Minimax Manifold Estimation
Christopher Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman; 13(May):1263−1291, 2012.
AbstractWe 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.