Minimax Manifold Estimation

arxiv: 1007.0549 · v3 · pith:OHJSR7K2new · submitted 2010-07-04 · 📊 stat.ML · cs.LG· math.ST· stat.TH

Minimax Manifold Estimation

Christopher Genovese , Marco Perone-Pacifico , Isabella Verdinelli , Larry Wasserman This is my paper

classification 📊 stat.ML cs.LGmath.STstat.TH

keywords manifolddimensionminimaxrateconvergenceembeddedassumecompact

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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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Minimax Manifold Estimation

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