Learning rates of regularized regression on the unit sphere

被引：7

作者：

Cao FeiLong ^{[1
]}

Lin ShaoBo ^{[2
]}

Chang XiangYu ^{[2
]}

Xu ZongBen ^{[2
]}

机构：

[1] China Jiliang Univ, Inst Metrol & Computat Sci, Hangzhou 310018, Zhejiang, Peoples R China

[2] Xi An Jiao Tong Univ, Inst Informat & Syst Sci, Xian 710049, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 04期

基金：

中国国家自然科学基金;

关键词：

sphere; regularized regression; spherical harmonics kernel; rate of convergence; JACKSON-TYPE INEQUALITY; APPROXIMATION; ERROR;

D O I：

10.1007/s11425-012-4505-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses the learning algorithm on the unit sphere. The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel. The excess error can be estimated by the sum of sample errors and regularization errors. Our study shows that by introducing a suitable spherical harmonics kernel, the regularization parameter can decrease arbitrarily fast with the sample size.

引用

页码：861 / 876

页数：16

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