Generalized Mercer Kernels and Reproducing Kernel Banach...

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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Yuesheng Xu, Qi Ye

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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 $1\leq p\leq\infty$.

Yıl:

2019

Baskı:

Yayımcı:

American Mathematical Society

Dil:

english

Sayfalar:

134

ISBN 10:

1470450771

ISBN 13: