Graph Classification via Reference Distribution Learning: Theory and Practice

TL;DR

This paper introduces Graph Reference Distribution Learning (GRDL), a novel graph classification method that models node embeddings as distributions, avoiding pooling, with proven generalization advantages and significant efficiency improvements over existing methods.

Contribution

The paper proposes GRDL, a new graph classification approach using reference distribution learning, with theoretical generalization bounds and extensive empirical validation showing superior performance.

Findings

GRDL outperforms state-of-the-art methods on various datasets.

GRDL is at least 10 times faster in training and inference.

Theoretical bounds confirm GRDL's stronger generalization ability.

Abstract

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs). Graph kernels often suffer from computational costs and manual feature engineering, while GNNs commonly utilize global pooling operations, risking the loss of structural or semantic information. This work introduces Graph Reference Distribution Learning (GRDL), an efficient and accurate graph classification method. GRDL treats each graph's latent node embeddings given by GNN layers as a discrete distribution, enabling direct classification without global pooling, based on maximum mean discrepancy to adaptively learned reference distributions. To fully understand this new model (the existing theories do not apply) and guide its configuration (e.g., network architecture, references' sizes, number, and regularization) for practical use, we derive generalization error bounds for GRDL and verify them numerically. More importantly, our theoretical and numerical results both show that GRDL has a stronger generalization ability than GNNs with global pooling operations. Experiments on moderate-scale and large-scale graph datasets show the superiority of GRDL over the state-of-the-art, emphasizing its remarkable efficiency, being at least 10 times faster than leading competitors in both training and inference stages.