mlsanityData to 7 Oct 2026

Causal Effect Identification in Cluster DAGs

arXiv 2202.12263 ↗First posted 22 Feb 2022stat.ME cs.AI cs.LGcited by 33

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Abstract (arXiv)

Reasoning about the effect of interventions and counterfactuals is a fundamental task found throughout the data sciences. A collection of principles, algorithms, and tools has been developed for performing such tasks in the last decades (Pearl, 2000). One of the pervasive requirements found throughout this literature is the articulation of assumptions, which commonly appear in the form of causal diagrams. Despite the power of this approach, there are significant settings where the knowledge necessary to specify a causal diagram over all variables is not available, particularly in complex, high-dimensional domains. In this paper, we introduce a new graphical modeling tool called cluster DAGs (for short, C-DAGs) that allows for the partial specification of relationships among variables based on limited prior knowledge, alleviating the stringent requirement of specifying a full causal diagram. A C-DAG specifies relationships between clusters of variables, while the relationships between the variables within a cluster are left unspecified, and can be seen as a graphical representation of an equivalence class of causal diagrams that share the relationships among the clusters. We develop the foundations and machinery for valid inferences over C-DAGs about the clusters of variables at each layer of Pearl's Causal Hierarchy (Pearl and Mackenzie 2018; Bareinboim et al. 2020) - L1 (probabilistic), L2 (interventional), and L3 (counterfactual). In particular, we prove the soundness and completeness of d-separation for probabilistic inference in C-DAGs. Further, we demonstrate the validity of Pearl's do-calculus rules over C-DAGs and show that the standard ID identification algorithm is sound and complete to systematically compute causal effects from observational data given a C-DAG. Finally, we show that C-DAGs are valid for performing counterfactual inferences about clusters of variables.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 6 of its 35 references that are in the map. First posted on arXiv 22 Feb 2022.

Builds on

6 of 35 references.

References · 6

  1. 2017Causal Consistency of Structural Equation Modelscited by 114
  2. 2018Abstracting Causal Modelscited by 104
  3. 2014Visual Causal Feature Learningcited by 59
  4. 2021Nested Counterfactual Identification from Arbitrary Surrogate Experimentscited by 38
  5. 2015Multi-Level Cause-Effect Systemscited by 30
  6. 2018Identifying Causal Effects with the R Package causaleffectcited by 18

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 5; 2025: 16; 2026: 8.

33 papers.

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  1. 2025Foundation Models for Causal Inference via Prior-Data Fitted Networkscited by 30
  2. 2023Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimationcited by 20
  3. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 17
  4. 2023Identifiability of total effects from abstractions of time series causal graphscited by 13
  5. 2024Learning Causal Abstractions of Linear Structural Causal Modelscited by 9
  6. 2023Expert-Aided Causal Discovery of Ancestral Graphscited by 8
  7. 2025What is causal about causal models and representations?cited by 6
  8. 2024Causally Abstracted Multi-armed Banditscited by 5
  9. 2024Towards identifiability of micro total effects in summary causal graphs with latent confounding: extension of the front-door criterioncited by 5
  10. 2025Identifying Macro Causal Effects in a C-DMG over ADMGscited by 3
  11. 2025Nonlinear Causal Discovery for Grouped Datacited by 3
  12. 2025Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clusteringcited by 3
21 more
  1. 2023A Causal Framework for Decomposing Spurious Variationscited by 2
  2. 2025Causal DAG Summarization (Full Version)cited by 2
  3. 2025Complete Characterization for Adjustment in Summary Causal Graphs of Time Seriescited by 2
  4. 2025Identifying Macro Causal Effects in C-DMGs over DMGscited by 2
  5. 2026Coarsening Causal DAG Modelscited by 2
  6. 2026Coarsening Linear Non-Gaussian Causal Models with Cyclescited by 2
  7. 2024Average Controlled and Average Natural Micro Direct Effects in Summary Causal Graphscited by 1
  8. 2025Your Assumed DAG is Wrong and Here's How To Deal With Itcited by 1
  9. 2025On the Identifiability of Causal Abstractionscited by 1
  10. 2025Clustering and Pruning in Causal Data Fusioncited by 1
  11. 2025Identifiability in Causal Abstractions: A Hierarchy of Criteriacited by 1
  12. 2025GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomescited by 1
  13. 2025Cluster-Dags as Powerful Background Knowledge For Causal Discoverycited by 1
  14. 2025Causal Abstractions, Categorically Unifiedcited by 0
  15. 2025On Efficient Adjustment for Micro Causal Effects in Summary Causal Graphscited by 0
  16. 2026A pipeline for enabling path-specific causal fairness in observational health datacited by 0
  17. 2026Multi-Level Causal Embeddingscited by 0
  18. 2026Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variablescited by 0
  19. 2026From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variablescited by 0
  20. 2026Interpretable Causal Discovery via Causal-Effect Constraintscited by 0
  21. 2026Joint Causal Structure and Cluster Discovery Using Variational Inferencecited by 0