  When each data point is a large graph, graph statistics such as densities of
certain subgraphs (motifs) can be used as feature vectors for machine learning.
While intuitive, motif counts are expensive to compute and difficult to work
with theoretically. Via graphon theory, we give an explicit quantitative bound
for the ability of motif homomorphisms to distinguish large networks under both
generative and sampling noise. Furthermore, we give similar bounds for the
graph spectrum and connect it to homomorphism densities of cycles. This results
in an easily computable classifier on graph data with theoretical performance
guarantee. Our method yields competitive results on classification tasks for
the autoimmune disease Lupus Erythematosus.
