mlsanityData to 7 Oct 2026

Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification

arXiv 2110.14012 ↗First posted 26 Oct 2021stat.ML cs.LGcited by 79

Not on the map. Why?

Abstract (arXiv)

The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent node-level predictions is under-explored. In this work, we explore uncertainty quantification for node classification in three ways: (1) We derive three axioms explicitly characterizing the expected predictive uncertainty behavior in homophilic attributed graphs. (2) We propose a new model Graph Posterior Network (GPN) which explicitly performs Bayesian posterior updates for predictions on interdependent nodes. GPN provably obeys the proposed axioms. (3) We extensively evaluate GPN and a strong set of baselines on semi-supervised node classification including detection of anomalous features, and detection of left-out classes. GPN outperforms existing approaches for uncertainty estimation in the experiments.

Key facts. Cited by 79 papers in the map (data through 7 Oct 2026). Builds on 73 of its 116 references that are in the map. First posted on arXiv 26 Oct 2021.

Builds on

73 of 116 references.

References · 73

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  4. 2017Graph Attention Networkscited by 8,854
  5. 2017On Calibration of Modern Neural Networkscited by 4,860
  6. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  7. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  8. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  9. 2015Variational Inference with Normalizing Flowscited by 2,161
  10. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  11. 2017Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networkscited by 1,325
  12. 2020Energy-based Out-of-distribution Detectioncited by 1,296
38 more
  1. 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,274
  2. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  3. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  4. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  5. 2018Evidential Deep Learning to Quantify Classification Uncertaintycited by 728
  6. 2015Image-based Recommendations on Styles and Substitutescited by 702
  7. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  8. 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 583
  9. 2018Predictive Uncertainty Estimation via Prior Networkscited by 555
  10. 2019A Simple Baseline for Bayesian Uncertainty in Deep Learningcited by 555
  11. 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 542
  12. 2018Do Deep Generative Models Know What They Don't Know?cited by 443
  13. 2019Diffusion Improves Graph Learningcited by 414
  14. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 402
  15. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 395
  16. 2020Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awarenesscited by 389
  17. 2020BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learningcited by 368
  18. 2019Deep Evidential Regressioncited by 354
  19. 2017Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Rankingcited by 332
  20. 2018Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problemcited by 323
  21. 2019Adversarial Attacks on Graph Neural Networks via Meta Learningcited by 261
  22. 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 253
  23. 2020Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networkscited by 227
  24. 2020Why Normalizing Flows Fail to Detect Out-of-Distribution Datacited by 220
  25. 2020Combining Label Propagation and Simple Models Out-performs Graph Neural Networkscited by 199
  26. 2020Contrastive Training for Improved Out-of-Distribution Detectioncited by 186
  27. 2020Training independent subnetworks for robust predictioncited by 177
  28. 2020Efficient and Scalable Bayesian Neural Nets with Rank-1 Factorscited by 171
  29. 2020Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Countscited by 163
  30. 2019Ensemble Distribution Distillationcited by 158
  31. 2020Hyperparameter Ensembles for Robustness and Uncertainty Quantificationcited by 149
  32. 2019Uncertainty-based Continual Learning with Adaptive Regularizationcited by 144
  33. 2019Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustnesscited by 104
  34. 2020Unifying Graph Convolutional Neural Networks and Label Propagationcited by 98
  35. 2020Uncertainty Aware Semi-Supervised Learning on Graph Datacited by 95
  36. 2018Bayesian graph convolutional neural networks for semi-supervised classificationcited by 88
  37. 2020Bayesian Graph Neural Networks with Adaptive Connection Samplingcited by 81
  38. 2016Hiding Individuals and Communities in a Social Networkcited by 77

50 most cited of 73 All 73 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 9; 2023: 16; 2024: 18; 2025: 25; 2026: 11.

79 papers.

