单位球上散乱数据核正则化回归的误差分析  

Error Analysis of Kernel Regularized Regression with Deterministic Spherical Scattered Data

作　　者：李峻屹[1] 盛宝怀[2] LI Junyi;SHENG Baohuai(Department of Information Technology,Shanxi Police College,Xi’an 710021,China;Department of Applied Statistics,Shaoxing University,Shaoxing 312000,China)

机构地区：[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

出　　处：《应用数学》2022年第1期172-179,共8页Mathematica Applicata

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)。

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.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.

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 

分 类 号：O174.41[理学—数学]