Keywords: [ OPT: Learning for Optimization ] [ OPT: Sampling and Optimization ] [ DL: Theory ] [ OPT: Non-Convex ] [ T: Deep Learning ] [ T: Learning Theory ] [ T: Optimization ] [ DL: Graph Neural Networks ]
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 diminishing generalization error. Moreover, our method tackles the non-convex 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.