Geometric Median and Robust Estimation in Banach Spaces

@article{Minsker2015GeometricMA,
  title={Geometric Median and Robust Estimation in Banach Spaces},
  author={Stanislav Minsker},
  journal={Bernoulli},
  year={2015},
  volume={21},
  pages={2308-2335}
}
  • Stanislav Minsker
  • Published 2015
  • Mathematics
  • Bernoulli
  • 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… CONTINUE READING

    Figures from this paper.

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 124 CITATIONS

    Non-Asymptotic Inference in a Class of Optimization Problems

    VIEW 9 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    A Unified Approach to Robust Mean Estimation

    VIEW 6 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    On Weighted Multivariate Sign Functions

    VIEW 4 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    Robust Estimation via Robust Gradient Estimation

    VIEW 7 EXCERPTS
    CITES METHODS & BACKGROUND
    HIGHLY INFLUENCED

    Distributed Statistical Estimation and Rates of Convergence in Normal Approximation

    VIEW 4 EXCERPTS
    CITES BACKGROUND & METHODS

    Sub-Gaussian estimators of the mean of a random vector

    VIEW 5 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    Loss Minimization and Parameter Estimation with Heavy Tails

    VIEW 4 EXCERPTS
    HIGHLY INFLUENCED

    On the estimation of the mean of a random vector

    VIEW 5 EXCERPTS
    CITES BACKGROUND
    HIGHLY INFLUENCED

    Estimation robuste pour des distributions à queue lourde

    VIEW 9 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    FILTER CITATIONS BY YEAR

    2014
    2020

    CITATION STATISTICS

    • 14 Highly Influenced Citations

    • Averaged 27 Citations per year from 2017 through 2019

    • 171% Increase in citations per year in 2019 over 2018

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 45 REFERENCES

    Regression Shrinkage and Selection via the Lasso

    VIEW 8 EXCERPTS
    HIGHLY INFLUENTIAL

    Robust empirical mean estimators. arXiv preprint arXiv:1112.3914

    • M. Lerasle, R. I. Oliveira
    • 2011
    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Problem Complexity and Method Efficiency in Optimization

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    Bandits With Heavy Tail

    Robust Lasso With Missing and Grossly Corrupted Observations

    VIEW 2 EXCERPTS

    Bandits with heavy tail. arXiv preprint arXiv:1209.1727

    • S. Bubeck, N. Cesa-Bianchi, G. Lugosi
    • 2012
    VIEW 1 EXCERPT

    A novel M-estimator for robust PCA