Learning rates of least-square regularized regression with polynomial kernels  

作　　者：LI BingZheng WANG GuoMao 

机构地区：[1]Department of Mathematics,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China Mathematics》2009年第4期687-700,共14页中国科学：数学（英文版）

摘　　要：This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in $ L_{\rho _X }^2 $ with Borel probability measure.This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in Lρ2X with Borel probability measure.

关 键 词：learning theory reproducing kernel Hilbert space polynomial kernel regularization error Bernstein-Durrmeyer operators covering number regularization scheme 68T05 62J02 

分 类 号：O241.5[理学—计算数学]