# Evidential Uncertainty Probes for Graph Neural Networks

arXiv: https://arxiv.org/abs/2503.08097 · HTML: https://mlsanity.com/paper/2503.08097/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Energy-based Out-of-Distribution Detection for Graph Neural Networks](https://mlsanity.com/paper/2302.02914/) (2023)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [Packed-Ensembles for Efficient Uncertainty Estimation](https://mlsanity.com/paper/2210.09184/) (2022)
- [Learn to Accumulate Evidence from All Training Samples: Theory and Practice](https://mlsanity.com/paper/2306.11113/) (2023)
- [Binary Classification from Positive-Confidence Data](https://mlsanity.com/paper/1710.07138/) (2017)
- [Provable Multi-Task Representation Learning by Two-Layer ReLU Neural Networks](https://mlsanity.com/paper/2307.06887/) (2023)
- [Improvements on Uncertainty Quantification for Node Classification via Distance-Based Regularization](https://mlsanity.com/paper/2311.05795/) (2023)
- [Batch-Ensemble Stochastic Neural Networks for Out-of-Distribution Detection](https://mlsanity.com/paper/2206.12911/) (2022)
- [Trajectory Planning for Autonomous Driving in Unstructured Scenarios Based on Graph Neural Network and Numerical Optimization](https://mlsanity.com/paper/2406.08855/) (2024)

## Abstract (arXiv)

Accurate quantification of both aleatoric and epistemic uncertainties is essential when deploying Graph Neural Networks (GNNs) in high-stakes applications such as drug discovery and financial fraud detection, where reliable predictions are critical. Although Evidential Deep Learning (EDL) efficiently quantifies uncertainty using a Dirichlet distribution over predictive probabilities, existing EDL-based GNN (EGNN) models require modifications to the network architecture and retraining, failing to take advantage of pre-trained models. We propose a plug-and-play framework for uncertainty quantification in GNNs that works with pre-trained models without the need for retraining. Our Evidential Probing Network (EPN) uses a lightweight Multi-Layer-Perceptron (MLP) head to extract evidence from learned representations, allowing efficient integration with various GNN architectures. We further introduce evidence-based regularization techniques, referred to as EPN-reg, to enhance the estimation of epistemic uncertainty with theoretical justifications. Extensive experiments demonstrate that the proposed EPN-reg achieves state-of-the-art performance in accurate and efficient uncertainty quantification, making it suitable for real-world deployment.