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Identifying Macro Causal Effects in C-DMGs over DMGs

NeurIPS 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Causal effect identification · 0 citations (OpenAlex)

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Shows that sigma-separation and the do-calculus are sound and complete for identifying macro causal effects in cluster-directed mixed graphs (C-DMGs) over cyclic DMGs induced by ioSCMs, and extends SC-hedge non-identifiability to such graphs when cyclic clusters have size at least 2.

Problem

Identifying macro-level causal effects between clusters of variables when the underlying causal structure may contain cycles (ioSCMs/DMGs) and only a partially specified cluster graph (C-DMG) is known.

Approach

Extends sigma-separation and the sigma-do-calculus to C-DMGs over DMGs, proving unconditional soundness and completeness of macro-level identification (unlike the ADMG case, which needs cluster-size conditions), and generalizes SC-hedge non-identifiability under a cluster-size-at-least-2 assumption for cyclic clusters.

Key results

• Proves sigma-separation is sound and complete in C-DMGs over DMGs (Theorems on soundness/completeness of sigma-separation).
• Proves do-calculus with sigma-separation is sound and complete for macro causal effects in C-DMGs over DMGs without cluster-size constraints.
• Shows SC-hedge existence implies non-identifiability in C-DMGs over DMGs when every cyclic cluster has size at least 2.

Surprising findings

• Unlike the ADMG setting, do-calculus completeness for macro effects holds unconditionally in C-DMGs over DMGs.

Limitations

• Completeness of the do-calculus is relative to compatible DMGs and does not cover other possible identification rules; sigma-do-calculus completeness in DMGs is not proven.
• The SC-hedge criterion is only proven sound under the assumption that clusters in cycles have size at least 2 and is not proven complete.
• No empirical evaluation; results are purely theoretical.

Experimental setup

Baselines: C-DMG over ADMGs identification results hedge criterion

Builds on: do-calculus sigma-separation ioSCM C-DMG over ADMGs SC-hedge

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