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.
基金
supported by National Natural Science Foundation of China (Grant No.10871226)
Natural Science Foundation of Zhejiang Province (Grant No. Y6100096)
关键词
再生核HILBERT空间
收敛速度
学习算法
取样
假设空间
学习计划
抽样误差
插值算子
function reconstruction, reproducing kernel Hilbert spaces, Shannon sampling learning algorithm,learning theory, sample error, regularization error
