Differential privacy for symmetric log-concave mechanisms

Staal A. Vinterbo
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6270-6291, 2022.

Abstract

Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for Gaussian noise was published. This condition allows the computation of the minimum privacy-preserving scale for this distribution. We extend this work and provide a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for all symmetric and log-concave noise densities. Our results allow fine-grained tailoring of the noise distribution to the dimensionality of the query result. We demonstrate that this can yield significantly lower mean squared errors than those incurred by the currently used Laplace and Gaussian mechanisms for the same $\epsilon$ and $\delta$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-vinterbo22a, title = { Differential privacy for symmetric log-concave mechanisms }, author = {Vinterbo, Staal A.}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6270--6291}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/vinterbo22a/vinterbo22a.pdf}, url = {https://proceedings.mlr.press/v151/vinterbo22a.html}, abstract = { Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for Gaussian noise was published. This condition allows the computation of the minimum privacy-preserving scale for this distribution. We extend this work and provide a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for all symmetric and log-concave noise densities. Our results allow fine-grained tailoring of the noise distribution to the dimensionality of the query result. We demonstrate that this can yield significantly lower mean squared errors than those incurred by the currently used Laplace and Gaussian mechanisms for the same $\epsilon$ and $\delta$. } }
Endnote
%0 Conference Paper %T Differential privacy for symmetric log-concave mechanisms %A Staal A. Vinterbo %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-vinterbo22a %I PMLR %P 6270--6291 %U https://proceedings.mlr.press/v151/vinterbo22a.html %V 151 %X Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for Gaussian noise was published. This condition allows the computation of the minimum privacy-preserving scale for this distribution. We extend this work and provide a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for all symmetric and log-concave noise densities. Our results allow fine-grained tailoring of the noise distribution to the dimensionality of the query result. We demonstrate that this can yield significantly lower mean squared errors than those incurred by the currently used Laplace and Gaussian mechanisms for the same $\epsilon$ and $\delta$.
APA
Vinterbo, S.A.. (2022). Differential privacy for symmetric log-concave mechanisms . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6270-6291 Available from https://proceedings.mlr.press/v151/vinterbo22a.html.

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