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DOI: 10.4230/LIPIcs.ITCS.2024.3

Differentially Private Medians and Interior Points for Non-Pathological Data

Authors: Maryam Aliakbarpour, Rose Silver, Thomas Steinke, and Jonathan Ullman

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract

We construct sample-efficient differentially private estimators for the approximate-median and interior-point problems, that can be applied to arbitrary input distributions over ℝ satisfying very mild statistical assumptions. Our results stand in contrast to the surprising negative result of Bun et al. (FOCS 2015), which showed that private estimators with finite sample complexity cannot produce interior points on arbitrary distributions.

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Maryam Aliakbarpour, Rose Silver, Thomas Steinke, and Jonathan Ullman. Differentially Private Medians and Interior Points for Non-Pathological Data. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{aliakbarpour_et_al:LIPIcs.ITCS.2024.3,
  author =	{Aliakbarpour, Maryam and Silver, Rose and Steinke, Thomas and Ullman, Jonathan},
  title =	{{Differentially Private Medians and Interior Points for Non-Pathological Data}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{3:1--3:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.3},
  URN =		{urn:nbn:de:0030-drops-195313},
  doi =		{10.4230/LIPIcs.ITCS.2024.3},
  annote =	{Keywords: Differential Privacy, Statistical Estimation, Approximate Medians, Interior Point Problem}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2020.69

Testing Properties of Multiple Distributions with Few Samples

Authors: Maryam Aliakbarpour and Sandeep Silwal

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

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.

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Maryam Aliakbarpour and Sandeep Silwal. Testing Properties of Multiple Distributions with Few Samples. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 69:1-69:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aliakbarpour_et_al:LIPIcs.ITCS.2020.69,
  author =	{Aliakbarpour, Maryam and Silwal, Sandeep},
  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 =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.69},
  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}
}

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Documents authored by Aliakbarpour, Maryam

Differentially Private Medians and Interior Points for Non-Pathological Data

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Testing Properties of Multiple Distributions with Few Samples

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