Minimax Manifold Estimation
Abstract
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in ℝD given a noisy sample from the manifold. Under certain conditions, 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
Text
Genovese et al. "Minimax Manifold Estimation." Journal of Machine Learning Research, 2012.Markdown
[Genovese et al. "Minimax Manifold Estimation." Journal of Machine Learning Research, 2012.](https://mlanthology.org/jmlr/2012/genovese2012jmlr-minimax/)BibTeX
@article{genovese2012jmlr-minimax,
title = {{Minimax Manifold Estimation}},
author = {Genovese, Christopher and Perone-Pacifico, Marco and Verdinelli, Isabella and Wasserman, Larry},
journal = {Journal of Machine Learning Research},
year = {2012},
pages = {1263-1291},
volume = {13},
url = {https://mlanthology.org/jmlr/2012/genovese2012jmlr-minimax/}
}