Article
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Convergence Rate of Regularized Regression Associated with Zonal Translation Networks
Version 1
: Received: 4 August 2024 / Approved: 5 August 2024 / Online: 5 August 2024 (08:21:15 CEST)
How to cite: Ran, X.; Sheng, B.; Wang, S. Convergence Rate of Regularized Regression Associated with Zonal Translation Networks. Preprints 2024, 2024080275. https://doi.org/10.20944/preprints202408.0275.v1 Ran, X.; Sheng, B.; Wang, S. Convergence Rate of Regularized Regression Associated with Zonal Translation Networks. Preprints 2024, 2024080275. https://doi.org/10.20944/preprints202408.0275.v1
Abstract
Neural network regularized learning has garnered significant attention in recent years. We give a systematic investigation on the performance of regularized regression associated zonal translation networks. We propose the concept of Marcinkiewicz-Zygmund inequality Setting (MZIS) for the scattered nodes collected from the unit sphere. We show that, under the MZIS, the corresponding convolutional zonal translation network has reproducing property. Based on these facts,we propose a kind of kernel regularized regression learning framework and provide upper bound estimate for the learning rate with the kernel approach. We also give proof for the density of the zonal translation network with spherical Fourier analysis.We provide the approximation error with a K-functional.
Keywords
regularized regression learning; convolution translation network; reproducing property; Marcinkiewicz-Zygmund inequality; quadrature rule; convergence rate
Subject
Computer Science and Mathematics, Artificial Intelligence and Machine Learning
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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