再生核Hilbert空间中回归损失函数的V_γ维  

On the V_γ dimension of regressional loss functions in RKHS

作　　者：魏小燕[1] 潘志斌[2] 

机构地区：[1]湖北经济学院经济信息系,湖北武汉430205 [2]华中农业大学理学院,湖北武汉430070

出　　处：《湖北大学学报（自然科学版）》2007年第3期238-241,共4页Journal of Hubei University：Natural Science

摘　　要：在机器学习问题中,学习机器的一致性和推广能力是非常重要的研究课题,通常,学习机器的推广能力与VC维和Vγ维有密切的关系,证明了再生核Hilbert空间中一类范围较广的回归损失函数集的Vγ维对于任意的γ>0有限,并给出了它的一个上界,使得刻划这种类型的学习机器的推广能力成为可能.In the machine learning problems, the consistence and generalization performance are the main research points. The generalization performance of the learning machine is usually closely related to VC dimension and Vγ dimension, whose bound is more compact using Vγ dimension. This paper proves that the Vγ dimension of a wide kind of regressional loss functions in Reproducing Kernel Hilbert Spaces in finite for any γ〉0, and gives an upper bound of it, so that can studied the generalization ability of the learning machine of this kind.

关 键 词：再生核HILBERT空间 学习机器 推广能力 Vγ维 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]