文献类型：期刊文献

中文题名：单位球上散乱数据核正则化回归的误差分析

英文题名：Error Analysis of Kernel Regularized Regression with Deterministic Spherical Scattered Data

作者：李峻屹[1];盛宝怀[2]

机构：[1]陕西警官职业学院信息技术系,陕西西安710021;[2]绍兴文理学院应用统计系,浙江绍兴312000

年份：2022

卷号：35

期号：1

起止页码：172

中文期刊名：应用数学

外文期刊名：Mathematica Applicata

收录：CSTPCD、、北大核心、CSCD、北大核心2020、CSCD_E2021_2022

基金：Supported partially by the NSF (61877039);NSFC/RGC Joint Research Scheme of China (12061160462 and N-CityU102/20);NSF of Zhejiang Province (LY19F020013)。

语种：中文

中文关键词：数值积分公式;球盖;最差误差;二次损失函数;核正则化回归;学习速度

外文关键词：Number integration formula;Spherical cap;Worst-case error;Quadratic function loss;Kernel regularized regression;Learning rate

中文摘要：给出基于二次损失的单位球盖(单位球)上确定型散乱数据核正则化回归误差的上界估计,将学习误差估计转化为核函数积分的误差分析,借助于学习理论中的K-泛函与光滑模的等价性刻画了学习速度.研究结果表明学习速度由网格范数所控制.

外文摘要：We investigate the error bounds of kernel regularized regression learning associated with deterministic data on the spherical cap(and the whole unit sphere) and the quadratic loss. We transform the learning error as the upper bound estimate for the numerical integration error and obtain the learning rates with the convergence rates of kernel-based quadrature. We express the learning rates with a modulus of smoothness which is equivalent to a K-functional in learning theory. The research results show that the learning rates are controlled by the mesh norm of the scattered data.