A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a joint probability density over a set of random variables, and exhibit sparse structure that can be used to reason about causation and conditional independence. This work builds on recent work on Markov categories of probabilistic mappings to define a category whose morphisms combine a joint density, factorized over each sample space, with a deterministic mapping from samples to return values. This is a step towards closing the gap between recent category-theoretic descriptions of probability measures, and the operational definitions of factorized densities that are commonly employed in probabilistic programming and causal inference.

翻译：概率程序与因果模型领域日益增长的研究表明，需要以组合方式对扩展有向图模型的模型类进行推理。概率程序和因果模型均定义了随机变量集合上的联合概率密度，并展现出可用于推理因果关系和条件独立性的稀疏结构。本文基于概率映射的马尔可夫范畴相关研究成果，定义了一个范畴，其态射将每个样本空间上因子化的联合密度与从样本到返回值的确定性映射相结合。这一工作旨在缩小近期概率测度范畴论描述与概率编程及因果推断中常用的因子化密度操作定义之间的差距。