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Generalized Mercer kernels and reproducing kernel Banach spaces
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 implem...
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Lenguaje: | eng |
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American Mathematical Society
2019
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Acceso en línea: | http://cds.cern.ch/record/2685661 |
_version_ | 1780963455243649024 |
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author | Xu, Yuesheng Ye, Qi |
author_facet | Xu, Yuesheng Ye, Qi |
author_sort | Xu, Yuesheng |
collection | CERN |
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 1\leq p\leq\infty. |
id | cern-2685661 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2019 |
publisher | American Mathematical Society |
record_format | invenio |
spelling | cern-26856612021-04-21T18:20:32Zhttp://cds.cern.ch/record/2685661engXu, YueshengYe, QiGeneralized Mercer kernels and reproducing kernel Banach spacesMathematical Physics and MathematicsThis 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.American Mathematical Societyoai:cds.cern.ch:26856612019 |
spellingShingle | Mathematical Physics and Mathematics Xu, Yuesheng Ye, Qi Generalized Mercer kernels and reproducing kernel Banach spaces |
title | Generalized Mercer kernels and reproducing kernel Banach spaces |
title_full | Generalized Mercer kernels and reproducing kernel Banach spaces |
title_fullStr | Generalized Mercer kernels and reproducing kernel Banach spaces |
title_full_unstemmed | Generalized Mercer kernels and reproducing kernel Banach spaces |
title_short | Generalized Mercer kernels and reproducing kernel Banach spaces |
title_sort | generalized mercer kernels and reproducing kernel banach spaces |
topic | Mathematical Physics and Mathematics |
url | http://cds.cern.ch/record/2685661 |
work_keys_str_mv | AT xuyuesheng generalizedmercerkernelsandreproducingkernelbanachspaces AT yeqi generalizedmercerkernelsandreproducingkernelbanachspaces |