文献类型：期刊文献

英文题名：Reproducing property of bounded linear operators and kernel regularized least square regressions

作者：Sheng, Baohuai[1,2]

机构：[1]Zhejiang Yuexiu Univ, Dept Econ Stat, Shaoxing 312000, Zhejiang, Peoples R China;[2]Shaoxing Univ, Dept Appl Stat, Shaoxing 312000, Zhejiang, Peoples R China

年份：2024

外文期刊名：INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING

收录：SCI-EXPANDED(收录号：WOS:001206342100004)、、EI(收录号：20241815996561)、Scopus(收录号：2-s2.0-85191368787)、WOS

基金：This work is supported by the NSFC/RGC Joint Research Scheme (Project No. 12061160462 of China and N-CityU102/20) and the NSFC (Project No. 61877039) of China.The author expresses his deep gratitude to the anonymous reviewers for their valuable revision suggestions and comments.

语种：英文

外文关键词：Functional reproducing kernel Hilbert space; kernel regularized regression; convergence rate; bounded linear operator

外文摘要：We consider bounded linear operators from the view of functional reproducing property. For some bounded linear operators associated with orthogonal polynomials we define an inner product space associated with a kernel constructed with orthogonal polynomials, show that it is a functional reproducing kernel Hilbert space (FRKHS) associated with these bounded linear operators and give decay rate for the best FRKHS approximation with a K-functional associated with the FRKHS. On this basis, we provide a learning rate for kernel regularized regression whose hypothesis space is the defined FRKHS. As applications, we define some concrete FRKHSs associated with polynomial operators such as the Bernstein-Durrmeyer operators, the de la Vall & eacute;e Poussin operators on both the unit sphere Sd-1 and the unit ball B-d. We show that these polynomial operators have reproducing property with respect to the corresponding concrete FRKHSs and show the learning rate for the kernel regularized regression. In short, we provide a way of constructing FRKHS operators with Fourier multipliers and show a learning framework from the view of operator approximation.