# A General Framework for quantifying Aleatoric and Epistemic uncertainty in Graph Neural Networks

arXiv: https://arxiv.org/abs/2205.09968 · HTML: https://mlsanity.com/paper/2205.09968/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 26 of 26)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [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)
- [Lightweight Probabilistic Deep Networks](https://mlsanity.com/paper/1805.11327/) (2018)
- [A Bit More Bayesian: Domain-Invariant Learning with Uncertainty](https://mlsanity.com/paper/2105.04030/) (2021)
- [Tractable Inference for Complex Stochastic Processes](https://mlsanity.com/paper/1301.7362/) (2013)
- [Ensemble Bayesian Decision Making with Redundant Deep Perceptual Control Policies](https://mlsanity.com/paper/1811.12555/) (2018)
- [Overcoming Catastrophic Forgetting by Generative Regularization](https://mlsanity.com/paper/1912.01238/) (2019)
- [Policy Gradient Bayesian Robust Optimization for Imitation Learning](https://mlsanity.com/paper/2106.06499/) (2021)
- [Scalable Graph Neural Network-based framework for identifying critical nodes and links in Complex Networks](https://mlsanity.com/paper/2012.15725/) (2020)
- [Bayesian Graph Convolutional Neural Networks Using Non-Parametric Graph Learning](https://mlsanity.com/paper/1910.12132/) (2019)
- [Bayesian Graph Neural Network for Fast identification of critical nodes in Uncertain Complex Networks](https://mlsanity.com/paper/2012.15733/) (2020)
- [Neighborhood Random Walk Graph Sampling for Regularized Bayesian Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.07743/) (2021)

## Built on by (most cited first, 12 of 12)

- [Challenges and Opportunities in Deep Reinforcement Learning with Graph Neural Networks: A Comprehensive review of Algorithms and Applications](https://mlsanity.com/paper/2206.07922/) (2022)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Uncertainty Quantification via Stable Distribution Propagation](https://mlsanity.com/paper/2402.08324/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Graph Convolutional Network with Connectivity Uncertainty for EEG-based Emotion Recognition](https://mlsanity.com/paper/2310.14165/) (2023)
- [Conditional Prediction ROC Bands for Graph Classification](https://mlsanity.com/paper/2410.15239/) (2024)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [GraMeR: Graph Meta Reinforcement Learning for Multi-Objective Influence Maximization](https://mlsanity.com/paper/2205.14834/) (2022)
- [A General Framework for Uncertainty Quantification via Neural SDE-RNN](https://mlsanity.com/paper/2306.01189/) (2023)
- [Credal Graph Neural Networks](https://mlsanity.com/paper/2512.02722/) (2025)
- [Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs](https://mlsanity.com/paper/2304.14680/) (2023)
- [Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints](https://mlsanity.com/paper/2606.02038/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN stemming from modeling errors and measurement uncertainty. We consider aleatoric uncertainty in the form of probabilistic links and noise in feature vector of nodes, while epistemic uncertainty is incorporated via a probability distribution over the model parameters. We propose a unified approach to treat both sources of uncertainty in a Bayesian framework, where Assumed Density Filtering is used to quantify aleatoric uncertainty and Monte Carlo dropout captures uncertainty in model parameters. Finally, the two sources of uncertainty are aggregated to estimate the total uncertainty in predictions of a GNN. Results in the real-world datasets demonstrate that the Bayesian model performs at par with a frequentist model and provides additional information about predictions uncertainty that are sensitive to uncertainties in the data and model.