正则化学习算法的数学基础  

Mathematics of Regularization Learning Algorithm

作　　者：甄新[1] 胡政发[1] 

机构地区：[1]湖北汽车工业学院理学系,湖北十堰442002

出　　处：《湖北汽车工业学院学报》2009年第3期61-64,共4页Journal of Hubei University Of Automotive Technology

基　　金：湖北汽车工业学院科研基金(2008YQ27)

摘　　要：正则化方法使经验风险最小化学习算法变得适定。从数学基础的角度,给出求解不适定问题的正则化方法的思想,证明了正则化算法的核心定理以及Hilbert空间上的正则化方法的有关定理。最后作为一个典型范例介绍了在再生核Hilbert空间上学习算法的正则化方法的基本思想。Regularization method is used to make the algorithm of empirical risk minimization well-posed.From the point of view of mathematic foundation,the ideal of regularization method for solving ill-posed problem is given and the key theorem of regularization method,as well as theorem of regularization in Hilbert space are proved.As a classical example,the basic ideal of regularization learning algorithm in reproducing kernel Hilbert space is introduced.

关 键 词：学习算法 算子方程 适定性 正则化 再生核HILBERT空间 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] O29[自动化与计算机技术—控制科学与工程]