# Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization

arXiv: https://arxiv.org/abs/2306.01103 · HTML: https://mlsanity.com/paper/2306.01103/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 96 of its 125 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 30 of 96)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)

## Built on by (most cited first, 29 of 29)

- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [Pairwise Alignment Improves Graph Domain Adaptation](https://mlsanity.com/paper/2403.01092/) (2024)
- [Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency](https://mlsanity.com/paper/2406.07598/) (2024)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNs](https://mlsanity.com/paper/2406.15156/) (2024)
- [How Interpretable Are Interpretable Graph Neural Networks?](https://mlsanity.com/paper/2406.07955/) (2024)
- [Is the MMI Criterion Necessary for Interpretability? Degenerating Non-causal Features to Plain Noise for Self-Rationalization](https://mlsanity.com/paper/2410.06003/) (2024)
- [Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective](https://mlsanity.com/paper/2502.02719/) (2025)
- [Graph Structure and Feature Extrapolation for Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.08076/) (2023)
- [Identifying Semantic Component for Robust Molecular Property Prediction](https://mlsanity.com/paper/2311.04837/) (2023)
- [Out-of-Distribution Learning with Human Feedback](https://mlsanity.com/paper/2408.07772/) (2024)
- [Breaking Free from MMI: A New Frontier in Rationalization by Probing Input Utilization](https://mlsanity.com/paper/2503.06202/) (2025)
- [Adversarial Cooperative Rationalization: The Risk of Spurious Correlations in Even Clean Datasets](https://mlsanity.com/paper/2505.02118/) (2025)
- [Spatio-Temporal Fluid Dynamics Modeling via Physical-Awareness and Parameter Diffusion Guidance](https://mlsanity.com/paper/2403.13850/) (2024)
- [When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlook](https://mlsanity.com/paper/2312.12477/) (2023)
- [Measure-Theoretic Anti-Causal Representation Learning](https://mlsanity.com/paper/2510.18052/) (2025)
- [A Survey of Out-of-distribution Generalization for Graph Machine Learning from a Causal View](https://mlsanity.com/paper/2409.09858/) (2024)
- [Virtual Nodes Can Help: Tackling Distribution Shifts in Federated Graph Learning](https://mlsanity.com/paper/2412.19229/) (2024)
- [Pruning Spurious Subgraphs for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2506.05957/) (2025)
- [Invariant Graph Learning Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2408.01697/) (2024)
- [Quantifying Distributional Invariance in Causal Subgraph for IRM-Free Graph Generalization](https://mlsanity.com/paper/2510.20295/) (2025)
- [Evolving Graph Learning for Out-of-Distribution Generalization in Non-stationary Environments](https://mlsanity.com/paper/2511.02354/) (2025)
- [Improving Graph Out-of-distribution Generalization Beyond Causality](https://mlsanity.com/paper/2407.10204/) (2024)
- [SCL-GNN: Towards Generalizable Graph Neural Networks via Spurious Correlation Learning](https://mlsanity.com/paper/2603.08270/) (2026)
- [Structure-agnostic Causal Representation Learning](https://mlsanity.com/paper/2610.00968/) (2026)
- [Catch Causal Signals from Edges for Label Imbalance in Graph Classification](https://mlsanity.com/paper/2501.01707/) (2025)
- [Out-of-Distribution Graph Models Merging](https://mlsanity.com/paper/2506.03674/) (2025)
- [Rethinking Graph Generalization through the Lens of Sharpness-Aware Minimization](https://mlsanity.com/paper/2602.08855/) (2026)

## Abstract (arXiv)

We tackle the problem of graph out-of-distribution (OOD) generalization. Existing graph OOD algorithms either rely on restricted assumptions or fail to exploit environment information in training data. In this work, we propose to simultaneously incorporate label and environment causal independence (LECI) to fully make use of label and environment information, thereby addressing the challenges faced by prior methods on identifying causal and invariant subgraphs. We further develop an adversarial training strategy to jointly optimize these two properties for causal subgraph discovery with theoretical guarantees. Extensive experiments and analysis show that LECI significantly outperforms prior methods on both synthetic and real-world datasets, establishing LECI as a practical and effective solution for graph OOD generalization. Our code is available at https://github.com/divelab/LECI.