GOPHER: Categorical probabilistic forecasting with graph structure via local continuous-time dynamics

TL;DR

GOPHER is a novel method for probabilistic categorical forecasting on graphs that combines graph neural networks and neural ODEs to improve accuracy and sample efficiency, highlighting the importance of graph structure.

Contribution

The paper introduces GOPHER, integrating graph neural networks with neural ODEs for probabilistic forecasting, and analyzes the impact of local continuous-time dynamics.

Findings

Capturing graph structure improves in-domain prediction accuracy.

Graph structure enhances sample efficiency of models.

Continuous-time dynamics offer limited additional benefits.

Abstract

We consider the problem of probabilistic forecasting over categories with graph structure, where the dynamics at a vertex depends on its local connectivity structure. We present GOPHER, a method that combines the inductive bias of graph neural networks with neural ODEs to capture the intrinsic local continuous-time dynamics of our probabilistic forecasts. We study the benefits of these two inductive biases by comparing against baseline models that help disentangle the benefits of each. We find that capturing the graph structure is crucial for accurate in-domain probabilistic predictions and more sample efficient models. Surprisingly, our experiments demonstrate that the continuous time evolution inductive bias brings little to no benefit despite reflecting the true probability dynamics.