论文标题
分类概率中的D分隔标准
The d-separation criterion in Categorical Probability
论文作者
论文摘要
D分离标准通过某些条件独立性检测到关节概率分布与定向无环图的兼容性。在这项工作中，我们通过引入因果模型的分类定义，D分隔的分类概念，并证明了D-Exaration Criterion的抽象版本，从而在分类概率理论的背景下研究了这个问题。这种方法有两个主要好处。首先，分类D分隔是基于拓扑连接的非常直观的标准。其次，我们的结果既适用于测量理论概率（具有标准的Borel空间）和超越概率理论，包括确定性和可能的网络。因此，它提供了局部和全局马尔可夫特性与连续和混合随机变量以及确定性和可能变量的因果关系的简洁证明。
The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability theory by introducing a categorical definition of causal models, a categorical notion of d-separation, and proving an abstract version of the d-separation criterion. This approach has two main benefits. First, categorical d-separation is a very intuitive criterion based on topological connectedness. Second, our results apply both to measure-theoretic probability (with standard Borel spaces) and beyond probability theory, including to deterministic and possibilistic networks. It therefore provides a clean proof of the equivalence of local and global Markov properties with causal compatibility for continuous and mixed random variables as well as deterministic and possibilistic variables.
