| Paper ID | D2-S1-T4.1 |
| Paper Title |
Local Differential Privacy Is Equivalent to Contraction of an f-Divergence |
| Authors |
Shahab Asoodeh, Harvard University, United States; Maryam Aliakbarpour, University of Massachusetts Amherst, United States; Flavio P. Calmon, Harvard University, United States |
| Session |
D2-S1-T4: Local Differential Privacy |
| Chaired Session: |
Tuesday, 13 July, 22:00 - 22:20 |
| Engagement Session: |
Tuesday, 13 July, 22:20 - 22:40 |
| 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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