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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.01396 |
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| _version_ | 1866914132305903616 |
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| author | Yvernes, Clément Devijver, Emilie Ribeiro, Adèle H. Clausel--Lesourd, Marianne Gaussier, Éric |
| author_facet | Yvernes, Clément Devijver, Emilie Ribeiro, Adèle H. Clausel--Lesourd, Marianne Gaussier, Éric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering Yvernes, Clément Devijver, Emilie Ribeiro, Adèle H. Clausel--Lesourd, Marianne Gaussier, Éric Artificial Intelligence Methodology 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. |
| title | Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering |
| topic | Artificial Intelligence Methodology |
| url | https://arxiv.org/abs/2511.01396 |