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：关于概率程序和因果模型的日益增多的研究强调了需要对扩展有向图模型的模型类进行组合推理。概率程序和因果模型都定义了随机变量集上的联合概率密度，并展现出可用于推理因果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的最新研究，定义了一个态射结合联合密度（在每个样本空间上因子化）与从样本到返回值的确定映射的范畴。这是向缩小概率测度的最近范畴论描述与概率编程和因果推断中常用的因子化密度操作定义之间差距迈出的一步。