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RANDOM
Private Data Stream Analysis for Universal Symmetric Norm Estimation

Authors: Vladimir Braverman, Joel Manning, Zhiwei Steven Wu, and Samson Zhou

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)


Abstract
We study how to release summary statistics on a data stream subject to the constraint of differential privacy. In particular, we focus on releasing the family of symmetric norms, which are invariant under sign-flips and coordinate-wise permutations on an input data stream and include L_p norms, k-support norms, top-k norms, and the box norm as special cases. Although it may be possible to design and analyze a separate mechanism for each symmetric norm, we propose a general parametrizable framework that differentially privately releases a number of sufficient statistics from which the approximation of all symmetric norms can be simultaneously computed. Our framework partitions the coordinates of the underlying frequency vector into different levels based on their magnitude and releases approximate frequencies for the "heavy" coordinates in important levels and releases approximate level sizes for the "light" coordinates in important levels. Surprisingly, our mechanism allows for the release of an arbitrary number of symmetric norm approximations without any overhead or additional loss in privacy. Moreover, our mechanism permits (1+α)-approximation to each of the symmetric norms and can be implemented using sublinear space in the streaming model for many regimes of the accuracy and privacy parameters.

Cite as

Vladimir Braverman, Joel Manning, Zhiwei Steven Wu, and Samson Zhou. Private Data Stream Analysis for Universal Symmetric Norm Estimation. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 45:1-45:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{braverman_et_al:LIPIcs.APPROX/RANDOM.2023.45,
  author =	{Braverman, Vladimir and Manning, Joel and Wu, Zhiwei Steven and Zhou, Samson},
  title =	{{Private Data Stream Analysis for Universal Symmetric Norm Estimation}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{45:1--45:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.45},
  URN =		{urn:nbn:de:0030-drops-188701},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.45},
  annote =	{Keywords: Differential privacy, norm estimation}
}
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