# Relating Graph Neural Networks to Structural Causal Models

arXiv: https://arxiv.org/abs/2109.04173 · HTML: https://mlsanity.com/paper/2109.04173/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Representation Learning via Invariant Causal Mechanisms](https://mlsanity.com/paper/2010.07922/) (2020)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [Persistent Message Passing](https://mlsanity.com/paper/2103.01043/) (2021)

## Built on by (most cited first, 30 of 41)

- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [Automated Cyber Defence: A Review](https://mlsanity.com/paper/2303.04926/) (2023)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Mitigating attribute amplification in counterfactual image generation](https://mlsanity.com/paper/2403.09422/) (2024)
- [Machine Learning and Deep Learning -- A review for Ecologists](https://mlsanity.com/paper/2204.05023/) (2022)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Exploring Causal Learning through Graph Neural Networks: An In-depth Review](https://mlsanity.com/paper/2311.14994/) (2023)
- [Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challenges](https://mlsanity.com/paper/2405.05025/) (2024)
- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [BusyBot: Learning to Interact, Reason, and Plan in a BusyBoard Environment](https://mlsanity.com/paper/2207.08192/) (2022)
- [Behaviour Modelling of Social Animals via Causal Structure Discovery and Graph Neural Networks](https://mlsanity.com/paper/2312.14333/) (2023)
- [CEGRL-TKGR: A Causal Enhanced Graph Representation Learning Framework for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2408.07911/) (2024)
- [A Taxonomy for Inference in Causal Model Families](https://mlsanity.com/paper/2110.12052/) (2021)
- [Disentanglement of Latent Representations via Causal Interventions](https://mlsanity.com/paper/2302.00869/) (2023)
- [Towards Causal Classification: A Comprehensive Study on Graph Neural Networks](https://mlsanity.com/paper/2401.15444/) (2024)
- [Caformer: Rethinking Time Series Analysis from Causal Perspective](https://mlsanity.com/paper/2403.08572/) (2024)
- [A Causal Graph-Enhanced Gaussian Process Regression for Modeling Engine-out NOx](https://mlsanity.com/paper/2410.18424/) (2024)
- [Learning Structural Causal Models from Ordering: Identifiable Flow Models](https://mlsanity.com/paper/2412.09843/) (2024)
- [ACTIVA: Amortized Causal Effect Estimation via Transformer-based Variational Autoencoder](https://mlsanity.com/paper/2503.01290/) (2025)
- [Causal Process Models: Reframing Dynamic Causal Graph Discovery as a Reinforcement Learning Problem](https://mlsanity.com/paper/2507.13920/) (2025)
- [Causal Graph Neural Networks for Healthcare](https://mlsanity.com/paper/2511.02531/) (2025)

## 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.