mlsanityData to 7 Oct 2026

Relating Graph Neural Networks to Structural Causal Models

arXiv 2109.04173 ↗First posted 9 Sep 2021cs.LG stat.MLcited by 39

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Abstract (arXiv)

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries leveraging the exposed. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a more general view on neural-causal models, revealing several novel connections between GNN and SCM. We establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 19 of its 52 references that are in the map. First posted on arXiv 9 Sep 2021.

Builds on

19 of 52 references.

References · 19

  1. 2017Attention Is All You Needcited by 59,932
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
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  7. 2016Variational Inference: A Review for Statisticianscited by 1,466
  8. 2016Variational Graph Auto-Encoderscited by 1,373
  9. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
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  12. 2018Neural Relational Inference for Interacting Systemscited by 339
7 more
  1. 2020Deep Structural Causal Models for Tractable Counterfactual Inferencecited by 210
  2. 2020Representation Learning via Invariant Causal Mechanismscited by 197
  3. 2021ETA Prediction with Graph Neural Networks in Google Mapscited by 130
  4. 2019On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Datasetcited by 100
  5. 2021The Causal-Neural Connection: Expressiveness, Learnability, and Inferencecited by 97
  6. 2019Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounderscited by 74
  7. 2021Persistent Message Passingcited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 5; 2023: 11; 2024: 11; 2025: 7; 2026: 2.

39 papers.

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  1. 2021Causal Attention for Interpretable and Generalizable Graph Classificationcited by 108
  2. 2022Diffusion Causal Models for Counterfactual Estimationcited by 87
  3. 2022Neural Causal Models for Counterfactual Identification and Estimationcited by 54
  4. 2023High Fidelity Image Counterfactuals with Probabilistic Causal Modelscited by 53
  5. 2023Causal normalizing flows: from theory to practicecited by 49
  6. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  7. 2023Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queriescited by 23
  8. 2023Automated Cyber Defence: A Reviewcited by 19
  9. 2021VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queriescited by 18
  10. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  11. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  12. 2024Mitigating attribute amplification in counterfactual image generationcited by 12
27 more
  1. 2022Machine Learning and Deep Learning -- A review for Ecologistscited by 11
  2. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  3. 2023Exploring Causal Learning through Graph Neural Networks: An In-depth Reviewcited by 8
  4. 2024Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challengescited by 8
  5. 2025DeCaFlow: A deconfounding causal generative modelcited by 8
  6. 2023A Survey of Methods, Challenges and Perspectives in Causalitycited by 6
  7. 2022BusyBot: Learning to Interact, Reason, and Plan in a BusyBoard Environmentcited by 3
  8. 2023Behaviour Modelling of Social Animals via Causal Structure Discovery and Graph Neural Networkscited by 2
  9. 2024CEGRL-TKGR: A Causal Enhanced Graph Representation Learning Framework for Temporal Knowledge Graph Reasoningcited by 2
  10. 2021A Taxonomy for Inference in Causal Model Familiescited by 1
  11. 2023Disentanglement of Latent Representations via Causal Interventionscited by 1
  12. 2024Towards Causal Classification: A Comprehensive Study on Graph Neural Networkscited by 1
  13. 2024Caformer: Rethinking Time Series Analysis from Causal Perspectivecited by 1
  14. 2024A Causal Graph-Enhanced Gaussian Process Regression for Modeling Engine-out NOxcited by 1
  15. 2025ACTIVA: Amortized Causal Effect Estimation via Transformer-based Variational Autoencodercited by 1
  16. 2025Causal Process Models: Reframing Dynamic Causal Graph Discovery as a Reinforcement Learning Problemcited by 1
  17. 2025Causal Graph Neural Networks for Healthcarecited by 1
  18. 2023GDBN: a Graph Neural Network Approach to Dynamic Bayesian Networkcited by 0
  19. 2024Blood Glucose Control Via Pre-trained Counterfactual Invertible Neural Networkscited by 0
  20. 2024Towards Understanding Link Predictor Generalizability Under Distribution Shiftscited by 0
  21. 2024Teleporter Theory: A General and Simple Approach for Modeling Cross-World Counterfactual Causalitycited by 0
  22. 2024Learning Structural Causal Models from Ordering: Identifiable Flow Modelscited by 0
  23. 2025Integrating Causality with Neurochaos Learning: Proposed Approach and Research Agendacited by 0
  24. 2025Causal Mean Field Multi-Agent Reinforcement Learningcited by 0
  25. 2025From Observations to Causations: A GNN-based Probabilistic Prediction Framework for Causal Discoverycited by 0
  26. 2026Learning Graphs through Continuous Information Entropy Fieldscited by 0
  27. 2026Explainable Artificial Intelligence (XAI) in Computational Pathology: Definitions, Taxonomy, and Recommendationscited by 0