Manifold estimation and singular deconvolution under Hausdorff loss

2011/09/30 by Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli +1
Computer Science · Mathematics · #Deconvolution #Distributed Sensor Networks and Detection Algorithms #Estimation #Hausdorff distance #Hausdorff space #Manifold (fluid mechanics) #Point processes and geometric inequalities #Singular value #Statistical Methods and Inference #Statistical manifold #Upper and lower bounds #cs.LG #math.ST #stat.ML #stat.TH

paper · pdf · doi:10.1214/12-aos994

published as Annals of Statistics 2012, Vol. 40, No. 2, 941-963 · Published in at http://dx.doi.org/10.1214/12-AOS994 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2012/04/01 · arxiv created 2012/06/05 · arxiv updated 2012/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• A Topological View of Unsupervised Learning from Noisy Data
• On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems