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.2018.44
URN: urn:nbn:de:0030-drops-83449
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8344/
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Karwa, Vishesh ; Vadhan, Salil

Finite Sample Differentially Private Confidence Intervals

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LIPIcs-ITCS-2018-44.pdf (0.5 MB)

Abstract

We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially private algorithms to estimate confidence intervals. Crucially, our algorithms guarantee a finite sample coverage, as opposed to an asymptotic coverage. Unlike most previous differentially private algorithms, we do not require the domain of the samples to be bounded. We also prove lower bounds on the expected size of any differentially private confidence set showing that our the parameters are optimal up to polylogarithmic factors.

BibTeX - Entry

@InProceedings{karwa_et_al:LIPIcs:2018:8344,
  author =	{Vishesh Karwa and Salil Vadhan},
  title =	{{Finite Sample Differentially Private Confidence Intervals}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{44:1--44:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Anna R. Karlin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8344},
  URN =		{urn:nbn:de:0030-drops-83449},
  doi =		{10.4230/LIPIcs.ITCS.2018.44},
  annote =	{Keywords: Differential Privacy, Confidence Intervals, Lower bounds, Finite Sample}
}

Keywords: Differential Privacy, Confidence Intervals, Lower bounds, Finite Sample
Collection: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Issue Date: 2018
Date of publication: 12.01.2018

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