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Operator-Valued Kernels, Machine Learning, and Dynamical Systems (2405.09315v2)
Published 15 May 2024 in math.OA, math-ph, math.FA, math.MP, and quant-ph
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.