Operator-Valued Kernels, Machine Learning, and Dynamical Systems
Operator Algebras
2024-10-14 v2 Mathematical Physics
Functional Analysis
math.MP
Quantum Physics
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.
Cite
@article{arxiv.2405.09315,
title = {Operator-Valued Kernels, Machine Learning, and Dynamical Systems},
author = {Palle E. T. Jorgensen and James Tian},
journal= {arXiv preprint arXiv:2405.09315},
year = {2024}
}