A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks
This work provides tighter generalization bounds for GNNs, which is important for researchers and practitioners in graph machine learning to better understand and predict model performance.
This paper derives PAC-Bayesian generalization bounds for Graph Convolutional Networks (GCNs) and Message Passing GNNs (MPGNNs). The bounds are governed by the maximum node degree and spectral norm of weights, and for MPGNNs, the bound shows a tighter dependency on maximum node degree and hidden dimension compared to prior Rademacher complexity bounds.
In this paper, we derive generalization bounds for the two primary classes of graph neural networks (GNNs), namely graph convolutional networks (GCNs) and message passing GNNs (MPGNNs), via a PAC-Bayesian approach. Our result reveals that the maximum node degree and spectral norm of the weights govern the generalization bounds of both models. We also show that our bound for GCNs is a natural generalization of the results developed in arXiv:1707.09564v2 [cs.LG] for fully-connected and convolutional neural networks. For message passing GNNs, our PAC-Bayes bound improves over the Rademacher complexity based bound in arXiv:2002.06157v1 [cs.LG], showing a tighter dependency on the maximum node degree and the maximum hidden dimension. The key ingredients of our proofs are a perturbation analysis of GNNs and the generalization of PAC-Bayes analysis to non-homogeneous GNNs. We perform an empirical study on several real-world graph datasets and verify that our PAC-Bayes bound is tighter than others.