用随机偏微分方程建模图上不确定性，提升分布外检测能力。
Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations
- 基于高斯过程的随机偏微分方程设计新消息传递机制。
- 在不同标签信息量数据集上均实现更优的分布外检测性能。
- 可控制协方差核平滑度，适用于高低标签信息场景。
图神经网络在多种网络建模任务中表现优异，但图上不确定性估计仍具挑战，尤其在分布外情形下。传统方法未充分考虑图结构与标签分布共同带来的随机性。本文类比由马特恩高斯过程驱动的随机偏微分方程演化与GNN层的消息传递过程，提出一种基于高斯过程的新型消息传递框架，引入时空噪声以捕捉空间与时间上的不确定性。该方法能显式控制协方差核的平滑度，从而在低与高标签信息量图上均提升不确定性估计效果。在具有不同标签信息量的多个图数据集上的分布外检测实验表明，所提模型优于现有方法。
原文摘要 · Abstract (English)
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.
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