Sort:

By area:

  1. 2023Uncertainty Quantification over Graph with Conformalized Graph Neural Networkscited by 79
  2. 2023Energy-based Out-of-Distribution Detection for Graph Neural Networkscited by 67
  3. 2024A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challengescited by 54
  4. 2022GOOD-D: On Unsupervised Graph Out-Of-Distribution Detectioncited by 47
  5. 2022What Makes Graph Neural Networks Miscalibrated?cited by 39
  6. 2023Class-Imbalanced Graph Learning without Class Rebalancingcited by 29
  7. 2022Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learningcited by 27
  8. 2024Uncertainty in Graph Neural Networks: A Surveycited by 20
  9. 2023Random-Set Neural Networks (RS-NN)cited by 19
  10. 2023AMIGO: Sparse Multi-Modal Graph Transformer with Shared-Context Processing for Representation Learning of Giga-pixel Imagescited by 18
  11. 2023Calibrating Multimodal Learningcited by 17
  12. 2024GOODAT: Towards Test-time Graph Out-of-Distribution Detectioncited by 17
38 more
  1. 2024Graph Learning under Distribution Shifts: A Comprehensive Survey on Domain Adaptation, Out-of-distribution, and Continual Learningcited by 17
  2. 2025GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generationcited by 15
  3. 2022JuryGCN: Quantifying Jackknife Uncertainty on Graph Convolutional Networkscited by 14
  4. 2022You Can Have Better Graph Neural Networks by Not Training Weights at All: Finding Untrained GNNs Ticketscited by 14
  5. 2025Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approachcited by 14
  6. 2022Towards OOD Detection in Graph Classification from Uncertainty Estimation Perspectivecited by 13
  7. 2022Graph Neural Networks in Particle Physics: Implementations, Innovations, and Challengescited by 12
  8. 2022Robust Node Classification on Graphs: Jointly from Bayesian Label Transition and Topology-based Label Propagationcited by 12
  9. 2023Uncertainty Estimation for Molecules: Desiderata and Methodscited by 11
  10. 2024Uncertainty for Active Learning on Graphscited by 11
  11. 2023Uncertainty Estimation on Sequential Labeling via Uncertainty Transmissioncited by 10
  12. 2024Conformal Inductive Graph Neural Networkscited by 9
  13. 2025Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphscited by 9
  14. 2024Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equationscited by 8
  15. 2025Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'cited by 8
  16. 2025Position: Epistemic uncertainty estimation methods are fundamentally incompletecited by 8
  17. 2023Evaluating Robustness and Uncertainty of Graph Models Under Structural Distributional Shiftscited by 7
  18. 2023Training, Architecture, and Prior for Deterministic Uncertainty Methodscited by 7
  19. 2024Multitask Active Learning for Graph Anomaly Detectioncited by 7
  20. 2025Prior2Former -- Evidential Modeling of Mask Transformers for Assumption-Free Open-World Panoptic Segmentationcited by 7
  21. 2022A Graph Is More Than Its Nodes: Towards Structured Uncertainty-Aware Learning on Graphscited by 6
  22. 2025Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Trainingcited by 6
  23. 2025Bounded and Uniform Energy-based Out-of-distribution Detection for Graphscited by 6
  24. 2025Understanding and Mitigating Under-Confidence in GNNs from the Final Layercited by 6
  25. 2023Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attentioncited by 5
  26. 2023dugMatting: Decomposed-Uncertainty-Guided Mattingcited by 4
  27. 2023On the Temperature of Bayesian Graph Neural Networks for Conformal Predictioncited by 4
  28. 2023Improvements on Uncertainty Quantification for Node Classification via Distance-Based Regularizationcited by 4
  29. 2024RSEA-MVGNN: Multi-View Graph Neural Network with Reliable Structural Enhancement and Aggregationcited by 4
  30. 2025Uncertainty-Aware Graph Structure Learningcited by 4
  31. 2024Uplift Modeling Under Limited Supervisioncited by 3
  32. 2024Uncertainty Quantification on Graph Learning: A Surveycited by 3
  33. 2025Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networkscited by 3
  34. 2026Random-Set Graph Neural Networkscited by 3
  35. 2023Uncertainty Propagation in Node Classificationcited by 2
  36. 2024Predictive Uncertainty Quantification for Bird's Eye View Segmentation: A Benchmark and Novel Loss Functioncited by 2
  37. 2024Linear Opinion Pooling for Uncertainty Quantification on Graphscited by 2
  38. 2024Learning Divergence Fields for Shift-Robust Graph Representationscited by 2

50 most cited of 79 All 79 (JSON)