Local Differential Privacy Is Equivalent to Contraction of $E_γ$-Divergence
This work provides a new theoretical framework for understanding LDP, which is significant for researchers working on privacy-preserving data analysis.
This paper redefines Local Differential Privacy (LDP) constraints using the contraction coefficient of the E_γ-divergence, and then generalizes this to arbitrary f-divergences. This new formulation enables the study of privacy-utility trade-offs in various statistical problems, including testing and estimation.
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 $E_γ$-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.