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Theoretical analyses for graph learning methods often assume a completeobservation of the input graph. Such an assumption might not be useful forhandling any-size graphs due to the scalability issues in practice. In thiswork, we develop a theoretical framework for graph classification problems inthe partial observation setting (i.e., subgraph samplings). Equipped withinsights from graph limit theory, we propose a new graph classification modelthat works on a randomly sampled subgraph and a novel topology to characterizethe representability of the model. Our theoretical framework contributes atheoretical validation of mini-batch learning on graphs and leads to newlearning-theoretic results on generalization bounds as well assize-generalizability without assumptions on the input.

Learning on Random Balls is Sufficient for Estimating (Some) Graph Parameters