粗糙空间上基于VC维的风险泛函的界

Bounds on risk functional based on VC dimension in rough space

为了完善粗糙空间上学习过程收敛速度的界,根据粗糙空间上的信赖性测度的性质和传统的统计学习理论的相关知识,在粗糙空间上学习理论的关键定理和学习过程一致收敛速度的界的基础上,给出了粗糙空间上退火熵、生长函数、VC维的概念及其相关的性质,以此为基础构建了粗糙空间上基于VC维的构造性的与分布无关的界,为系统地建立粗糙空间上的统计学习理论及其相应的支持向量机奠定了理论基础。

In order to improve the bounds on the convergence rate of learning processes on rough space,according to the properties of trust measure on rough space and the knowledge of traditional statistical theory,the concepts of annealed entropy,growth function and VC dimension as well as their properties on rough space are given based on the key theorem of learning theory and the bounds on the uniform convergence rate of learning theory on rough space. Therefore,the distribution-independent bounds with VC dimension on rough space are established,which lays a theoretical foundation for the statistical theory on rough space and the corresponding Support Vector Machine.