对齐图形化与功能性因果抽象
Aligning Graphical and Functional Causal Abstractions
AI总结：
本文对齐图形化与功能性因果抽象的一致性概念，证明 Cluster DAG、双射范围的一致 α-abstraction 与构造性 τ-abstraction 等价，并提出 Partial Cluster DAG 以增强表达能力。
摘要：
因果抽象使我们能够关联不同粒度层级上的因果模型。为确保模型在因果关系上保持一致，因果抽象框架定义了一致性概念。文献中常见两种不同的因果抽象方法：（i）图形化抽象，例如 Cluster DAG，在结构层面关联模型；（ii）功能性抽象，例如 α-abstraction，通过变量及其取值范围之间的映射来关联模型。本文将对齐图形化一致性与功能性一致性的概念，并证明 Cluster DAG 类别、被抽象变量取值范围经双射映射的一致 α-abstraction，以及构造性 τ-abstraction 之间的等价性。此外，我们通过引入 Partial Cluster DAG，扩展了这种对齐以及图形化抽象的表达能力。我们的结果在功能性框架与图形化框架之间建立了严谨的桥梁，并使二者之间的成果采用与转移成为可能。
英文摘要：
Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal abstraction are common in the literature: (i) graphical abstractions, such as Cluster DAGs, which relate models on a structural level, and (ii) functional abstractions, like $α$-abstractions, which relate models by maps between variables and their ranges. In this paper we will align the notions of graphical and functional consistency and show an equivalence between the class of Cluster DAGs, consistent $α$-abstractions with the range of abstracted variables mapped bijectively, and constructive $τ$-abstractions. Furthermore, we extend this alignment and the expressivity of graphical abstractions by introducing Partial Cluster DAGs. Our results provide a rigorous bridge between the functional and graphical frameworks and allow for adoption and transfer of results between them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
