Manifold estimation and singular deconvolution under Hausdorff loss

TL;DR

This paper investigates the theoretical limits of estimating manifolds using Hausdorff distance and explores the connection between manifold estimation and singular measure deconvolution.

Contribution

It provides bounds on estimation risk and reveals links between manifold estimation and singular measure deconvolution problems.

Findings

Established lower and upper bounds for manifold estimation risk.

Identified connections between manifold estimation and singular measure deconvolution.

Enhanced understanding of Hausdorff distance in manifold estimation.

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.