Optimal Private Discrete Distribution Estimation with One-bit Communication

Autor:	Nam, Seung-Hyun, Tan, Vincent Y. F., Lee, Si-Hyeon
Rok vydání:	2023
Předmět:	Computer Science - Information Theory Computer Science - Cryptography and Security
Druh dokumentu:	Working Paper
Popis:	We consider a private discrete distribution estimation problem with one-bit communication constraint. The privacy constraints are imposed with respect to the local differential privacy and the maximal leakage. The estimation error is quantified by the worst-case mean squared error. We completely characterize the first-order asymptotics of this privacy-utility trade-off under the one-bit communication constraint for both types of privacy constraints by using ideas from local asymptotic normality and the resolution of a block design mechanism. These results demonstrate the optimal dependence of the privacy-utility trade-off under the one-bit communication constraint in terms of the parameters of the privacy constraint and the size of the alphabet of the discrete distribution. Comment: 13 pages, 5 figures, and 1 page of supplementary material
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.11005 Zobrazit plný text záznamu View this record from Arxiv