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.
Code (0)
등록된 구현이 없습니다.
Tasks
Out-of-Distribution DetectionPredictionSimilar Papers 제목 키워드 기반
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 quan…
Uncertainty QuantificationUniversal approximation property of neural stochastic differential equations
We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochas…
Scalable Gradients for Stochastic Differential Equations
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory comp…
SensitivityVariational InferenceVideo PredictionDeep Forward-Backward SDEs for Min-max Control
This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parab…
Set-Valued Risk Measures as Backward Stochastic Difference Inclusions and Equations
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and st…