正则化学习算法的数学基础

Mathematics of Regularization Learning Algorithm

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.