Credal Graph Neural Networks

TL;DR

This work introduces Credal Graph Neural Networks (CGNNs), a framework that extends credal learning to graphs to produce set-valued predictions and disentangle aleatoric and epistemic uncertainty. By leveraging a novel Credal Layer and a joint latent representation that aggregates information across all GNN layers, CGNNs provide more faithful uncertainty estimates, particularly under distributional shift and in heterophilic graphs. Training with a Distributionally Robust Optimization objective further enhances robustness, and extensive experiments show state-of-the-art OOD detection on heterophilic benchmarks while maintaining competitive performance on homophilic graphs. The results emphasize the critical role of graph structure in shaping uncertainty estimates and establish a new direction for uncertainty-aware graph learning.

Abstract

Uncertainty quantification is essential for deploying reliable Graph Neural Networks (GNNs), where existing approaches primarily rely on Bayesian inference or ensembles. In this paper, we introduce the first credal graph neural networks (CGNNs), which extend credal learning to the graph domain by training GNNs to output set-valued predictions in the form of credal sets. To account for the distinctive nature of message passing in GNNs, we develop a complementary approach to credal learning that leverages different aspects of layer-wise information propagation. We assess our approach on uncertainty quantification in node classification under out-of-distribution conditions. Our analysis highlights the critical role of the graph homophily assumption in shaping the effectiveness of uncertainty estimates. Extensive experiments demonstrate that CGNNs deliver more reliable representations of epistemic uncertainty and achieve state-of-the-art performance under distributional shift on heterophilic graphs.

Figures (2)

• Figure 1: Visualization of aleatoric uncertainty (AU) and epistemic uncertainty (EU) for a 3-class classification problem. The top row shows a Bayesian continuous representation, while the bottom row shows the corresponding credal set representation. (a) Low AU and low EU: the model is confident in its prediction. (b) High AU, low EU: the model attributes uncertainty to noisy data. (c) High AU and high EU: the model faces out-of-distribution data. (d) Low AU, high EU: the model encounters novel data and attributes uncertainty to its parameters rather than to noise. In the credal set representation (bottom row), the shaded regions inside the simplex correspond to lower and upper probability bounds for each class.
• Figure 2: Overview of the proposed credal prediction framework. An input graph is processed by a Graph Neural Network (GNN), which iteratively aggregates node representations across layers ($Z^0, \ldots, Z^L$), gaining and losing information at each step. The latent joint representation $Z^{\text{joint}}$ allows recovery of the full trajectory of each node across layers. A credal layer then maps $Z^{\text{joint}}$ to a credal prediction, providing an informative representation of uncertainty. Green credal sets correspond to reliable predictions, while red credal sets indicate nodes that are likely out-of-distribution (OOD) due to high aleatoric or epistemic uncertainty.