Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering

📝 Original Info

• Title: Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering
• ArXiv ID: 2511.01396
• Date: 2025-11-03
• Authors: 정보 없음 (논문에 저자 정보가 제공되지 않음)

📝 Abstract

Cluster DAGs (C-DAGs) provide an abstraction of causal graphs in which nodes represent clusters of variables, and edges encode both cluster-level causal relationships and dependencies arisen from unobserved confounding. C-DAGs define an equivalence class of acyclic causal graphs that agree on cluster-level relationships, enabling causal reasoning at a higher level of abstraction. However, when the chosen clustering induces cycles in the resulting C-DAG, the partition is deemed inadmissible under conventional C-DAG semantics. In this work, we extend the C-DAG framework to support arbitrary variable clusterings by relaxing the partition admissibility constraint, thereby allowing cyclic C-DAG representations. We extend the notions of d-separation and causal calculus to this setting, significantly broadening the scope of causal reasoning across clusters and enabling the application of C-DAGs in previously intractable scenarios. Our calculus is both sound and atomically complete with respect to the do-calculus: all valid interventional queries at the cluster level can be derived using our rules, each corresponding to a primitive do-calculus step.

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