yuexiu University, Shaoxing 312000, China
Shuhua Wang: School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China

Mathematics, 2024, vol. 12, issue 18, 1-27

Abstract: We give a systematic investigation on the reproducing property of the zonal translation network and apply this property to kernel regularized regression. We propose the concept of the Marcinkiewicz–Zygmund setting (MZS) for the scattered nodes collected from the unit sphere. We show that under the MZ condition, the corresponding convolutional zonal translation network is a reproducing kernel Hilbert space. Based on these facts, we propose a kind of kernel regularized regression learning framework and provide the upper bound estimate for the learning rate. We also give proof for the density of the zonal translation network with spherical Fourier-Laplace series.

Keywords: kernel regularized regression; learning theory; convolution translation network; reproducing kernel Hilbert space; Marcinkiewicz–Zygmund inequality; quadrature rule; learning rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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