Minimax Manifold Estimation

Details Minimax Manifold Estimation Minimax Manifold Estimation

2010-07-04

arxiv.org/abs/1007.0549v3

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Machine Learning

journal submission, revision with some errors corrected

Scientific paper

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D 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.

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