Nonparametric regression on random geometric graphs sampled from submanifolds
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Abstract (arXiv)
We consider the nonparametric regression problem when the covariates are located on an unknown smooth compact submanifold of a Euclidean space. Under defining a random geometric graph structure over the covariates we analyze the asymptotic frequentist behaviour of the posterior distribution arising from Bayesian priors designed through random basis expansion in the graph Laplacian eigenbasis. Under Holder smoothness assumption on the regression function and the density of the covariates over the submanifold, we prove that the posterior contraction rates of such methods are minimax optimal (up to logarithmic factors) for any positive smoothness index.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 21 of its 58 references that are in the map. First posted on arXiv 31 May 2024.
Builds on
21 of 58 references.
References · 21
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9 more
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