Investigating the Interplay between Features and Structures in Graph Learning

TL;DR

This paper empirically explores how the relationship between node features and labels affects graph learning, challenging existing metrics and providing new insights through synthetic experiments with various models.

Contribution

It introduces formal generative processes for node classification, evaluates feature influence with a new metric, and demonstrates limitations of existing metrics in relaxed assumptions.

Findings

Existing metrics are inadequate when feature-label correlation is weak.

Models can perform well on heterophilic graphs despite low feature informativeness.

Synthetic tasks reveal nuanced effects of features and structure on model performance.

Abstract

In the past, the dichotomy between homophily and heterophily has inspired research contributions toward a better understanding of Deep Graph Networks' inductive bias. In particular, it was believed that homophily strongly correlates with better node classification predictions of message-passing methods. More recently, however, researchers pointed out that such dichotomy is too simplistic as we can construct node classification tasks where graphs are completely heterophilic but the performances remain high. Most of these works have also proposed new quantitative metrics to understand when a graph structure is useful, which implicitly or explicitly assume the correlation between node features and target labels. Our work empirically investigates what happens when this strong assumption does not hold, by formalising two generative processes for node classification tasks that allow us to build and study ad-hoc problems. To quantitatively measure the influence of the node features on the target labels, we also use a metric we call Feature Informativeness. We construct six synthetic tasks and evaluate the performance of six models, including structure-agnostic ones. Our findings reveal that previously defined metrics are not adequate when we relax the above assumption. Our contribution to the workshop aims at presenting novel research findings that could help advance our understanding of the field.