基于弱相关抽样的系数正则化的一致性分析  

Asymptotic Convergence of Coefficient Regularization Based on Weakly Dependent Samples

作　　者：郭芹[1] 孙红卫[1] 

机构地区：[1]济南大学理学院,山东济南250022

出　　处：《济南大学学报（自然科学版）》2010年第1期99-103,共5页Journal of University of Jinan(Science and Technology)

基　　金：山东省自然科学基金(Y2007A11);济南大学博士基金(XBS0832)

摘　　要：针对满足强混合条件的弱相关抽样,且α系数满足多项式衰减αi≤ai-t的情形,利用样本算子与积分算子的技巧,证明最小二乘系数正则化算法的一致性,并且得出在满足正则化条件LK-rfρ∈Lρ2X(X),0<r≤21下的学习速度为o(m-2rmin{t,1}logm)。同时得出了基于弱相关抽样的系数正则化算法的饱和指数为2,说明与通常的最小二乘Tikhonov正则化算法相比,系数正则化算法在学习光滑函数时具有一定的优势。Abstract：We consider the asymptotic convergence of coefficient regularization based on the weakly dependent samples. When strongmixing coefficients satisfy a polynomial decay αi≤ai^-1, the asymptotic convergence of coefficient regularization based on weakly dependent samples is proved by means of the integral operator techniques and sample operator. When it satisfies the regularization conditionLK^-rfp∈L^2px（X）,0〈r≤1/2, the learning rate is o （m^-1/2min{t,1}log m）. Moreover, we make some discussions by comparing with the learning rates derived from Tikhonov regularization algorithm. The saturation index for coefficient regularization based on the weakly depended samples is 2, which shows coefficient regularization is powerful in learning smooth functions.

关 键 词：系数正则化 强混合序列 样本误差 逼近误差 学习速率 

分 类 号：O177[理学—数学]