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

Abstract: 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 classic 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 all the 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. In this paper we show that for estimating the integrated square of a density, sequentially interactive procedures improve substantially over the best possible non-interactive procedure in terms of minimax rate of estimation. In particular, in the non-interactive scenario we identify an elbow in the minimax rate at s=34, whereas in the sequentially interactive scenario the elbow is at s=12. This is markedly different from both, the case of direct observations, where the elbow is well known to be at s=14, as well as from the case where Laplace noise is added to the original data, where an elbow at s=94 is obtained. The fact that a particular locally differentially private, but interactive, mechanism improves over the simple non-interactive one is also of great importance for practical implementations of local differential privacy

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Edition: Preprint
• Language: Englisch

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2021
• Creator: Butucea, Cristina ; Rohde, Angelika ; Steinberger, Lukas
• Contributor: Abteilung für Mathematische Stochastik, Prof. Dr. Angelika Rohde

Further information

• URN: urn:nbn:de:bsz:25-freidok-2202550
• Rights: Kein Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:48 PM CET