Operator-Valued Kernels, Machine Learning, and Dynamical Systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929537027145728 |
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| author | Jorgensen, Palle E. T. Tian, James |
| author_facet | Jorgensen, Palle E. T. Tian, James |
| contents | In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued Gaussian processes, as they arise in applications to dynamics and to machine learning. Further applications are given in non-commutative probability theory, including a new non-commutative Radon--Nikodym theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator-Valued Kernels, Machine Learning, and Dynamical Systems Jorgensen, Palle E. T. Tian, James Operator Algebras Mathematical Physics Functional Analysis Quantum Physics Primary: 81P15, secondary: 46E22, 46L53, 47A20, 60G15, 68T07, 81P47 In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued Gaussian processes, as they arise in applications to dynamics and to machine learning. Further applications are given in non-commutative probability theory, including a new non-commutative Radon--Nikodym theorem. |
| title | Operator-Valued Kernels, Machine Learning, and Dynamical Systems |
| topic | Operator Algebras Mathematical Physics Functional Analysis Quantum Physics Primary: 81P15, secondary: 46E22, 46L53, 47A20, 60G15, 68T07, 81P47 |
| url | https://arxiv.org/abs/2405.09315 |