Node Regression on Latent Position Random Graphs via Local Averaging

Дата публикации: 17-08-2026 20:26:00

Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. We perform a theoretical study where the graph is generated by
a Latent Position Model: each node has a latent position and the probability of connection
depends on the distance between latent positions.
We begin by studying the simplest estimator: averaging the label at all neighboring
nodes. We show that in Latent Position Models this estimator tends to a Nadaraya-Watson
estimator in the latent space, with the same rate of convergence.
One issue with this estimator is that it averages over all neighbors of a node, which may
be too large or too small a region depending on the graph model. An alternative consists
in first estimating the "true" distances between latent positions, then injecting these into
a classical Nadaraya-Watson estimator. This enables averaging in regions either smaller
or larger than the typical graph neighborhood. We show that this method can achieve
standard nonparametric rates even when the graph neighborhood is too large or too small.

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Классификация: Наука. Схожих патентов: 0. Схожих новостей: 10. Тональность: 0. Информативность: 4.07. Источник: jmlr.org.