Kernel smoothing on manifolds
Statistics Theory
2026-01-26 v1 Machine Learning
Differential Geometry
Machine Learning
Statistics Theory
Abstract
Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type bounds. Special cases include kernel density estimation, kernel regression and the heat kernel signature. Connections to the graph Laplacian are also discussed.
Cite
@article{arxiv.2601.16777,
title = {Kernel smoothing on manifolds},
author = {Eunseong Bae and Wolfgang Polonik},
journal= {arXiv preprint arXiv:2601.16777},
year = {2026}
}