Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shifts

TL;DR

This paper introduces HEI, a framework that learns invariant node representations on heterophilic graphs to address distribution shifts caused by mixed local node structures, improving semi-supervised learning performance.

Contribution

The paper proposes HEI, a novel invariant learning framework that infers latent environments in heterophilic graphs without data augmentation, addressing structural distribution shifts.

Findings

HEI achieves guaranteed performance under heterophilic graph distribution shifts.

Extensive experiments show HEI outperforms state-of-the-art baselines.

Theoretical analysis supports the effectiveness of HEI.

Abstract

Heterophilic Graph Neural Networks (HGNNs) have shown promising results for semi-supervised learning tasks on graphs. Notably, most real-world heterophilic graphs are composed of a mixture of nodes with different neighbor patterns, exhibiting local node-level homophilic and heterophilic structures. However, existing works are only devoted to designing better HGNN backbones or architectures for node classification tasks on heterophilic and homophilic graph benchmarks simultaneously, and their analyses of HGNN performance with respect to nodes are only based on the determined data distribution without exploring the effect caused by this structural difference between training and testing nodes. How to learn invariant node representations on heterophilic graphs to handle this structure difference or distribution shifts remains unexplored. In this paper, we first discuss the limitations of previous graph-based invariant learning methods from the perspective of data augmentation. Then, we propose \textbf{HEI}, a framework capable of generating invariant node representations through incorporating heterophily information to infer latent environments without augmentation, which are then used for invariant prediction, under heterophilic graph structure distribution shifts. We theoretically show that our proposed method can achieve guaranteed performance under heterophilic graph structure distribution shifts. Extensive experiments on various benchmarks and backbones can also demonstrate the effectiveness of our method compared with existing state-of-the-art baselines. The code is available at https://github.com/Yangjinluan/HEI