Generalization Guarantee of Training Graph Convolutional Networks with Graph Topology Sampling

TL;DR

This paper provides the first theoretical analysis of graph topology sampling in training shallow GCNs, establishing conditions under which it guarantees diminishing generalization error and analyzing its impact on sample complexity.

Contribution

It offers a novel theoretical framework for understanding how graph topology sampling affects GCN training and generalization, addressing nonconvex interactions across layers.

Findings

Conditions for diminishing generalization error with topology sampling

Explicit characterization of graph structure impact on generalization

Numerical experiments validating theoretical results

Abstract

Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been proposed to reduce the memory and computational cost of training GCNs, and it has achieved comparable test performance to those without topology sampling in many empirical studies. To the best of our knowledge, this paper provides the first theoretical justification of graph topology sampling in training (up to) three-layer GCNs for semi-supervised node classification. We formally characterize some sufficient conditions on graph topology sampling such that GCN training leads to a diminishing generalization error. Moreover, our method tackles the nonconvex interaction of weights across layers, which is under-explored in the existing theoretical analyses of GCNs. This paper characterizes the impact of graph structures and topology sampling on the generalization performance and sample complexity explicitly, and the theoretical findings are also justified through numerical experiments.