# CUQ-GNN: Committee-based Graph Uncertainty Quantification using Posterior Networks

arXiv: https://arxiv.org/abs/2409.04159 · HTML: https://mlsanity.com/paper/2409.04159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 51 references that are in the map.
- First posted on arXiv 6 Sep 2024.

## 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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Fake News Detection on Social Media: A Data Mining Perspective](https://mlsanity.com/paper/1708.01967/) (2017)
- [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)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [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)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [Evaluating Robustness of Predictive Uncertainty Estimation: Are Dirichlet-based Models Reliable?](https://mlsanity.com/paper/2010.14986/) (2020)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Uncertainty on Asynchronous Time Event Prediction](https://mlsanity.com/paper/1911.05503/) (2019)
- [Fusion of Probability Density Functions](https://mlsanity.com/paper/2202.11633/) (2022)
- [Second-Order Uncertainty Quantification: Variance-Based Measures](https://mlsanity.com/paper/2401.00276/) (2023)
- [Evidential Uncertainty Quantification: A Variance-Based Perspective](https://mlsanity.com/paper/2311.11367/) (2023)
- [A Novel Higher-order Weisfeiler-Lehman Graph Convolution](https://mlsanity.com/paper/2007.00346/) (2020)
- [Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks](https://mlsanity.com/paper/2312.11230/) (2023)
- [Linear Opinion Pooling for Uncertainty Quantification on Graphs](https://mlsanity.com/paper/2406.04041/) (2024)

## Built on by (most cited first, 1 of 1)

- [Rethinking Epistemic Uncertainty in Node Classification through Information Growth](https://mlsanity.com/paper/2610.03418/) (2026)

## Abstract (arXiv)

In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.