# Improving Graph Out-of-distribution Generalization Beyond Causality

arXiv: https://arxiv.org/abs/2407.10204 · HTML: https://mlsanity.com/paper/2407.10204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 14 Jul 2024.

## Builds on (most cited first, 30 of 31)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [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)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Correct-N-Contrast: A Contrastive Approach for Improving Robustness to Spurious Correlations](https://mlsanity.com/paper/2203.01517/) (2022)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Learning on Large-scale Text-attributed Graphs via Variational Inference](https://mlsanity.com/paper/2210.14709/) (2022)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Generalizing Graph Neural Networks on Out-Of-Distribution Graphs](https://mlsanity.com/paper/2111.10657/) (2021)
- [Generalized Variational Inference: Three arguments for deriving new Posteriors](https://mlsanity.com/paper/1904.02063/) (2019)
- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [Unleashing the Power of Graph Data Augmentation on Covariate Distribution Shift](https://mlsanity.com/paper/2211.02843/) (2022)
- [Mind the Label Shift of Augmentation-based Graph OOD Generalization](https://mlsanity.com/paper/2303.14859/) (2023)
- [Graph Out-of-Distribution Generalization via Causal Intervention](https://mlsanity.com/paper/2402.11494/) (2024)
- [Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.01103/) (2023)
- [Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2311.11114/) (2023)
- [Learning Invariant Molecular Representation in Latent Discrete Space](https://mlsanity.com/paper/2310.14170/) (2023)
- [Graph Invariant Learning with Subgraph Co-mixup for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2312.10988/) (2023)
- [Individual and Structural Graph Information Bottlenecks for Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.15902/) (2023)
- [Empowering Graph Invariance Learning with Deep Spurious Infomax](https://mlsanity.com/paper/2407.11083/) (2024)

## Built on by (most cited first, 1 of 1)

- [Unifying Graph Neural Networks Through a Common Layer Equation](https://mlsanity.com/paper/2608.16097/) (2026)

## Abstract (arXiv)

Existing methods for graph out-of-distribution (OOD) generalization primarily rely on empirical studies on synthetic datasets. Such approaches tend to overemphasize the causal relationships between invariant sub-graphs and labels, thereby neglecting the non-negligible role of environment in real-world scenarios. In contrast to previous studies that impose rigid independence assumptions on environments and invariant sub-graphs, this paper presents the theorems of environment-label dependency and mutable rationale invariance, where the former characterizes the usefulness of environments in determining graph labels while the latter refers to the mutable importance of graph rationales. Based on analytic investigations, a novel variational inference based method named ``Probability Dependency on Environments and Rationales for OOD Graphs on Real-world Data'' (DEROG) is introduced. To alleviate the adverse effect of unknown prior knowledge on environments and rationales, DEROG utilizes generalized Bayesian inference. Further, DEROG employs an EM-based algorithm for optimization. Finally, extensive experiments on real-world datasets under different distribution shifts are conducted to show the superiority of DEROG. Our code is publicly available at https://github.com/LEOXC1571/DEROG.