# Graph Out-of-Distribution Generalization with Controllable Data Augmentation

arXiv: https://arxiv.org/abs/2308.08344 · HTML: https://mlsanity.com/paper/2308.08344/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 54 references that are in the map.
- First posted on arXiv 16 Aug 2023.

## Builds on (most cited first, 30 of 39)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [How Does Mixup Help With Robustness and Generalization?](https://mlsanity.com/paper/2010.04819/) (2020)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [C2AE: Class Conditioned Auto-Encoder for Open-set Recognition](https://mlsanity.com/paper/1904.01198/) (2019)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networks](https://mlsanity.com/paper/2111.06283/) (2021)
- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Factorizable Graph Convolutional Networks](https://mlsanity.com/paper/2010.05421/) (2020)
- [OOD-GNN: Out-of-Distribution Generalized Graph Neural Network](https://mlsanity.com/paper/2112.03806/) (2021)
- [Robust Optimization as Data Augmentation for Large-scale Graphs](https://mlsanity.com/paper/2010.09891/) (2020)
- [Optimal Representations for Covariate Shift](https://mlsanity.com/paper/2201.00057/) (2021)
- [On the Generalization Effects of Linear Transformations in Data Augmentation](https://mlsanity.com/paper/2005.00695/) (2020)

## Built on by (most cited first, 9 of 9)

- [GraphMETRO: Mitigating Complex Graph Distribution Shifts via Mixture of Aligned Experts](https://mlsanity.com/paper/2312.04693/) (2023)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Temporal Generalization Estimation in Evolving Graphs](https://mlsanity.com/paper/2404.04969/) (2024)
- [Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2507.07621/) (2025)
- [Exploring Graph-Transformer Out-of-Distribution Generalization Abilities](https://mlsanity.com/paper/2506.20575/) (2025)
- [Constraint Multi-class Positive and Unlabeled Learning for Distantly Supervised Named Entity Recognition](https://mlsanity.com/paper/2504.04963/) (2025)
- [Out-of-Distribution Graph Models Merging](https://mlsanity.com/paper/2506.03674/) (2025)
- [SLASH the Sink: Sharpening Structural Attention Inside LLMs](https://mlsanity.com/paper/2605.10503/) (2026)
- [Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspective](https://mlsanity.com/paper/2605.13597/) (2026)

## Abstract (arXiv)

Graph Neural Network (GNN) has demonstrated extraordinary performance in classifying graph properties. However, due to the selection bias of training and testing data (e.g., training on small graphs and testing on large graphs, or training on dense graphs and testing on sparse graphs), distribution deviation is widespread. More importantly, we often observe hybrid structure distribution shift of both scale and density, despite of one-sided biased data partition. The spurious correlations over hybrid distribution deviation degrade the performance of previous GNN methods and show large instability among different datasets. To alleviate this problem, we propose textttOOD-GMixup to jointly manipulate the training distribution with controllable data augmentation in metric space. Specifically, we first extract the graph rationales to eliminate the spurious correlations due to irrelevant information. Secondly, we generate virtual samples with perturbation on graph rationale representation domain to obtain potential OOD training samples. Finally, we propose OOD calibration to measure the distribution deviation of virtual samples by leveraging Extreme Value Theory, and further actively control the training distribution by emphasizing the impact of virtual OOD samples. Extensive studies on several real-world datasets on graph classification demonstrate the superiority of our proposed method over state-of-the-art baselines.