Hypothesis Testing Interpretations and Renyi Differential Privacy

Borja Balle, Gilles Barthe, Marco Gaboardi, Justin Hsu, Tetsuya Sato
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2496-2506, 2020.

Abstract

Differential privacy is a de facto standard in data privacy, with applicationsin the public and private sectors. One way of explaining differential privacy,which is particularly appealing to statistician and social scientists, is bymeans of its statistical hypothesis testing interpretation. Informally, onecannot effectively test whether a specific individual has contributed her databy observing the output of a private mechanism—any test cannot have bothhigh significance and high power.In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation.These conditions are useful to analyze the distinguishing power of divergencesand we use them to study the hypothesis testing interpretation of somerelaxations of differential privacy based on Renyi divergence. Ouranalysis also results in an improved conversion rule between these definitionsand differential privacy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-balle20a, title = {Hypothesis Testing Interpretations and Renyi Differential Privacy}, author = {Balle, Borja and Barthe, Gilles and Gaboardi, Marco and Hsu, Justin and Sato, Tetsuya}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2496--2506}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/balle20a/balle20a.pdf}, url = {https://proceedings.mlr.press/v108/balle20a.html}, abstract = {Differential privacy is a de facto standard in data privacy, with applicationsin the public and private sectors. One way of explaining differential privacy,which is particularly appealing to statistician and social scientists, is bymeans of its statistical hypothesis testing interpretation. Informally, onecannot effectively test whether a specific individual has contributed her databy observing the output of a private mechanism—any test cannot have bothhigh significance and high power.In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation.These conditions are useful to analyze the distinguishing power of divergencesand we use them to study the hypothesis testing interpretation of somerelaxations of differential privacy based on Renyi divergence. Ouranalysis also results in an improved conversion rule between these definitionsand differential privacy.} }
Endnote
%0 Conference Paper %T Hypothesis Testing Interpretations and Renyi Differential Privacy %A Borja Balle %A Gilles Barthe %A Marco Gaboardi %A Justin Hsu %A Tetsuya Sato %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-balle20a %I PMLR %P 2496--2506 %U https://proceedings.mlr.press/v108/balle20a.html %V 108 %X Differential privacy is a de facto standard in data privacy, with applicationsin the public and private sectors. One way of explaining differential privacy,which is particularly appealing to statistician and social scientists, is bymeans of its statistical hypothesis testing interpretation. Informally, onecannot effectively test whether a specific individual has contributed her databy observing the output of a private mechanism—any test cannot have bothhigh significance and high power.In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation.These conditions are useful to analyze the distinguishing power of divergencesand we use them to study the hypothesis testing interpretation of somerelaxations of differential privacy based on Renyi divergence. Ouranalysis also results in an improved conversion rule between these definitionsand differential privacy.
APA
Balle, B., Barthe, G., Gaboardi, M., Hsu, J. & Sato, T.. (2020). Hypothesis Testing Interpretations and Renyi Differential Privacy. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2496-2506 Available from https://proceedings.mlr.press/v108/balle20a.html.

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