The convergence rates of Shannon sampling learning algorithms  

作　　者：SHENG BaoHuai 

机构地区：[1]Department of Mathematics,Shaoxing College of Arts and Sciences,Shaoxing 312000,China

出　　处：《Science China Mathematics》2012年第6期1243-1256,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871226);Natural Science Foundation of Zhejiang Province (Grant No. Y6100096)

摘　　要：In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kernel and a determined net.We show that if the sample is taken according to the determined set,then,the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net.The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator.The paper is an investigation on a remark provided by Smale and Zhou.In the present paper, we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space （RKHS） derived by a Mercer kernel and a determined net. We show that if the sample is taken according to the determined set, then, the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net. The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator. The paper is an investigation on a remark provided by Smale and Zhou.

关 键 词：function reconstruction reproducing kernel Hilbert spaces Shannon sampling learning algorithm learning theory sample error regularization error 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O212.1[自动化与计算机技术—计算机科学与技术]