• Bernoulli
  • Volume 21, Number 4 (2015), 2308-2335.

Geometric median and robust estimation in Banach spaces

Stanislav Minsker

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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.

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Bernoulli, Volume 21, Number 4 (2015), 2308-2335.

Received: November 2013
Revised: May 2014
First available in Project Euclid: 5 August 2015

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distributed computing heavy-tailed noise large deviations linear models low-rank matrix estimation principal component analysis robust estimation


Minsker, Stanislav. Geometric median and robust estimation in Banach spaces. Bernoulli 21 (2015), no. 4, 2308--2335. doi:10.3150/14-BEJ645.

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