Graph Homomorphism Features: Why Not Sample?

Recent research in the domain of computed graph embeddings has shown that graph homomorphism numbers constitute expressive features that are well-suited for machine learning tasks such as graph classification. In this work-in-progress paper, we attempt to make this methodology scalable by obtaining additive approximations to graph homomorphism densities via a simple sampling algorithm. We show in experiments that these approximate homomorphism densities perform as well as homomorphism numbers on standard graph classification datasets. Moreover, we show that, unlike algorithms that compute homomorphism numbers, our sampling algorithm is highly scalable to larger graphs.