We view regularized learning of a function in a Banach space from its finite samples as an optimization problem. Within the framework of reproducing kernel Banach spaces, we prove the representer theorem for the minimizer of regularized learning schemes with a general loss function and a...

Tropical cyclones represent major natural disasters in low- and mid-latitude coastal areas. Effective assessment of tropical cyclone disasters provides a scientific reference for the formulation of tropical cyclone prevention and disaster-relief measures. Tropical cyclone disasters in Zhejiang...

Support vector machines (SVMs) are special kernel based methods and have been among the most successful learning methods for more than a decade. SVMs can informally be described as kinds of regularized M-estimators for functions and have demonstrated their usefulness in many complicated...

In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods (simply called SVMs here) can be seen as regularized...