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

2025-11-03

AI Summary

Traditional cluster-DAGs (C-DAGs) impose partition admissibility—requiring variable clustering to yield an acyclic C-DAG—severely limiting applicability in complex systems. This work breaks that restriction by introducing *cyclic C-DAGs*, which admit arbitrary variable clusterings, including those inducing cycles. To support sound causal reasoning under cyclicity, we reformulate d-separation for clustered variables, extend the do-calculus with cluster-level inference rules, and establish a complete and sound framework for cluster-level causal identification. We prove that the framework correctly identifies all cluster-intervention effects that are causally identifiable from the underlying causal graph. Empirical evaluation demonstrates that cyclic C-DAGs significantly broaden the scope of C-DAGs in macro-scale modeling, modular system analysis, and multi-scale causal inference, thereby providing a rigorous foundation for higher-order causal abstraction.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Extending C-DAGs to support arbitrary variable clusterings
• Allowing cyclic C-DAG representations by relaxing admissibility constraints
• Developing causal calculus for cluster-level reasoning in cyclic C-DAGs

Innovation

• Relaxing partition admissibility for cyclic C-DAGs
• Extending d-separation to arbitrary clusterings
• Providing sound calculus for cluster-level interventions