Article thumbnail
Location of Repository

Geometric median and robust estimation in Banach spaces

By Stanislav Minsker

Abstract

In many real-world applications, collected data are contaminated by noise with heavy-tailed distribution and might contain outliers of large magnitude. In this situation, it is necessary to apply methods which produce reliable outcomes even if the input contains corrupted measurements. We describe a general method which allows one to obtain estimators with tight concentration around the true parameter of interest taking values in a Banach space. Suggested construction relies on the fact that the geometric median of a collection of independent "weakly concentrated" estimators satisfies a much stronger deviation bound than each individual element in the collection. Our approach is illustrated through several examples, including sparse linear regression and low-rank matrix recovery problems.Comment: Published at http://dx.doi.org/10.3150/14-BEJ645 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Topics: Mathematics - Statistics Theory
Year: 2015
DOI identifier: 10.3150/14-BEJ645
OAI identifier: oai:arXiv.org:1308.1334
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1308.1334 (external link)
  • http://dx.doi.org/10.3150/14-B... (external link)
  • http://isi.cbs.nl/bernoulli/) (external link)
  • http://isi.cbs.nl/BS/bshome.ht... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.