mlsanityData to 7 Oct 2026

Uncertainty Quantification over Graph with Conformalized Graph Neural Networks

arXiv 2305.14535 ↗First posted 23 May 2023cs.LG stat.MLcited by 79

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Abstract (arXiv)

Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is significant. We propose conformalized GNN (CF-GNN), extending conformal prediction (CP) to graph-based models for guaranteed uncertainty estimates. Given an entity in the graph, CF-GNN produces a prediction set/interval that provably contains the true label with pre-defined coverage probability (e.g. 90%). We establish a permutation invariance condition that enables the validity of CP on graph data and provide an exact characterization of the test-time coverage. Moreover, besides valid coverage, it is crucial to reduce the prediction set size/interval length for practical use. We observe a key connection between non-conformity scores and network structures, which motivates us to develop a topology-aware output correction model that learns to update the prediction and produces more efficient prediction sets/intervals. Extensive experiments show that CF-GNN achieves any pre-defined target marginal coverage while significantly reducing the prediction set/interval size by up to 74% over the baselines. It also empirically achieves satisfactory conditional coverage over various raw and network features.

Key facts. Cited by 79 papers in the map (data through 7 Oct 2026). Builds on 39 of its 55 references that are in the map. First posted on arXiv 23 May 2023.

Builds on

39 of 55 references.

References · 39

  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. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  6. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  7. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  8. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  9. 2019Simplifying Graph Convolutional Networkscited by 1,470
  10. 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,274
  11. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  12. 2019Conformalized Quantile Regressioncited by 620
27 more
  1. 2020Graph Neural Networks in Recommender Systems: A Surveycited by 493
  2. 2018Accurate Uncertainties for Deep Learning Using Calibrated Regressioncited by 417
  3. 2020Classification with Valid and Adaptive Coveragecited by 390
  4. 2020Uncertainty Sets for Image Classifiers using Conformal Predictioncited by 365
  5. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
  6. 2019Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibrationcited by 359
  7. 2022Conformal prediction beyond exchangeabilitycited by 348
  8. 2021What Are Bayesian Neural Network Posteriors Really Like?cited by 307
  9. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  10. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  11. 2020Fast Differentiable Sorting and Rankingcited by 196
  12. 2020Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learningcited by 190
  13. 2022Adaptive Conformal Predictions for Time Seriescited by 155
  14. 2020Conformal Inference of Counterfactuals and Individual Treatment Effectscited by 150
  15. 2021Learning Optimal Conformal Classifierscited by 108
  16. 2020Calibration of Neural Networks using Splinescited by 97
  17. 2020Uncertainty Aware Semi-Supervised Learning on Graph Datacited by 95
  18. 2021Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibrationcited by 91
  19. 2021Graph Representation Learning in Biomedicinecited by 79
  20. 2021Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classificationcited by 79
  21. 2022Selection by Prediction with Conformal p-valuescited by 66
  22. 2021Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approachcited by 62
  23. 2021Conformal Sensitivity Analysis for Individual Treatment Effectscited by 40
  24. 2022What Makes Graph Neural Networks Miscalibrated?cited by 39
  25. 2022Distribution Free Prediction Sets for Node Classificationcited by 28
  26. 2023Conformal Prediction for Network-Assisted Regressioncited by 14
  27. 2017Conformal k-NN Anomaly Detector for Univariate Data Streamscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 36; 2025: 24; 2026: 15.

79 papers.

