Manifold estimation and singular deconvolution under Hausdorff loss

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

doi:10.1214/12-aos994

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arXiv · 1109.4540

Manifold estimation and singular deconvolution under Hausdorff loss

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

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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.

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BibTeX RIS

Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman. 2012-06-05. Manifold estimation and singular deconvolution under Hausdorff loss. https://doi.org/10.1214/12-aos994

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