Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration
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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
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2017Graph Attention Networkscited by 8,854
- 2017Inductive Representation Learning on Large Graphscited by 6,284
- 2017On Calibration of Modern Neural Networkscited by 4,860
- 2018How Powerful are Graph Neural Networks?cited by 4,355
- 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
- 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
- 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
- 2016Concrete Problems in AI Safetycited by 1,582
- 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
- 2019Simplifying Graph Convolutional Networkscited by 1,470
- 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
19 more
- 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
- 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
- 2018Link Prediction Based on Graph Neural Networkscited by 829
- 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
- 2019Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibrationcited by 359
- 2017Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Rankingcited by 332
- 2021In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learningcited by 301
- 2019A Fair Comparison of Graph Neural Networks for Graph Classificationcited by 244
- 2020Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learningcited by 190
- 2020Design Space for Graph Neural Networkscited by 182
- 2018Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecastingcited by 145
- 2020AM-GCN: Adaptive Multi-channel Graph Convolutional Networkscited by 121
- 2019Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labelscited by 111
- 2020Uncertainty Aware Semi-Supervised Learning on Graph Datacited by 95
- 2021Trusted Multi-View Classificationcited by 94
- 2020Intra Order-preserving Functions for Calibration of Multi-Class Neural Networkscited by 65
- 2019Distance-Based Learning from Errors for Confidence Calibrationcited by 23
- 2018Learning Region Features for Object Detectioncited by 15
- 2019Are Graph Neural Networks Miscalibrated?cited by 14
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Citing papers per year: 2022: 15; 2023: 24; 2024: 24; 2025: 16; 2026: 12.
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- 2026HyGRAIL: Cost-Aware and Evidence-Grounded Scientific Hypothesis Discovery over Knowledge Graphs2 Sep 2026
- 2026HeAD-CP: Heterophily-Aware Diffused Conformal Prediction Sets for Graph Neural Networks28 Jul 2026
- 2026When does distribution shift break graph neural networks calibration?12 Jul 2026
- 2026The Confidence Trap: Calibration Attacks for Graph Neural Networks7 Jun 2026
- 2026Random-Set Graph Neural Networks12 May 2026
- 2026GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs8 May 2026
- 2026Model-to-Data Distillation for Graph Neural Networks7 May 2026
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