Approximating the distribution of the median and other robust estimators on uncertain data

Kevin A. Buchin, Jeff M. Phillips, Pingfan Tang

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Abstract

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has a discrete probability distribution describing its location. The probabilistic nature of uncertain data makes it challenging to compute such estimators, since the true value of the estimator is now described by a distribution rather than a single point. We show how to construct and estimate the distribution of the median of a point set. Building the approximate support of the distribution takes near-linear time, and assigning probability to that support takes quadratic time. We also develop a general approximation technique for distributions of robust estimators with respect to ranges with bounded VC dimension. This includes the geometric median for high dimensions and the Siegel estimator for linear regression.
Original languageEnglish
Title of host publication34th International Symposium on Computational Geometry, SoCG 2018
EditorsCsaba D. Toth, Bettina Speckmann
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Number of pages14
ISBN (Electronic)9783959770668
DOIs
Publication statusPublished - 1 Jun 2018
Event34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Hungary
Duration: 11 Jun 201814 Jun 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume99
ISSN (Print)1868-8969

Conference

Conference34th International Symposium on Computational Geometry, SoCG 2018
CountryHungary
CityBudapest
Period11/06/1814/06/18

Keywords

  • Uncertain Data
  • Robust Estimators
  • Geometric Median
  • Tukey Median
  • Robust estimators
  • Geometric median
  • Tukey median
  • Uncertain data

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  • Cite this

    Buchin, K. A., Phillips, J. M., & Tang, P. (2018). Approximating the distribution of the median and other robust estimators on uncertain data. In C. D. Toth, & B. Speckmann (Eds.), 34th International Symposium on Computational Geometry, SoCG 2018 [16] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 99). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.16