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Operator-valued kernels, machine learning, and dynamical systems
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DOI：10.1016/j.physd.2025.134657.png)
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Abstract
En 中文
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.
Keywords:
Positive definite functions
Gaussian processes
Covariance
Dilation
Non-commutative Radon-Nikodym derivatives
Completely positive maps
Measurement
Quantum states
Quantum gates
Kernel method
Journal
P
IF:
2.9
Papers:
389
Citations:
1.5W