Journal article
Operator-valued kernels, machine learning, and dynamical systems
Physica. D, Vol.476, 134657
06/2025
DOI: 10.1016/j.physd.2025.134657
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.
•Introduces factorizations of operator-valued kernels for ML and dynamical systems.•Extends kernel methods to Hilbert space-valued Gaussian processes for modeling.•Proposes a Bayesian framework for kernel optimization to improve generalization.•Offers insights into non-commutative probability and Radon–Nikodym theorems.•Shows applications to quantum states, quantum gates, and quantum information.
Details
- Title: Subtitle
- Operator-valued kernels, machine learning, and dynamical systems
- Creators
- Palle E.T. Jorgensen - Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USAJames Tian - Mathematical Reviews, 416 4th Street, Ann Arbor, MI 48103-4816, USA
- Resource Type
- Journal article
- Publication Details
- Physica. D, Vol.476, 134657
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.physd.2025.134657
- ISSN
- 0167-2789
- eISSN
- 1872-8022
- Language
- English
- Date published
- 06/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984808530102771
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