mlsanityData to 7 Oct 2026

Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration

arXiv 2109.14285 ↗First posted 29 Sep 2021cs.LG cs.AIcited by 91

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Abstract (arXiv)

Despite Graph Neural Networks (GNNs) have achieved remarkable accuracy, whether the results are trustworthy is still unexplored. Previous studies suggest that many modern neural networks are over-confident on the predictions, however, surprisingly, we discover that GNNs are primarily in the opposite direction, i.e., GNNs are under-confident. Therefore, the confidence calibration for GNNs is highly desired. In this paper, we propose a novel trustworthy GNN model by designing a topology-aware post-hoc calibration function. Specifically, we first verify that the confidence distribution in a graph has homophily property, and this finding inspires us to design a calibration GNN model (CaGCN) to learn the calibration function. CaGCN is able to obtain a unique transformation from logits of GNNs to the calibrated confidence for each node, meanwhile, such transformation is able to preserve the order between classes, satisfying the accuracy-preserving property. Moreover, we apply the calibration GNN to self-training framework, showing that more trustworthy pseudo labels can be obtained with the calibrated confidence and further improve the performance. Extensive experiments demonstrate the effectiveness of our proposed model in terms of both calibration and accuracy.

Key facts. Cited by 91 papers in the map (data through 7 Oct 2026). Builds on 31 of its 48 references that are in the map. First posted on arXiv 29 Sep 2021.

Builds on

31 of 48 references.

References · 31

  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. 2017On Calibration of Modern Neural Networkscited by 4,860
  5. 2018How Powerful are Graph Neural Networks?cited by 4,355
  6. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  7. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  8. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  9. 2016Concrete Problems in AI Safetycited by 1,582
  10. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  11. 2019Simplifying Graph Convolutional Networkscited by 1,470
  12. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
19 more
  1. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  2. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  3. 2018Link Prediction Based on Graph Neural Networkscited by 829
  4. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  5. 2019Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibrationcited by 359
  6. 2017Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Rankingcited by 332
  7. 2021In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learningcited by 301
  8. 2019A Fair Comparison of Graph Neural Networks for Graph Classificationcited by 244
  9. 2020Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learningcited by 190
  10. 2020Design Space for Graph Neural Networkscited by 182
  11. 2018Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecastingcited by 145
  12. 2020AM-GCN: Adaptive Multi-channel Graph Convolutional Networkscited by 121
  13. 2019Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labelscited by 111
  14. 2020Uncertainty Aware Semi-Supervised Learning on Graph Datacited by 95
  15. 2021Trusted Multi-View Classificationcited by 94
  16. 2020Intra Order-preserving Functions for Calibration of Multi-Class Neural Networkscited by 65
  17. 2019Distance-Based Learning from Errors for Confidence Calibrationcited by 23
  18. 2018Learning Region Features for Object Detectioncited by 15
  19. 2019Are Graph Neural Networks Miscalibrated?cited by 14

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 15; 2023: 24; 2024: 24; 2025: 16; 2026: 12.

91 papers.

