A Graph Is More Than Its Nodes: Towards Structured Uncertainty-Aware Learning on Graphs

TL;DR

This paper introduces edgewise metrics for uncertainty estimation in graph neural networks, emphasizing the importance of structured prediction for improved uncertainty quantification beyond traditional nodewise evaluations.

Contribution

It proposes novel edgewise metrics for uncertainty estimation and demonstrates that structured prediction models improve uncertainty quantification on graphs.

Findings

Edgewise metrics complement nodewise results.

Structured prediction models yield better uncertainty estimates.

Edgewise metrics provide new insights into GNN uncertainty.

Abstract

Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not fully characterize the joint distribution given the graph structure. In this work, we propose novel edgewise metrics, namely the edgewise expected calibration error (ECE) and the agree/disagree ECEs, which provide criteria for uncertainty estimation on graphs beyond the nodewise setting. Our experiments demonstrate that the proposed edgewise metrics can complement the nodewise results and yield additional insights. Moreover, we show that GNN models which consider the structured prediction problem on graphs tend to have better uncertainty estimations, which illustrates the benefit of going beyond the nodewise setting.