Emergent Mind
Minimax Manifold Estimation
(1007.0549)
Published Jul 4, 2010
in
stat.ML
,
cs.LG
,
math.ST
,
and
stat.TH
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. 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.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.