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

NeurIPS 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Differentiable and score-based DAG learning · 0 citations (OpenAlex)

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Extends Cluster-DAG (C-DAG) causal abstractions to allow cyclic cluster-level graphs by introducing structures of interest, canonical and unfolded graphs, and a sound, atomically complete do-calculus over clusters.

Problem

Causal reasoning over clusters of variables in C-DAGs is limited to acyclic cluster graphs (partition admissibility); arbitrary clusterings can induce cycles between clusters, making standard C-DAG semantics inapplicable.

Approach

Relax partition admissibility so C-DAGs may have self-loops and cycles; define d-connection via structures of interest (ancestral substructures with collider-directed paths), a canonical compatible graph guaranteeing realizability, and an unfolded graph as search space, yielding do-calculus rules for cluster queries.

Key results

• Calculus for cyclic C-DAGs is sound and atomically complete with respect to Pearl's do-calculus rules, each rule corresponding to a primitive do-calculus step.
• Any cluster can be reduced to size at most three without losing relevant d-separation/intervention information (Theorem 'Infinity is at most three'), and this bound is tight.
• Recovers the standard acyclic C-DAG results when the C-DAG is acyclic.

Surprising findings

• Mutilating all compatible graphs of a C-DAG yields a strictly smaller set than the compatible class of the mutilated C-DAG, so do-calculus cannot be applied directly on the class of the mutilated C-DAG.

Limitations

• Calculus is only atomically complete, not globally complete.
• Rule 3 cannot be directly encoded on the unfolded graph because the mutilation depends on the particular compatible graph.
• Results assume known cluster cardinalities; wrong cardinalities break completeness or soundness.

Experimental setup

Builds on: C-DAG framework do-calculus d-separation ADMG

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