|| Local Differential Privacy Is Equivalent to Contraction of an f-Divergence
||Shahab Asoodeh, Harvard University, United States; Maryam Aliakbarpour, University of Massachusetts Amherst, United States; Flavio P. Calmon, Harvard University, United States|
||D2-S1-T4: Local Differential Privacy
||Tuesday, 13 July, 22:00 - 22:20
||Tuesday, 13 July, 22:20 - 22:40
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.