Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations

We address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODE) are effective in learning node representations, they fail to quantify uncertainty. To address this, we introduce Latent Graph Neural Stochastic Differential Equations (LGNSDE), which enhance GNODE by embedding randomness through Brownian motion to quantify uncertainty. We provide theoretical guarantees for LGNSDE and empirically show better performance in uncertainty quantification.

Graph Neural Stochastic Differential Equations

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using Brownian motion. This inclusion allows for the assessment of prediction uncertainty, a crucial aspect frequently missed in current models. In our framework, we spotlight the \textit{Latent Graph Neural SDE} variant, demonstrating its effectiveness. Through empirical studies, we find that Latent Graph Neural SDEs surpass conventional models like Graph Convolutional Networks and Graph Neural ODEs, especially in confidence prediction, making them superior in handling out-of-distribution detection across both static and spatio-temporal contexts.