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DOI: 10.4230/LIPIcs.ICALP.2017.8

Near-Optimal Closeness Testing of Discrete Histogram Distributions

Authors: Ilias Diakonikolas, Daniel M. Kane, and Vladimir Nikishkin

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract

We investigate the problem of testing the equivalence between two discrete histograms. A k-histogram over [n] is a probability distribution that is piecewise constant over some set of k intervals over [n]. Histograms have been extensively studied in computer science and statistics. Given a set of samples from two k-histogram distributions p, q over [n], we want to distinguish (with high probability) between the cases that p = q and ||p ? q||_1 >= epsilon. The main contribution of this paper is a new algorithm for this testing problem and a nearly matching information-theoretic lower bound. Specifically, the sample complexity of our algorithm matches our lower bound up to a logarithmic factor, improving on previous work by polynomial factors in the relevant parameters. Our algorithmic approach applies in a more general setting and yields improved sample upper bounds for testing closeness of other structured distributions as well.

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Ilias Diakonikolas, Daniel M. Kane, and Vladimir Nikishkin. Near-Optimal Closeness Testing of Discrete Histogram Distributions. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{diakonikolas_et_al:LIPIcs.ICALP.2017.8,
  author =	{Diakonikolas, Ilias and Kane, Daniel M. and Nikishkin, Vladimir},
  title =	{{Near-Optimal Closeness Testing of Discrete Histogram Distributions}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.8},
  URN =		{urn:nbn:de:0030-drops-74937},
  doi =		{10.4230/LIPIcs.ICALP.2017.8},
  annote =	{Keywords: distribution testing, histograms, closeness testing}
}

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Near-Optimal Closeness Testing of Discrete Histogram Distributions

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