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  1. 2024Conformal Alignment: Knowing When to Trust Foundation Models with Guaranteescited by 50
  2. 2024Conformal prediction for multi-dimensional time series by ellipsoidal setscited by 37
  3. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  4. 2024Boosted Conformal Prediction Intervalscited by 25
  5. 2024Conformal Prediction: A Data Perspectivecited by 25
  6. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  7. 2025E-Values Expand the Scope of Conformal Predictioncited by 23
  8. 2023Transductive conformal inference with adaptive scorescited by 21
  9. 2024Uncertainty in Graph Neural Networks: A Surveycited by 20
  10. 2024Trustworthy Classification through Rank-Based Conformal Prediction Setscited by 20
  11. 2024Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibrationcited by 18
  12. 2024Robust Yet Efficient Conformal Prediction Setscited by 16
38 more
  1. 2024Safety in Graph Machine Learning: Threats and Safeguardscited by 11
  2. 2024Conformal Load Prediction with Transductive Graph Autoencoderscited by 11
  3. 2024Optimized Conformal Selection: Powerful Selective Inference After Conformity Score Optimizationcited by 11
  4. 2025Relational Conformal Prediction for Correlated Time Seriescited by 11
  5. 2025Conformal Prediction Sets for Deep Generative Models via Reduction to Conformal Regressioncited by 10
  6. 2026U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecastercited by 10
  7. 2023Conformal link prediction for false discovery rate controlcited by 9
  8. 2024TorchCP: A Python Library for Conformal Predictioncited by 9
  9. 2024Conformal Inductive Graph Neural Networkscited by 9
  10. 2024Scalable Training of Trustworthy and Energy-Efficient Predictive Graph Foundation Models for Atomistic Materials Modeling: A Case Study with HydraGNNcited by 8
  11. 2024Conformalized Interval Arithmetic with Symmetric Calibrationcited by 8
  12. 2024GraphAgent: Agentic Graph Language Assistantcited by 8
  13. 2026HealthMamba: An Uncertainty-aware Spatiotemporal Graph State Space Model for Effective and Reliable Healthcare Facility Visit Predictioncited by 8
  14. 2024Similarity-Navigated Conformal Prediction for Graph Neural Networkscited by 7
  15. 2024C-Adapter: Adapting Deep Classifiers for Efficient Conformal Prediction Setscited by 7
  16. 2024DA-MoE: Addressing Depth-Sensitivity in Graph-Level Analysis through Mixture of Expertscited by 7
  17. 2025Parametric Scaling Law of Tuning Bias in Conformal Predictioncited by 7
  18. 2025A Generic Framework for Conformal Fairnesscited by 7
  19. 2024Valid Conformal Prediction for Dynamic GNNscited by 6
  20. 2025Understanding and Mitigating Under-Confidence in GNNs from the Final Layercited by 6
  21. 2024Spatial-Aware Conformal Prediction for Trustworthy Hyperspectral Image Classificationcited by 5
  22. 2025Enhanced Route Planning with Calibrated Uncertainty Setcited by 5
  23. 2025Conformal Inference for Time Series over Graphscited by 5
  24. 2023On the Temperature of Bayesian Graph Neural Networks for Conformal Predictioncited by 4
  25. 2025Exploring the Noise Robustness of Online Conformal Predictioncited by 4
  26. 2025Robust Conformal Prediction with a Single Binary Certificatecited by 4
  27. 2024In-n-Out: Calibrating Graph Neural Networks for Link Predictioncited by 3
  28. 2024Uplift Modeling Under Limited Supervisioncited by 3
  29. 2024Uncertainty Quantification on Graph Learning: A Surveycited by 3
  30. 2024Conformal Trajectory Prediction with Multi-View Data Integration in Cooperative Drivingcited by 3
  31. 2024GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networkscited by 3
  32. 2024Conditional Prediction ROC Bands for Graph Classificationcited by 3
  33. 2024Conditional Uncertainty Quantification for Tensorized Topological Neural Networkscited by 3
  34. 2025Topology-Aware Conformal Prediction for Stream Networkscited by 3
  35. 2025HybridFlow: Quantification of Aleatoric and Epistemic Uncertainty with a Single Hybrid Modelcited by 3
  36. 2023On the Validity of Conformal Prediction for Network Data Under Non-Uniform Samplingcited by 2
  37. 2025Transductive Conformal Inference for Full Rankingcited by 2
  38. 2025Residual Reweighted Conformal Prediction for Graph Neural Networkscited by 2

50 most cited of 79 All 79 (JSON)