License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FORC.2021.1
URN: urn:nbn:de:0030-drops-138698
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13869/
Ganesh, Arun ;
Zhao, Jiazheng
Privately Answering Counting Queries with Generalized Gaussian Mechanisms
Abstract
We give the first closed-form privacy guarantees for the Generalized Gaussian mechanism (the mechanism that adds noise x to a vector with probability proportional to exp(-(||x||_p/σ)^p) for some σ, p), in the setting of answering k counting (i.e. sensitivity-1) queries about a database with (ε, δ)-differential privacy (in particular, with low ?_∞-error). Just using Generalized Gaussian noise, we obtain a mechanism such that if the true answers to the queries are the vector d, the mechanism outputs answers d̃ with the ?_∞-error guarantee:
?[||d̃ - d||_∞] = O(√{k log log k log(1/δ)}/ε).
This matches the error bound of [Steinke and Ullman, 2017], but using a much simpler mechanism. By composing this mechanism with the sparse vector mechanism (generalizing a technique of [Steinke and Ullman, 2017]), we obtain a mechanism improving the √{k log log k} dependence on k to √{k log log log k}, Our main technical contribution is showing that certain powers of Generalized Gaussians, which follow a Generalized Gamma distribution, are sub-gamma.
In subsequent work, the optimal ?_∞-error bound of O(√{k log (1/δ)}/ε) has been achieved by [Yuval Dagan and Gil Kur, 2020] and [Badih Ghazi et al., 2020] independently. However, the Generalized Gaussian mechanism has some qualitative advantages over the mechanisms used in these papers which may make it of interest to both practitioners and theoreticians, both in the setting of answering counting queries and more generally.
BibTeX - Entry
@InProceedings{ganesh_et_al:LIPIcs.FORC.2021.1,
author = {Ganesh, Arun and Zhao, Jiazheng},
title = {{Privately Answering Counting Queries with Generalized Gaussian Mechanisms}},
booktitle = {2nd Symposium on Foundations of Responsible Computing (FORC 2021)},
pages = {1:1--1:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-187-0},
ISSN = {1868-8969},
year = {2021},
volume = {192},
editor = {Ligett, Katrina and Gupta, Swati},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13869},
URN = {urn:nbn:de:0030-drops-138698},
doi = {10.4230/LIPIcs.FORC.2021.1},
annote = {Keywords: Differential privacy, counting queries, Generalized Gaussians}
}
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Keywords: |
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Differential privacy, counting queries, Generalized Gaussians |
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Collection: |
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2nd Symposium on Foundations of Responsible Computing (FORC 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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31.05.2021 |
