Learning Submanifolds for Subsequent Inference on Random Dot Product Graphs, Part 1: Theory

The paper introduces a framework for restricted inference on random dot product graphs whose latent positions lie on an unknown low‑dimensional support manifold. It proposes semisupervised decision rules that employ Isomap manifold learning to build a low‑dimensional Euclidean representation of the observed graph, and then apply an isometrically invariant function to map point configurations to actions. The authors analyze how the risk of these rules converges to that of an oracle rule as the amount of auxiliary data sampled from the manifold increases.

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