Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 9 of its 20 references that are in the map. First posted on arXiv 3 Nov 2025.
Builds on
9 of 20 references.
References · 9
- 2017Causal Consistency of Structural Equation Modelscited by 114
- 2018Abstracting Causal Modelscited by 104
- 2014Visual Causal Feature Learningcited by 59
- 2022Causal Effect Identification in Cluster DAGscited by 33
- 2015Multi-Level Cause-Effect Systemscited by 30
- 2023Foundations of Causal Discovery on Groups of Variablescited by 20
- 2023Identifiability of Direct Effects from Summary Causal Graphscited by 12
- 2022Vector causal inference between two groups of variablescited by 11
- 2024Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confoundingcited by 8
Built on by
Citing papers per year: 2025: 1; 2026: 2.
3 papers.
- 2025Cluster-Dags as Powerful Background Knowledge For Causal Discoverycited by 1
- 2026Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variablescited by 0
- 2026From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variablescited by 0
- 2026From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables24 Apr 2026
- 2026Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables27 Feb 2026
- 2025Cluster-Dags as Powerful Background Knowledge For Causal Discovery10 Dec 2025
Similar, not cited
Close in wording, no citation either way
- 2022Markov categories, causal theories, and the do-calculus
- 2022Relational Causal Models with Cycles:Representation and Reasoning
- 2024CausalGraph2LLM: Evaluating LLMs for Causal Queries
- 2024Large Language Models for Constrained-Based Causal Discovery
- 2026Externalized CPDAG Summaries Improve LLM Causal Deduction
- 2026CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery
- 2025Compressed Causal Reasoning: Quantization and GraphRAG Effects on Interventional and Counterfactual Accuracy
- 2025Gateways to Tractability for Satisfiability in Pearl's Causal Hierarchy