# Distribution Free Prediction Sets for Node Classification

arXiv: https://arxiv.org/abs/2211.14555 · HTML: https://mlsanity.com/paper/2211.14555/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 39 references that are in the map.
- First posted on arXiv 26 Nov 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Bayesian Graph Neural Networks with Adaptive Connection Sampling](https://mlsanity.com/paper/2006.04064/) (2020)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Bayesian graph convolutional neural networks via tempered MCMC](https://mlsanity.com/paper/2104.08438/) (2021)

## Built on by (most cited first, 28 of 28)

- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Split Conformal Prediction under Data Contamination](https://mlsanity.com/paper/2407.07700/) (2024)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (2024)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Conformal Inductive Graph Neural Networks](https://mlsanity.com/paper/2407.09173/) (2024)
- [TorchCP: A Python Library for Conformal Prediction](https://mlsanity.com/paper/2402.12683/) (2024)
- [Conformalized Link Prediction on Graph Neural Networks](https://mlsanity.com/paper/2406.18763/) (2024)
- [Similarity-Navigated Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2405.14303/) (2024)
- [Valid Conformal Prediction for Dynamic GNNs](https://mlsanity.com/paper/2405.19230/) (2024)
- [Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Training](https://mlsanity.com/paper/2501.02767/) (2025)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [On the Temperature of Bayesian Graph Neural Networks for Conformal Prediction](https://mlsanity.com/paper/2310.11479/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Non-exchangeable Conformal Prediction for Temporal Graph Neural Networks](https://mlsanity.com/paper/2507.02151/) (2025)
- [Residual Reweighted Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2506.07854/) (2025)
- [Conformal Prediction: A Theoretical Note and Benchmarking Transductive Node Classification in Graphs](https://mlsanity.com/paper/2409.18332/) (2024)
- [Conformalized Gaussian processes for online uncertainty quantification over graphs](https://mlsanity.com/paper/2510.06181/) (2025)
- [Conformal Prediction for Federated Graph Neural Networks with Missing Neighbor Information](https://mlsanity.com/paper/2410.14010/) (2024)
- [Graph Sparsification for Enhanced Conformal Prediction in Graph Neural Networks](https://mlsanity.com/paper/2410.21618/) (2024)
- [Conformal Unlearning: A New Paradigm for Unlearning in Conformal Predictors](https://mlsanity.com/paper/2508.03245/) (2025)
- [Softmax is not Enough (for Adaptive Conformal Classification)](https://mlsanity.com/paper/2602.19498/) (2026)
- [GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs](https://mlsanity.com/paper/2605.08074/) (2026)
- [Temporal Graph Prototype-conditioned Conformal Prediction for Fraud Detection](https://mlsanity.com/paper/2608.15768/) (2026)
- [Conformal Individual Treatment Effect Estimation under Networked Interference](https://mlsanity.com/paper/2609.15254/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are able to achieve high classification accuracy on many important real world datasets, but provide no rigorous notion of predictive uncertainty. Quantifying the confidence of GNN models is difficult due to the dependence between datapoints induced by the graph structure. We leverage recent advances in conformal prediction to construct prediction sets for node classification in inductive learning scenarios. We do this by taking an existing approach for conformal classification that relies on textitexchangeable data and modifying it by appropriately weighting the conformal scores to reflect the network structure. We show through experiments on standard benchmark datasets using popular GNN models that our approach provides tighter and better calibrated prediction sets than a naive application of conformal prediction.