Interactive versus non-interactive locally differentially private estimation: Two elbows for the quadratic functional

Understand

Local differential privacy has recently received increasing attention from the statistics community as a valuable tool to protect the privacy of individual data owners without the need of a trusted third party.

• Similar to the classical notion of randomized response, the idea is that data owners randomize their true information locally and only release the perturbed data.
• Many different protocols for such local perturbation procedures can be designed.
• In most estimation problems studied in the literature so far, however, no significant difference in terms of minimax risk between purely non-interactive protocols and protocols that allow for some amount of interaction between individual data providers could be observed.