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arXiv · 2102.01258

Local Differential Privacy Is Equivalent to Contraction of $E_\gamma$-Divergence

Shahab Asoodeh·Maryam Aliakbarpour·Flavio P. Calmon
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Abstract

We investigate the local differential privacy (LDP) guarantees of a randomized privacy mechanism via its contraction properties. We first show that LDP constraints can be equivalently cast in terms of the contraction coefficient of the $E_\gamma$-divergence. We then use this equivalent formula to express LDP guarantees of privacy mechanisms in terms of contraction coefficients of arbitrary $f$-divergences. When combined with standard estimation-theoretic tools (such as Le Cam's and Fano's converse methods), this result allows us to study the trade-off between privacy and utility in several testing and minimax and Bayesian estimation problems.

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Shahab Asoodeh, Maryam Aliakbarpour, Flavio P. Calmon. 2021-02-02. Local Differential Privacy Is Equivalent to Contraction of $E_\gamma$-Divergence. https://arxiv.org/abs/2102.01258

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