Minimax manifold estimation
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman · arXiv (Cornell University) · 2012
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.