mlsanityData to 7 Oct 2026

Handling Distribution Shifts on Graphs: An Invariance Perspective

arXiv 2202.02466 ↗First posted 5 Feb 2022cs.LG cs.AIcited by 163

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Abstract (arXiv)

There is increasing evidence suggesting neural networks' sensitivity to distribution shifts, so that research on out-of-distribution (OOD) generalization comes into the spotlight. Nonetheless, current endeavors mostly focus on Euclidean data, and its formulation for graph-structured data is not clear and remains under-explored, given two-fold fundamental challenges: 1) the inter-connection among nodes in one graph, which induces non-IID generation of data points even under the same environment, and 2) the structural information in the input graph, which is also informative for prediction. In this paper, we formulate the OOD problem on graphs and develop a new invariant learning approach, Explore-to-Extrapolate Risk Minimization (EERM), that facilitates graph neural networks to leverage invariance principles for prediction. EERM resorts to multiple context explorers (specified as graph structure editers in our case) that are adversarially trained to maximize the variance of risks from multiple virtual environments. Such a design enables the model to extrapolate from a single observed environment which is the common case for node-level prediction. We prove the validity of our method by theoretically showing its guarantee of a valid OOD solution and further demonstrate its power on various real-world datasets for handling distribution shifts from artificial spurious features, cross-domain transfers and dynamic graph evolution.

Key facts. Cited by 163 papers in the map (data through 7 Oct 2026). Builds on 54 of its 71 references that are in the map. First posted on arXiv 5 Feb 2022.

Builds on

54 of 71 references.

References · 54

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  5. 2019Invariant Risk Minimizationcited by 1,832
  6. 2019Do ImageNet Classifiers Generalize to ImageNet?cited by 1,507
  7. 2019Simplifying Graph Convolutional Networkscited by 1,470
  8. 2019Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalizationcited by 1,232
  9. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  10. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  11. 2020Simple and Deep Graph Convolutional Networkscited by 857
  12. 2020Out-of-Distribution Generalization via Risk Extrapolation (REx)cited by 737
38 more
  1. 2018Recognition in Terra Incognitacited by 655
  2. 2013Domain Generalization via Invariant Feature Representationcited by 622
  3. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  4. 2017One pixel attack for fooling deep neural networkscited by 579
  5. 2019Multi-scale Attributed Node Embeddingcited by 543
  6. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 533
  7. 2019EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphscited by 443
  8. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 368
  9. 2017Fairness in Criminal Justice Risk Assessments: The State of the Artcited by 315
  10. 2020Environment Inference for Invariant Learningcited by 306
  11. 2020The Risks of Invariant Risk Minimizationcited by 262
  12. 2020Domain Generalization using Causal Matchingcited by 224
  13. 2020How Neural Networks Extrapolate: From Feedforward to Graph Neural Networkscited by 218
  14. 2020Generalization and Representational Limits of Graph Neural Networkscited by 217
  15. 2020Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddingscited by 212
  16. 2019Topology Attack and Defense for Graph Neural Networks: An Optimization Perspectivecited by 196
  17. 2020Invariant Risk Minimization Gamescited by 188
  18. 2020Understanding the Failure Modes of Out-of-Distribution Generalizationcited by 146
  19. 2020Invariant Rationalizationcited by 131
  20. 2018Invariance, Causality and Robustnesscited by 123
  21. 2018Dark Model Adaptation: Semantic Image Segmentation from Daytime to Nighttimecited by 122
  22. 2020From Local Structures to Size Generalization in Graph Neural Networkscited by 119
  23. 2021A Unified Lottery Ticket Hypothesis for Graph Neural Networkscited by 118
  24. 2021Does Invariant Risk Minimization Capture Invariance?cited by 116
  25. 2021Heterogeneous Risk Minimizationcited by 90
  26. 2018Bayesian graph convolutional neural networks for semi-supervised classificationcited by 88
  27. 2021Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Datacited by 86
  28. 2021Size-Invariant Graph Representations for Graph Classification Extrapolationscited by 82
  29. 2019Stability and Generalization of Graph Convolutional Neural Networkscited by 81
  30. 2020Bayesian Graph Neural Networks with Adaptive Connection Samplingcited by 81
  31. 2021New Benchmarks for Learning on Non-Homophilous Graphscited by 81
  32. 2021Can Subnetwork Structure be the Key to Out-of-Distribution Generalization?cited by 75
  33. 2021Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalizationcited by 70
  34. 2021Subgroup Generalization and Fairness of Graph Neural Networkscited by 69
  35. 2020Towards Recognizing Unseen Categories in Unseen Domainscited by 56
  36. 2020When is invariance useful in an Out-of-Distribution Generalization problem ?cited by 52
  37. 2020Graph Policy Network for Transferable Active Learning on Graphscited by 49
  38. 2020Learning to Extrapolate Knowledge: Transductive Few-shot Out-of-Graph Link Predictioncited by 46

50 most cited of 54 All 54 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 18; 2023: 37; 2024: 63; 2025: 27; 2026: 18.

