用核方法学习函数、算子和动态系统，打通机器学习与数学理论的桥梁。
Learning functions, operators and dynamical systems with kernels
- 基于再生核希尔伯特空间构建机器学习框架，统一处理函数与算子学习
- 将动态系统建模转化为算子学习问题，利用柯普曼算子理论提升预测精度
- 适合想理解机器学习数学原理的研究生和科研人员
本文介绍基于再生核希尔伯特空间的统计机器学习方法。首先建立标量值学习的基本框架，进而扩展至算子学习。最后，将动态系统学习表述为合适的算子学习问题，利用柯普曼算子理论实现建模。本文内容是意大利切特拉罗举办的CIME学校‘机器学习：从数据到数学理解’课程的配套材料。
原文摘要 · Abstract (English)
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning dynamical systems is formulated as a suitable operator learning problem, leveraging Koopman operator theory. The manuscript collects the supporting material for the corresponding course taught at the CIME school "Machine Learning: From Data to Mathematical Understanding" in Cetraro.
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