Operator-Valued Kernels, Machine Learning, and Dynamical Systems

Palle E. T. Jorgensen; James Tian

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arXiv · 2405.09315

Operator-Valued Kernels, Machine Learning, and Dynamical Systems

Palle E. T. Jorgensen·James Tian

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Abstract

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.

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BibTeX RIS

Palle E. T. Jorgensen, James Tian. 2024-05-15. Operator-Valued Kernels, Machine Learning, and Dynamical Systems. https://arxiv.org/abs/2405.09315

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