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Graph convolutional networks (GCNs) have recently achieved great empiricalsuccess in learning graph-structured data. To address its scalability issue dueto the recursive embedding of neighboring features, graph topology sampling hasbeen proposed to reduce the memory and computational cost of training GCNs, andit has achieved comparable test performance to those without topology samplingin many empirical studies. To the best of our knowledge, this paper providesthe first theoretical justification of graph topology sampling in training (upto) three-layer GCNs for semi-supervised node classification. We formallycharacterize some sufficient conditions on graph topology sampling such thatGCN training leads to a diminishing generalization error. Moreover, our methodtackles the nonconvex interaction of weights across layers, which isunder-explored in the existing theoretical analyses of GCNs. This papercharacterizes the impact of graph structures and topology sampling on thegeneralization performance and sample complexity explicitly, and thetheoretical findings are also justified through numerical experiments.

Generalization Guarantee of Training Graph Convolutional Networks with Graph Topology Sampling