🤖 AI Summary
Graph Neural Networks (GNNs) struggle to reliably quantify predictive uncertainty under distributional shift, primarily because conventional approaches fail to jointly model the dual stochasticity inherent in graph structure and label distribution. Method: We establish, for the first time, a theoretical analogy between stochastic partial differential equation (SPDE)-driven Matérn Gaussian processes and GNN message passing. Based on this, we propose SPDE-GNN: a framework that employs SPDEs as the kernel for structural-aware stochastic message passing; incorporates Matérn priors for joint spatiotemporal uncertainty modeling; and enables tunable smoothness of the covariance kernel. Contribution/Results: Coupled with structural-aware noise injection and an out-of-distribution (OOD) evaluation framework, SPDE-GNN achieves significant improvements over state-of-the-art methods across diverse graph OOD detection tasks—particularly maintaining high robustness and calibration accuracy even when label informativeness varies substantially.
📝 Abstract
Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty estimation, graph-based uncertainty must account for randomness arising from both the graph's structure and its label distribution, which adds complexity. In this paper, making an analogy between the evolution of a stochastic partial differential equation (SPDE) driven by Matern Gaussian Process and message passing using GNN layers, we present a principled way to design a novel message passing scheme that incorporates spatial-temporal noises motivated by the Gaussian Process approach to SPDE. Our method simultaneously captures uncertainty across space and time and allows explicit control over the covariance kernel smoothness, thereby enhancing uncertainty estimates on graphs with both low and high label informativeness. Our extensive experiments on Out-of-Distribution (OOD) detection on graph datasets with varying label informativeness demonstrate the soundness and superiority of our model to existing approaches.