Minimax Manifold Estimation

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. [abs] [ pdf ][ bib ] © JMLR 2012. (edit, beta)