Pan-Private Uniformity Testing

Kareem Amin, Matthew Joseph, Jieming Mao
Proceedings of Thirty Third Conference on Learning Theory, PMLR 125:183-218, 2020.

Abstract

A centrally differentially private algorithm maps raw data to differentially private outputs. In contrast, a locally differentially private algorithm may only access data through public interaction with data holders, and this interaction must be a differentially private function of the data. We study the intermediate model of \emph{pan-privacy}. Unlike a locally private algorithm, a pan-private algorithm receives data in the clear. Unlike a centrally private algorithm, the algorithm receives data one element at a time and must maintain a differentially private internal state while processing this stream. First, we show that pan-privacy against multiple intrusions on the internal state is equivalent to sequentially interactive local privacy. Next, we contextualize pan-privacy against a single intrusion by analyzing the sample complexity of uniformity testing over domain [k]. Focusing on the dependence on k, centrally private uniformity testing has sample complexity Θ(√k), while noninteractive locally private uniformity testing has sample complexity Θ(k). We show that the sample complexity of pan-private uniformity testing is Θ(k2/3). By a new Ω(k) lower bound for the sequentially interactive setting, we also separate pan-private from sequentially interactive locally private and multi-intrusion pan-private uniformity testing.

Cite this Paper

BibTeX
@InProceedings{pmlr-v125-amin20a, title = {Pan-Private Uniformity Testing}, author = {Amin, Kareem and Joseph, Matthew and Mao, Jieming}, booktitle = {Proceedings of Thirty Third Conference on Learning Theory}, pages = {183--218}, year = {2020}, editor = {Abernethy, Jacob and Agarwal, Shivani}, volume = {125}, series = {Proceedings of Machine Learning Research}, month = {09--12 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v125/amin20a/amin20a.pdf}, url = {https://proceedings.mlr.press/v125/amin20a.html}, abstract = { A centrally differentially private algorithm maps raw data to differentially private outputs. In contrast, a locally differentially private algorithm may only access data through public interaction with data holders, and this interaction must be a differentially private function of the data. We study the intermediate model of \emph{pan-privacy}. Unlike a locally private algorithm, a pan-private algorithm receives data in the clear. Unlike a centrally private algorithm, the algorithm receives data one element at a time and must maintain a differentially private internal state while processing this stream. First, we show that pan-privacy against multiple intrusions on the internal state is equivalent to sequentially interactive local privacy. Next, we contextualize pan-privacy against a single intrusion by analyzing the sample complexity of uniformity testing over domain $[k]$. Focusing on the dependence on $k$, centrally private uniformity testing has sample complexity $\Theta(\sqrt{k})$, while noninteractive locally private uniformity testing has sample complexity $\Theta(k)$. We show that the sample complexity of pan-private uniformity testing is $\Theta(k^{2/3})$. By a new $\Omega(k)$ lower bound for the sequentially interactive setting, we also separate pan-private from sequentially interactive locally private and multi-intrusion pan-private uniformity testing.} }
Endnote
%0 Conference Paper %T Pan-Private Uniformity Testing %A Kareem Amin %A Matthew Joseph %A Jieming Mao %B Proceedings of Thirty Third Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2020 %E Jacob Abernethy %E Shivani Agarwal %F pmlr-v125-amin20a %I PMLR %P 183--218 %U https://proceedings.mlr.press/v125/amin20a.html %V 125 %X A centrally differentially private algorithm maps raw data to differentially private outputs. In contrast, a locally differentially private algorithm may only access data through public interaction with data holders, and this interaction must be a differentially private function of the data. We study the intermediate model of \emph{pan-privacy}. Unlike a locally private algorithm, a pan-private algorithm receives data in the clear. Unlike a centrally private algorithm, the algorithm receives data one element at a time and must maintain a differentially private internal state while processing this stream. First, we show that pan-privacy against multiple intrusions on the internal state is equivalent to sequentially interactive local privacy. Next, we contextualize pan-privacy against a single intrusion by analyzing the sample complexity of uniformity testing over domain $[k]$. Focusing on the dependence on $k$, centrally private uniformity testing has sample complexity $\Theta(\sqrt{k})$, while noninteractive locally private uniformity testing has sample complexity $\Theta(k)$. We show that the sample complexity of pan-private uniformity testing is $\Theta(k^{2/3})$. By a new $\Omega(k)$ lower bound for the sequentially interactive setting, we also separate pan-private from sequentially interactive locally private and multi-intrusion pan-private uniformity testing.
APA
Amin, K., Joseph, M. & Mao, J.. (2020). Pan-Private Uniformity Testing. Proceedings of Thirty Third Conference on Learning Theory, in Proceedings of Machine Learning Research 125:183-218 Available from https://proceedings.mlr.press/v125/amin20a.html.

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