用范畴论与几何方法解决统计、机器学习中的问题

Categorical and geometric methods in statistical, manifold, and machine learning

• 引入概率态射范畴处理学习任务的结构关系
• 结合几何方法提升对流形学习的理解
• 适合研究理论基础与数学建模的学者

我们介绍并讨论了概率态射范畴（initially developed in \\cite{Le2023}）的应用，以及一些几何方法在统计学习、机器学习和流形学习中的多个问题上的运用。这些内容将作为即将出版的著作 \\cite{LMPT2024} 的核心部分进行深入探讨。

原文摘要 · Abstract (English)

We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics, considered in depth in the forthcoming book \cite{LMPT2024}.

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