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Article Dans Une Revue Annals of Statistics Année : 2023

Interactive versus noninteractive locally differentially private estimation: Two elbows for the quadratic functional

Résumé

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 noninteractive 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 noninteractive procedure in terms of minimax rate of estimation.

Dates et versions

hal-04425360 , version 1 (29-01-2024)

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Cristina Butucea, Angelika Rohde, Lukas Steinberger. Interactive versus noninteractive locally differentially private estimation: Two elbows for the quadratic functional. Annals of Statistics, 2023, 51 (2), ⟨10.1214/22-AOS2254⟩. ⟨hal-04425360⟩
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