mlsanityData to 7 Oct 2026

Learning from Counterfactual Links for Link Prediction

arXiv 2106.02172 ↗First posted 3 Jun 2021cs.LGcited by 69

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Abstract (arXiv)

Learning to predict missing links is important for many graph-based applications. Existing methods were designed to learn the association between observed graph structure and existence of link between a pair of nodes. However, the causal relationship between the two variables was largely ignored for learning to predict links on a graph. In this work, we visit this factor by asking a counterfactual question: "would the link still exist if the graph structure became different from observation?" Its answer, counterfactual links, will be able to augment the graph data for representation learning. To create these links, we employ causal models that consider the information (i.e., learned representations) of node pairs as context, global graph structural properties as treatment, and link existence as outcome. We propose a novel data augmentation-based link prediction method that creates counterfactual links and learns representations from both the observed and counterfactual links. Experiments on benchmark data show that our graph learning method achieves state-of-the-art performance on the task of link prediction.

Key facts. Cited by 69 papers in the map (data through 7 Oct 2026). Builds on 43 of its 99 references that are in the map. First posted on arXiv 3 Jun 2021.

Builds on

43 of 99 references.

References · 43

  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. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
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  10. 2020Graph Contrastive Learning with Augmentationscited by 1,203
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  12. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
31 more
  1. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  2. 2018Link Prediction Based on Graph Neural Networkscited by 829
  3. 2017Counterfactual Fairnesscited by 802
  4. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  5. 2020Contrastive Multi-View Representation Learning on Graphscited by 651
  6. 2015Cyclical Learning Rates for Training Neural Networkscited by 627
  7. 2015Estimation and Inference of Heterogeneous Treatment Effects using Random Forestscited by 597
  8. 2015LINE: Large-scale Information Network Embeddingcited by 582
  9. 2020Deep Graph Contrastive Representation Learningcited by 535
  10. 2020Graph Contrastive Learning with Adaptive Augmentationcited by 519
  11. 2016Learning Representations for Counterfactual Inferencecited by 327
  12. 2020Graph Random Neural Network for Semi-Supervised Learning on Graphscited by 213
  13. 2020Deep Structural Causal Models for Tractable Counterfactual Inferencecited by 210
  14. 2020Data Augmentation for Graph Neural Networkscited by 200
  15. 2018SimplE Embedding for Link Prediction in Knowledge Graphscited by 195
  16. 2018Hyperspherical Variational Auto-Encoderscited by 188
  17. 2017Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processescited by 156
  18. 2020Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representationscited by 154
  19. 2017A Survey on Network Embeddingcited by 142
  20. 2020Learning to Drop: Robust Graph Neural Network via Topological Denoisingcited by 127
  21. 2021Generative Causal Explanations for Graph Neural Networkscited by 124
  22. 2020A Unified View on Graph Neural Networks as Graph Signal Denoisingcited by 110
  23. 2020Counterfactual Data Augmentation using Locally Factored Dynamicscited by 93
  24. 2020Line Graph Neural Networks for Link Predictioncited by 89
  25. 2021Size-Invariant Graph Representations for Graph Classification Extrapolationscited by 82
  26. 2020Counterfactual Representation Learning with Balancing Weightscited by 45
  27. 2019Stochastic Blockmodels meet Graph Neural Networkscited by 39
  28. 2020Information Theoretic Counterfactual Learning from Missing-Not-At-Random Feedbackcited by 30
  29. 2020Should Graph Convolution Trust Neighbors? A Simple Causal Inference Methodcited by 25
  30. 2020Adversarial Counterfactual Learning and Evaluation for Recommender Systemcited by 16
  31. 2020Action Sequence Augmentation for Early Graph-based Anomaly Detectioncited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 14; 2023: 20; 2024: 19; 2025: 11; 2026: 5.

69 papers.

