2012 JMLR JMLR 2012

Minimax Manifold Estimation

Abstract

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)

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📈 Trend Setter — Geometry
🧭 Keyword Pioneer — hausdorff distance
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