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 and the data generating process is too idealistic for practical applications, we believe that our small steps will contribute towards the theoretical understanding of more sophisticated methods such as Graph Neural Networks.
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