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.STACS.2016.25
URN: urn:nbn:de:0030-drops-57260
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5726/
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Canonne, Clément L. ; Diakonikolas, Ilias ; Gouleakis, Themis ; Rubinfeld, Ronitt

Testing Shape Restrictions of Discrete Distributions

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Abstract

We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution D over [n] and a property P, the goal is to distinguish between D in P and l_{1}(D,P)>epsilon. We develop a general algorithm for this question, which applies to a large range of "shape-constrained" properties, including monotone, log-concave, t-modal, piecewise-polynomial, and Poisson Binomial distributions. Moreover, for all cases considered, our algorithm has near-optimal sample complexity with regard to the domain size and is computationally efficient. For most of these classes, we provide the first non-trivial tester in the literature. In addition, we also describe a generic method to prove lower bounds for this problem, and use it to show our upper bounds are nearly tight. Finally, we extend some of our techniques to tolerant testing, deriving nearly-tight upper and lower bounds for the corresponding questions.

BibTeX - Entry

@InProceedings{canonne_et_al:LIPIcs:2016:5726,
  author =	{Cl{\'e}ment L. Canonne and Ilias Diakonikolas and Themis Gouleakis and Ronitt Rubinfeld},
  title =	{{Testing Shape Restrictions of Discrete Distributions}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5726},
  URN =		{urn:nbn:de:0030-drops-57260},
  doi =		{10.4230/LIPIcs.STACS.2016.25},
  annote =	{Keywords: property testing, probability distributions, statistics, lower bounds}
}

Keywords: property testing, probability distributions, statistics, lower bounds
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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