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  1. 2022Trusted Multi-View Classification with Dynamic Evidential Fusioncited by 167
  2. 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
  3. 2023Graph Foundation Models: Concepts, Opportunities and Challengescited by 101
  4. 2022Trustworthy Graph Neural Networks: Aspects, Methods and Trendscited by 88
  5. 2023Uncertainty Quantification over Graph with Conformalized Graph Neural Networkscited by 79
  6. 2022Better Uncertainty Calibration via Proper Scores for Classification and Beyondcited by 65
  7. 2022What Makes Graph Neural Networks Miscalibrated?cited by 39
  8. 2022Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shiftcited by 38
  9. 2022A Survey of Mix-based Data Augmentation: Taxonomy, Methods, Applications, and Explainabilitycited by 30
  10. 2023Learning on Graphs with Out-of-Distribution Nodescited by 29
  11. 2024Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Modelscited by 21
  12. 2022A Survey of Trustworthy Graph Learning: Reliability, Explainability, and Privacy Protectioncited by 20
38 more
  1. 2024Uncertainty in Graph Neural Networks: A Surveycited by 20
  2. 2025As Confidence Aligns: Exploring the Effect of AI Confidence on Human Self-confidence in Human-AI Decision Makingcited by 18
  3. 2023GraphSHA: Synthesizing Harder Samples for Class-Imbalanced Node Classificationcited by 17
  4. 2022JuryGCN: Quantifying Jackknife Uncertainty on Graph Convolutional Networkscited by 14
  5. 2025Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approachcited by 14
  6. 2023ALEX: Towards Effective Graph Transfer Learning with Noisy Labelscited by 11
  7. 2023Deep Insights into Noisy Pseudo Labeling on Graph Datacited by 11
  8. 2022Recent Advances in Reliable Deep Graph Learning: Inherent Noise, Distribution Shift, and Adversarial Attackcited by 10
  9. 2023Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Networkcited by 10
  10. 2023Consistent and Asymptotically Unbiased Estimation of Proper Calibration Errorscited by 10
  11. 2023SimCalib: Graph Neural Network Calibration based on Similarity between Nodescited by 10
  12. 2024Conformalized Link Prediction on Graph Neural Networkscited by 9
  13. 2024Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networkscited by 8
  14. 2022Birds of a Feather Trust Together: Knowing When to Trust a Classifier via Adaptive Neighborhood Aggregationcited by 7
  15. 2023GraphCleaner: Detecting Mislabelled Samples in Popular Graph Learning Benchmarkscited by 7
  16. 2024Distribution Consistency based Self-Training for Graph Neural Networks with Sparse Labelscited by 7
  17. 2024Similarity-Navigated Conformal Prediction for Graph Neural Networkscited by 7
  18. 2022A Graph Is More Than Its Nodes: Towards Structured Uncertainty-Aware Learning on Graphscited by 6
  19. 2023Towards Reliable Rare Category Analysis on Graphs via Individual Calibrationcited by 6
  20. 2024Understanding the Effects of Miscalibrated AI Confidence on User Trust, Reliance, and Decision Efficacycited by 6
  21. 2024Mitigating Label Noise on Graph via Topological Sample Selectioncited by 6
  22. 2024Minimum Topology Attacks for Graph Neural Networkscited by 6
  23. 2024AdapTable: Test-Time Adaptation for Tabular Data via Shift-Aware Uncertainty Calibrator and Label Distribution Handlercited by 6
  24. 2025Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Trainingcited by 6
  25. 2025Understanding and Mitigating Under-Confidence in GNNs from the Final Layercited by 6
  26. 2023Open-World Lifelong Graph Learningcited by 5
  27. 2023Mutually-paced Knowledge Distillation for Cross-lingual Temporal Knowledge Graph Reasoningcited by 4
  28. 2023Rethinking the Trigger-injecting Position in Graph Backdoor Attackcited by 4
  29. 2023A Hybrid of Generative and Discriminative Models Based on the Gaussian-coupled Softmax Layercited by 4
  30. 2023Making Binary Classification from Multiple Unlabeled Datasets Almost Free of Supervisioncited by 4
  31. 2023On the Temperature of Bayesian Graph Neural Networks for Conformal Predictioncited by 4
  32. 2023Improvements on Uncertainty Quantification for Node Classification via Distance-Based Regularizationcited by 4
  33. 2023Diffence: Fencing Membership Privacy With Diffusion Modelscited by 4
  34. 2024Cross-Space Adaptive Filter: Integrating Graph Topology and Node Attributes for Alleviating the Over-smoothing Problemcited by 4
  35. 2025Uncertainty-Aware Graph Structure Learningcited by 4
  36. 2024In-n-Out: Calibrating Graph Neural Networks for Link Predictioncited by 3
  37. 2024Uncertainty Quantification on Graph Learning: A Surveycited by 3
  38. 2024Optimizing Estimators of Squared Calibration Errors in Classificationcited by 3

50 most cited of 91 All 91 (JSON)