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.ITCS.2020.69
URN: urn:nbn:de:0030-drops-117545
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11754/
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Aliakbarpour, Maryam ; Silwal, Sandeep

Testing Properties of Multiple Distributions with Few Samples

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LIPIcs-ITCS-2020-69.pdf (0.7 MB)

Abstract

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from s distributions, p_1, p_2, …, p_s, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the p_i’s are uniform or ε-far from being uniform in ℓ_1-distance (2) Identity Testing: Testing whether all the p_i’s are equal to an explicitly given distribution q or ε-far from q in ℓ_1-distance, and (3) Closeness Testing: Testing whether all the p_i’s are equal to a distribution q which we have sample access to, or ε-far from q in ℓ_1-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.

BibTeX - Entry

@InProceedings{aliakbarpour_et_al:LIPIcs:2020:11754,
  author =	{Maryam Aliakbarpour and Sandeep Silwal},
  title =	{{Testing Properties of Multiple Distributions with Few Samples}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{69:1--69:41},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11754},
  URN =		{urn:nbn:de:0030-drops-117545},
  doi =		{10.4230/LIPIcs.ITCS.2020.69},
  annote =	{Keywords: Hypothesis Testing, Property Testing, Distribution Testing, Identity Testing, Closeness Testing, Multiple Sources}
}

Keywords: Hypothesis Testing, Property Testing, Distribution Testing, Identity Testing, Closeness Testing, Multiple Sources
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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