论文标题
马尔可夫类别，因果理论和do-calculus
Markov categories, causal theories, and the do-calculus
论文作者
论文摘要
我们提供了因果模型的类别理论处理，该方法通过将免费的Markov类别与DAG相关联，以通过规范的方式将因果推理的语法形式化。该框架使我们能够从抽象和“纯粹的因果”观点定义和研究因果推理中的重要概念，例如因果独立/分离，因果关系，以及干预效应的分解。我们关于这些概念的结果从通常采用的因果模型（例如（递归）结构方程模型或因果贝叶斯网络）的细节中抽象出来。因此，它们更广泛地适用，并且在概念上更清晰。我们的结果也与Judea Pearl著名的Do-Calculus密切相关，并产生了在所有因果模型中遗传的微积分核心部分的句法版本。特别是，它在因果贝叶斯网络的背景下引起了Pearl的Do-Calculus的更简单，更专业的版本，我们显示的与完整版本一样强。
We give a category-theoretic treatment of causal models that formalizes the syntax for causal reasoning over a directed acyclic graph (DAG) by associating a free Markov category with the DAG in a canonical way. This framework enables us to define and study important concepts in causal reasoning from an abstract and "purely causal" point of view, such as causal independence/separation, causal conditionals, and decomposition of intervention effects. Our results regarding these concepts abstract away from the details of the commonly adopted causal models such as (recursive) structural equation models or causal Bayesian networks. They are therefore more widely applicable and in a way conceptually clearer. Our results are also intimately related to Judea Pearl's celebrated do-calculus, and yield a syntactic version of a core part of the calculus that is inherited in all causal models. In particular, it induces a simpler and specialized version of Pearl's do-calculus in the context of causal Bayesian networks, which we show is as strong as the full version.
