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Computing Approximate Statistical Discrepancy

Authors Michael Matheny, Jeff M. Phillips

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Michael Matheny
  • University of Utah, Salt Lake City, USA
Jeff M. Phillips
  • University of Utah, Salt Lake City, USA

Funding

  • Phillips, Jeff M.: Thanks to supported by NSF CCF-1350888, IIS-1251019, ACI-1443046, CNS-1514520, and CNS-1564287.

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Michael Matheny and Jeff M. Phillips. Computing Approximate Statistical Discrepancy. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ISAAC.2018.32

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Scan Statistics
  • Discrepancy
  • Rectangles

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