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

• URL: http://arxiv.org/abs/2102.01258v1
• Date: Tue, 2 Feb 2021 02:18:12 GMT
• Title: Local Differential Privacy Is Equivalent to Contraction of $E_\gamma$-Divergence
• Authors: Shahab Asoodeh, Maryam Aliakbarpour, and Flavio P. Calmon
• Abstract summary: We 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.
• Score: 7.807294944710216
• License: http://creativecommons.org/licenses/by/4.0/
• 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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