Generalized Mercer Kernels and Reproducing Kernel Banach Spaces (Memoirs of the American Mathematical Society)

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces (Memoirs of the American Mathematical Society)
by: Yuesheng Xu (Author),Qi Ye(Author)
Publisher: Amer Mathematical Society
Publication Date: 2019/4/1
Language: English
Print Length: 122 pages
ISBN-10: 1470435500
ISBN-13: 9781470435509
Book Description
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct $p$-norm RKBSs for $1leq pleqinfty$.
About the Author
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct $p$-norm RKBSs for $1leq pleqinfty$. Read more