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.
翻译:我们对因果模型进行分类理论处理,这些模型通过将自由的马尔科夫类别与DAG联系起来,将定向循环图(DAG)的因果关系推理语法正式化。这个框架使我们能够从抽象和“纯粹因果”的观点中界定和研究因果推理中的重要概念,如因果独立/分离、因果条件和干预效果分解等。我们关于这些概念的结果与通常采用的因果模型的细节(如(再生)结构等式模型或因果贝叶斯网络)脱钩。因此,它们更加广泛适用,而且概念上更清晰。我们的结果还与Judea Pearls所庆祝的量度密切相关,并产生在所有因果模型中继承的计算核心部分的合成版本。特别是,它引出了珍珠在因果贝叶斯网络中出现的更简单和专门化的因果计算版本,我们所展示的完整版本同样强。