License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2018.32
URN: urn:nbn:de:0030-drops-99800
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Matheny, Michael ; Phillips, Jeff M.

Computing Approximate Statistical Discrepancy

LIPIcs-ISAAC-2018-32.pdf (0.9 MB)


Consider a geometric range space (X,A) where X is comprised of the union of a red set R and blue set B. Let Phi(A) define the absolute difference between the fraction of red and fraction of blue points which fall in the range A. The maximum discrepancy range A^* = arg max_{A in (X,A)} Phi(A). Our goal is to find some A^ in (X,A) such that Phi(A^*) - Phi(A^) <= epsilon. We develop general algorithms for this approximation problem for range spaces with bounded VC-dimension, as well as significant improvements for specific geometric range spaces defined by balls, halfspaces, and axis-aligned rectangles. This problem has direct applications in discrepancy evaluation and classification, and we also show an improved reduction to a class of problems in spatial scan statistics.

BibTeX - Entry

  author =	{Michael Matheny and Jeff M. Phillips},
  title =	{{Computing Approximate Statistical Discrepancy}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-99800},
  doi =		{10.4230/LIPIcs.ISAAC.2018.32},
  annote =	{Keywords: Scan Statistics, Discrepancy, Rectangles}

Keywords: Scan Statistics, Discrepancy, Rectangles
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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