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  1. 2023Large Language Models on Graphs: A Comprehensive Surveycited by 190
  2. 2022Data Augmentation for Deep Graph Learning: A Surveycited by 132
  3. 2022Out-Of-Distribution Generalization on Graphs: A Surveycited by 97
  4. 2022Graph Neural Networks for Link Prediction with Subgraph Sketchingcited by 81
  5. 2022Graph Rationalization with Environment-based Augmentationscited by 70
  6. 2022Empowering Graph Representation Learning with Test-Time Graph Transformationcited by 66
  7. 2022Graph Data Augmentation for Graph Machine Learning: A Surveycited by 61
  8. 2023Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?cited by 41
  9. 2022Linkless Link Prediction via Relational Distillationcited by 39
  10. 2022Multi-task Self-supervised Graph Neural Networks Enable Stronger Task Generalizationcited by 35
  11. 2022MLPInit: Embarrassingly Simple GNN Training Acceleration with MLP Initializationcited by 31
  12. 2022Global Counterfactual Explainer for Graph Neural Networkscited by 30
38 more
  1. 2023GraphPatcher: Mitigating Degree Bias for Graph Neural Networks via Test-time Augmentationcited by 29
  2. 2023PaGE-Link: Path-based Graph Neural Network Explanation for Heterogeneous Link Predictioncited by 25
  3. 2023Towards Fair Graph Neural Networks via Graph Counterfactualcited by 23
  4. 2023Counterfactual Learning on Graphs: A Surveycited by 22
  5. 2023Data-Centric Learning from Unlabeled Graphs with Diffusion Modelcited by 19
  6. 2023Modeling Dynamic Environments with Scene Graph Memorycited by 18
  7. 2023On Strengthening and Defending Graph Reconstruction Attack with Markov Chain Approximationcited by 16
  8. 2023Semi-Supervised Graph Imbalanced Regressioncited by 14
  9. 2023Knowledge Graph Completion with Counterfactual Augmentationcited by 13
  10. 2022Collaboration-Aware Graph Convolutional Network for Recommender Systemscited by 12
  11. 2022FakeEdge: Alleviate Dataset Shift in Link Predictioncited by 12
  12. 2022Link Prediction with Non-Contrastive Learningcited by 11
  13. 2023A Topological Perspective on Demystifying GNN-Based Link Prediction Performancecited by 11
  14. 2024Optimizing Long-tailed Link Prediction in Graph Neural Networks through Structure Representation Enhancementcited by 9
  15. 2023Exploring Causal Learning through Graph Neural Networks: An In-depth Reviewcited by 8
  16. 2024Cross-Domain Graph Data Scaling: A Showcase with Diffusion Modelscited by 8
  17. 2025GiGL: Large-Scale Graph Neural Networks at Snapchatcited by 8
  18. 2024Addressing Shortcomings in Fair Graph Learning Datasets: Towards a New Benchmarkcited by 7
  19. 2024Counterfactual Data Augmentation with Denoising Diffusion for Graph Anomaly Detectioncited by 7
  20. 2023Efficient Link Prediction via GNN Layers Induced by Negative Samplingcited by 6
  21. 2023Causal Lifting and Link Predictioncited by 5
  22. 2023Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attentioncited by 5
  23. 2023CARL-G: Clustering-Accelerated Representation Learning on Graphscited by 5
  24. 2023When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlookcited by 4
  25. 2024Node Duplication Improves Cold-start Link Predictioncited by 4
  26. 2024Heterophilic Graph Neural Networks Optimization with Causal Message-passingcited by 4
  27. 2025A Survey of Link Prediction in N-ary Knowledge Graphscited by 4
  28. 2022Causally-guided Regularization of Graph Attention Improves Generalizabilitycited by 3
  29. 2024Hierarchical Position Embedding of Graphs with Landmarks and Clustering for Link Predictioncited by 3
  30. 2024Navigating Beyond Dropout: An Intriguing Solution Towards Generalizable Image Super Resolutioncited by 3
  31. 2024Test-Time Training on Graphs with Large Language Models (LLMs)cited by 3
  32. 2024Motif-Consistent Counterfactuals with Adversarial Refinement for Graph-Level Anomaly Detectioncited by 3
  33. 2024A Survey of Out-of-distribution Generalization for Graph Machine Learning from a Causal Viewcited by 3
  34. 2024Can GNNs Learn Link Heuristics? A Concise Review and Evaluation of Link Prediction Methodscited by 3
  35. 2025Causal invariant geographic network representations with feature and structural distribution shiftscited by 3
  36. 2024CEGRL-TKGR: A Causal Enhanced Graph Representation Learning Framework for Temporal Knowledge Graph Reasoningcited by 2
  37. 2025Evolving Graph Learning for Out-of-Distribution Generalization in Non-stationary Environmentscited by 2
  38. 2024Counterfactual Reasoning with Knowledge Graph Embeddingscited by 1

50 most cited of 69 All 69 (JSON)