# Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration

arXiv: https://arxiv.org/abs/2109.14285 · HTML: https://mlsanity.com/paper/2109.14285/

## Key facts

- Cited by 92 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 29 Sep 2021.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting](https://mlsanity.com/paper/1802.07007/) (2018)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Trusted Multi-View Classification](https://mlsanity.com/paper/2102.02051/) (2021)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Distance-Based Learning from Errors for Confidence Calibration](https://mlsanity.com/paper/1912.01730/) (2019)
- [Learning Region Features for Object Detection](https://mlsanity.com/paper/1803.07066/) (2018)

## Built on by (most cited first, 30 of 92)

- [Trusted Multi-View Classification with Dynamic Evidential Fusion](https://mlsanity.com/paper/2204.11423/) (2022)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Graph Foundation Models: Concepts, Opportunities and Challenges](https://mlsanity.com/paper/2310.11829/) (2023)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shift](https://mlsanity.com/paper/2201.11349/) (2022)
- [A Survey of Mix-based Data Augmentation: Taxonomy, Methods, Applications, and Explainability](https://mlsanity.com/paper/2212.10888/) (2022)
- [Learning on Graphs with Out-of-Distribution Nodes](https://mlsanity.com/paper/2308.06714/) (2023)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models](https://mlsanity.com/paper/2404.15625/) (2024)
- [A Survey of Trustworthy Graph Learning: Reliability, Explainability, and Privacy Protection](https://mlsanity.com/paper/2205.10014/) (2022)
- [As Confidence Aligns: Exploring the Effect of AI Confidence on Human Self-confidence in Human-AI Decision Making](https://mlsanity.com/paper/2501.12868/) (2025)
- [GraphSHA: Synthesizing Harder Samples for Class-Imbalanced Node Classification](https://mlsanity.com/paper/2306.09612/) (2023)
- [JuryGCN: Quantifying Jackknife Uncertainty on Graph Convolutional Networks](https://mlsanity.com/paper/2210.05959/) (2022)
- [Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approach](https://mlsanity.com/paper/2506.13083/) (2025)
- [ALEX: Towards Effective Graph Transfer Learning with Noisy Labels](https://mlsanity.com/paper/2309.14673/) (2023)
- [Deep Insights into Noisy Pseudo Labeling on Graph Data](https://mlsanity.com/paper/2310.01634/) (2023)
- [Consistent and Asymptotically Unbiased Estimation of Proper Calibration Errors](https://mlsanity.com/paper/2312.08589/) (2023)
- [Recent Advances in Reliable Deep Graph Learning: Inherent Noise, Distribution Shift, and Adversarial Attack](https://mlsanity.com/paper/2202.07114/) (2022)
- [Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Network](https://mlsanity.com/paper/2302.00873/) (2023)
- [SimCalib: Graph Neural Network Calibration based on Similarity between Nodes](https://mlsanity.com/paper/2312.11858/) (2023)
- [Conformalized Link Prediction on Graph Neural Networks](https://mlsanity.com/paper/2406.18763/) (2024)
- [Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networks](https://mlsanity.com/paper/2401.03350/) (2024)
- [Birds of a Feather Trust Together: Knowing When to Trust a Classifier via Adaptive Neighborhood Aggregation](https://mlsanity.com/paper/2211.16466/) (2022)
- [GraphCleaner: Detecting Mislabelled Samples in Popular Graph Learning Benchmarks](https://mlsanity.com/paper/2306.00015/) (2023)
- [Distribution Consistency based Self-Training for Graph Neural Networks with Sparse Labels](https://mlsanity.com/paper/2401.10394/) (2024)
- [Similarity-Navigated Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2405.14303/) (2024)
- [A Graph Is More Than Its Nodes: Towards Structured Uncertainty-Aware Learning on Graphs](https://mlsanity.com/paper/2210.15575/) (2022)

## 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.