163 papers.

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  1. 2022Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphscited by 144
  2. 2022GOOD: A Graph Out-of-Distribution Benchmarkcited by 140
  3. 2023SGFormer: Simplifying and Empowering Transformers for Large-Graph Representationscited by 131
  4. 2022Out-Of-Distribution Generalization on Graphs: A Surveycited by 97
  5. 2023DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusioncited by 85
  6. 2022Debiasing Graph Neural Networks via Learning Disentangled Causal Substructurecited by 83
  7. 2024OpenGraph: Towards Open Graph Foundation Modelscited by 75
  8. 2023Energy-based Out-of-Distribution Detection for Graph Neural Networkscited by 67
  9. 2022Empowering Graph Representation Learning with Test-Time Graph Transformationcited by 66
  10. 2024A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensationcited by 57
  11. 2024A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challengescited by 54
  12. 2023Structural Re-weighting Improves Graph Domain Adaptationcited by 45
38 more
  1. 2023Does Invariant Graph Learning via Environment Augmentation Learn Invariance?cited by 42
  2. 2023Towards Understanding the Generalization of Graph Neural Networkscited by 41
  3. 2023Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?cited by 41
  4. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  5. 2022Unleashing the Power of Graph Data Augmentation on Covariate Distribution Shiftcited by 38
  6. 2023Mind the Label Shift of Augmentation-based Graph OOD Generalizationcited by 34
  7. 2024Graph Out-of-Distribution Generalization via Causal Interventioncited by 30
  8. 2023Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalizationcited by 29
  9. 2023GraphPatcher: Mitigating Degree Bias for Graph Neural Networks via Test-time Augmentationcited by 29
  10. 2023Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalizationcited by 26
  11. 2024Pairwise Alignment Improves Graph Domain Adaptationcited by 25
  12. 2022Geometric Knowledge Distillation: Topology Compression for Graph Neural Networkscited by 22
  13. 2024Graph Domain Adaptation with Dual-branch Encoder and Two-level Alignment for Whole Slide Image-based Survival Predictioncited by 20
  14. 2023GraphMETRO: Mitigating Complex Graph Distribution Shifts via Mixture of Aligned Expertscited by 19
  15. 2024Spectral Invariant Learning for Dynamic Graphs under Distribution Shiftscited by 18
  16. 2023GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labelscited by 17
  17. 2024Subgraph Pooling: Tackling Negative Transfer on Graphscited by 17
  18. 2024Graph Learning under Distribution Shifts: A Comprehensive Survey on Domain Adaptation, Out-of-distribution, and Continual Learningcited by 17
  19. 2024A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptationcited by 16
  20. 2023Individual and Structural Graph Information Bottlenecks for Out-of-Distribution Generalizationcited by 15
  21. 2023Explaining and Adapting Graph Conditional Shiftcited by 14
  22. 2024Empowering Graph Invariance Learning with Deep Spurious Infomaxcited by 14
  23. 2022Towards OOD Detection in Graph Classification from Uncertainty Estimation Perspectivecited by 13
  24. 2023Causality and Independence Enhancement for Biased Node Classificationcited by 13
  25. 2024Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directionscited by 13
  26. 2024Investigating Out-of-Distribution Generalization of GNNs: An Architecture Perspectivecited by 13
  27. 2024How Interpretable Are Interpretable Graph Neural Networks?cited by 13
  28. 2022FakeEdge: Alleviate Dataset Shift in Link Predictioncited by 12
  29. 2023GraphGLOW: Universal and Generalizable Structure Learning for Graph Neural Networkscited by 12
  30. 2024Online GNN Evaluation Under Test-time Graph Distribution Shiftscited by 12
  31. 2022Adversarial Camouflage for Node Injection Attack on Graphscited by 11
  32. 2023Improving Generalizability of Graph Anomaly Detection Models via Data Augmentationcited by 11
  33. 2023Contrastive Meta-Learning for Few-shot Node Classificationcited by 11
  34. 2024Safety in Graph Machine Learning: Threats and Safeguardscited by 11
  35. 2024Graph Representation Learning via Causal Diffusion for Out-of-Distribution Recommendationcited by 11
  36. 2022Towards Out-of-Distribution Sequential Event Prediction: A Causal Treatmentcited by 10
  37. 2023Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Networkcited by 10
  38. 2023Graph Structure and Feature Extrapolation for Out-of-Distribution Generalizationcited by 10

50 most cited of 163 All 163 (JSON)