The Graphical Nadaraya-Watson Estimator in Latent Position Models
Abstract
Given a graph with a subset of labeled nodes, we are interested in the quality of the averaging estimator which for an unlabeled node predicts the average of the observations of its labeled neighbours. We rigorously study concentration properties, variance bounds and risk bounds in this context. While the estimator itself is very simple we believe that our results will contribute towards the theoretical understanding of learning on graphs through more sophisticated methods such as Graph Neural Networks.
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