Minimax Manifold Estimation
Machine Learning
2011-09-29 v3 Machine Learning
Statistics Theory
Statistics Theory
Abstract
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D given a noisy sample from the manifold. We assume that the manifold satisfies a smoothness condition and that the noise distribution has compact support. We show that the optimal rate of convergence is n^{-2/(2+d)}. Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.
Cite
@article{arxiv.1007.0549,
title = {Minimax Manifold Estimation},
author = {Christopher Genovese and Marco Perone-Pacifico and Isabella Verdinelli and Larry Wasserman},
journal= {arXiv preprint arXiv:1007.0549},
year = {2011}
}
Comments
journal submission, revision with some errors corrected