# Conformal Inductive Graph Neural Networks

arXiv: https://arxiv.org/abs/2407.09173 · HTML: https://mlsanity.com/paper/2407.09173/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 12 Jul 2024.

## Builds on (most cited first, 20 of 20)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [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)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Conformal Prediction Sets with Limited False Positives](https://mlsanity.com/paper/2202.07650/) (2022)
- [Distribution Free Prediction Sets for Node Classification](https://mlsanity.com/paper/2211.14555/) (2022)
- [Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures](https://mlsanity.com/paper/1312.7857/) (2013)
- [Edge-exchangeable graphs and sparsity](https://mlsanity.com/paper/1603.06898/) (2016)

## Built on by (most cited first, 10 of 10)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Robust Conformal Prediction with a Single Binary Certificate](https://mlsanity.com/paper/2503.05239/) (2025)
- [Conformal Prediction: A Theoretical Note and Benchmarking Transductive Node Classification in Graphs](https://mlsanity.com/paper/2409.18332/) (2024)
- [RoCP-GNN: Robust Conformal Prediction for Graph Neural Networks in Node-Classification](https://mlsanity.com/paper/2408.13825/) (2024)
- [Focus Where It Matters: Graph Selective State Focused Attention Networks](https://mlsanity.com/paper/2410.15849/) (2024)
- [EvA: Evolutionary Attacks on Graphs](https://mlsanity.com/paper/2507.08212/) (2025)
- [Conformal Prediction for Multi-Source Detection on a Network](https://mlsanity.com/paper/2511.08867/) (2025)
- [Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better](https://mlsanity.com/paper/2601.21455/) (2026)
- [GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs](https://mlsanity.com/paper/2605.08074/) (2026)
- [Uncertainty in Representation Learning on Knowledge Graphs](https://mlsanity.com/paper/2610.06974/) (2026)

## Abstract (arXiv)

Conformal prediction (CP) transforms any model's output into prediction sets guaranteed to include (cover) the true label. CP requires exchangeability, a relaxation of the i.i.d. assumption, to obtain a valid distribution-free coverage guarantee. This makes it directly applicable to transductive node-classification. However, conventional CP cannot be applied in inductive settings due to the implicit shift in the (calibration) scores caused by message passing with the new nodes. We fix this issue for both cases of node and edge-exchangeable graphs, recovering the standard coverage guarantee without sacrificing statistical efficiency. We further prove that the guarantee holds independently of the prediction time, e.g. upon arrival of a new node/edge or at any subsequent moment.