{"ID":2846603,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.01396","arxiv_id":"2511.01396","title":"Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering","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.","short_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 relationship...","url_abs":"https://arxiv.org/abs/2511.01396","url_pdf":"https://arxiv.org/pdf/2511.01396v1","authors":"[\"Clément Yvernes\",\"Emilie Devijver\",\"Adèle H. Ribeiro\",\"Marianne Clausel--Lesourd\",\"Éric Gaussier\"]","published":"2025-11-03T09:44:58Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"stat.ME\"]","methods":"[]","has_code":false}