mlsanityData to 14 Oct 2026

Identifying Macro Causal Effects in C-DMGs over DMGs

arXiv 2506.19650 ↗First posted 24 Jun 2025cs.AI stat.MEcited by 3

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Abstract (arXiv)

The do-calculus is a sound and complete tool for identifying causal effects in acyclic directed mixed graphs (ADMGs) induced by structural causal models (SCMs). However, in many real-world applications, especially in high-dimensional setting, constructing a fully specified ADMG is often infeasible. This limitation has led to growing interest in partially specified causal representations, particularly through cluster-directed mixed graphs (C-DMGs), which group variables into clusters and offer a more abstract yet practical view of causal dependencies. While these representations can include cycles, recent work has shown that the do-calculus remains sound and complete for identifying macro-level causal effects in C-DMGs over ADMGs under the assumption that all clusters size are greater than 1. Nevertheless, real-world systems often exhibit cyclic causal dynamics at the structural level. To account for this, input-output structural causal models (ioSCMs) have been introduced as a generalization of SCMs that allow for cycles. ioSCMs induce another type of graph structure known as a directed mixed graph (DMG). Analogous to the ADMG setting, one can define C-DMGs over DMGs as high-level representations of causal relations among clusters of variables. In this paper, we prove that, unlike in the ADMG setting, the do-calculus is unconditionally sound and complete for identifying macro causal effects in C-DMGs over DMGs. Furthermore, we show that the graphical criteria for non-identifiability of macro causal effects previously established C-DMGs over ADMGs naturally extends to a subset of C-DMGs over DMGs.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 14 of its 30 references that are in the map. First posted on arXiv 24 Jun 2025.

Builds on

14 of 30 references.

References · 14

  1. 2022Causal Effect Identification in Cluster DAGscited by 36
  2. 2018Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounderscited by 35
  3. 2017Markov Properties for Graphical Models with Cycles and Latent Variablescited by 32
  4. 2023Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loopscited by 30
  5. 2023Foundations of Causal Discovery on Groups of Variablescited by 22
  6. 2019Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Biascited by 17
  7. 2023Identifiability of total effects from abstractions of time series causal graphscited by 14
  8. 2021Clustering and Structural Robustness in Causal Diagramscited by 12
  9. 2023Identifiability of Direct Effects from Summary Causal Graphscited by 12
  10. 2013A generalized back-door criterioncited by 9
  11. 2024Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confoundingcited by 9
  12. 2024Towards identifiability of micro total effects in summary causal graphs with latent confounding: extension of the front-door criterioncited by 5
2 more
  1. 2025Identifying Macro Causal Effects in a C-DMG over ADMGscited by 4
  2. 2025Note on the identification of total effect in Cluster-DAGs with cyclescited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2025Improving the Generation and Evaluation of Synthetic Data for Downstream Medical Causal Inferencecited by 4
  2. 2026From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variablescited by 0
  3. 2026Invariance of Clustering Operations in Causal Effect Identificationcited by 0