论文标题
统一高斯概率和非确定性的类别
A Category for unifying Gaussian Probability and Nondeterminism
论文作者
论文摘要
我们介绍了扩展的高斯地图和高斯关系的类别，这些类别以线性关系的形式将高斯概率分布统一性分布与关系非确定性。两者在统计，工程和控制理论中都有至关重要且充分理解的应用，但是将它们结合在单一形式主义中是具有挑战性的。它使我们能够严格地描述各种现象，例如嘈杂的物理定律，威廉姆斯的开放系统理论以及贝叶斯统计中的非信息性先验。核心想法是正式允许向量子空间$ d \ subseteq x $作为概括的统一概率分布。我们的形式主义代表了有关分类系统理论的文献（信号流图，线性关系，超图类别）与概率理论概念之间的第一个桥梁。
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in statistics, engineering, and control theory, but combining them in a single formalism is challenging. It enables us to rigorously describe a variety of phenomena like noisy physical laws, Willems' theory of open systems and uninformative priors in Bayesian statistics. The core idea is to formally admit vector subspaces $D \subseteq X$ as generalized uniform probability distribution. Our formalism represents a first bridge between the literature on categorical systems theory (signal-flow diagrams, linear relations, hypergraph categories) and notions of probability theory.
