Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations

Richard Bergna, Sergio Calvo Ordoñez, Felix Opolka, Pietro Lio, José Miguel Hernández-Lobato

Keywords: Graph Neural Networks, Neural SDEs, Stochastic Differential Equations, Uncertainty Quantification, Bayesian Inference

TL;DR: We introduce Latent Graph Neural SDEs (LGNSDEs), a model that quantifies uncertainty in graph-structured data while maintaining robustness to input perturbations, supported by theoretical guarantees and empirical evaluation.

Abstract: 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.

Submission Number: 18