# Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networks

arXiv: https://arxiv.org/abs/2401.03350 · HTML: https://mlsanity.com/paper/2401.03350/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 79 references that are in the map.
- First posted on arXiv 7 Jan 2024.

## Builds on (most cited first, 30 of 63)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Graph R-CNN for Scene Graph Generation](https://mlsanity.com/paper/1808.00191/) (2018)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)

## Built on by (most cited first, 8 of 8)

- [GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation](https://mlsanity.com/paper/2502.05780/) (2025)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Epistemic Wrapping for Uncertainty Quantification](https://mlsanity.com/paper/2505.02277/) (2025)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Uncertainty Estimation for Heterophilic Graphs Through the Lens of Information Theory](https://mlsanity.com/paper/2505.22152/) (2025)
- [Spiking Graph Predictive Coding for Reliable OOD Generalization](https://mlsanity.com/paper/2602.19392/) (2026)
- [When does distribution shift break graph neural networks calibration?](https://mlsanity.com/paper/2607.10804/) (2026)
- [A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion](https://mlsanity.com/paper/2609.35703/) (2026)

## Abstract (arXiv)

While graph neural networks (GNNs) are widely used for node and graph representation learning tasks, the reliability of GNN uncertainty estimates under distribution shifts remains relatively under-explored. Indeed, while post-hoc calibration strategies can be used to improve in-distribution calibration, they need not also improve calibration under distribution shift. However, techniques which produce GNNs with better intrinsic uncertainty estimates are particularly valuable, as they can always be combined with post-hoc strategies later. Therefore, in this work, we propose G-DeltaUQ, a novel training framework designed to improve intrinsic GNN uncertainty estimates. Our framework adapts the principle of stochastic data centering to graph data through novel graph anchoring strategies, and is able to support partially stochastic GNNs. While, the prevalent wisdom is that fully stochastic networks are necessary to obtain reliable estimates, we find that the functional diversity induced by our anchoring strategies when sampling hypotheses renders this unnecessary and allows us to support G-DeltaUQ on pretrained models. Indeed, through extensive evaluation under covariate, concept and graph size shifts, we show that G-DeltaUQ leads to better calibrated GNNs for node and graph classification. Further, it also improves performance on the uncertainty-based tasks of out-of-distribution detection and generalization gap estimation. Overall, our work provides insights into uncertainty estimation for GNNs, and demonstrates the utility of G-DeltaUQ in obtaining reliable estimates.