Manifold estimation and singular deconvolution under Hausdorff loss

Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman

The Annals of Statistics · 2012 · Volume 40 · Issue 2

Abstract

We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.

Keywords

62G05, 62G20, 62H12, Deconvolution, manifold learning, minimax

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