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Local Differential Privacy Is Equivalent to Contraction of -Divergence
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 -divergence. We then use this equivalent formula
to express LDP guarantees of privacy mechanisms in terms of contraction
coefficients of arbitrary -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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