算子值核，机器学习和动态系统

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-04-02 DOI:10.1016/j.physd.2025.134657

Palle E.T. Jorgensen , James Tian

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引用次数: 0

摘要

在核优化的背景下，我们证明了一个产生新的分解和实现的结果。我们的初始背景是一般的正算子值核。我们进一步提出希尔伯特空间值高斯过程的含义，因为它们出现在动力学和机器学习的应用中。进一步给出了在非交换概率论中的应用，包括一个新的非交换Radon-Nikodym定理。

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Operator-valued kernels, machine learning, and dynamical systems

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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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.