A Tighter Converse for the Locally Differentially Private Discrete Distribution Estimation Under the One-bit Communication Constraint

We consider a discrete distribution estimation problem under the local differential privacy and the one-bit communication constraints. A fundamental privacy-utility tradeoff in this problem is formulated as the minimax squared loss. We show a tighter lower bound on the minimax squared loss, which ha...

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Bibliographic Details
Published inIEEE signal processing letters Vol. 29; pp. 1923 - 1927
Main Authors Nam, Seung-Hyun, Lee, Si-Hyeon
Format Journal Article
LanguageEnglish
Published New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
communication constraint
Coordinates
Costs
Differential privacy
distribution estimation
Estimation
Fisher information
Local differential privacy
Lower bounds
Minimax technique
Privacy
Servers
Toy manufacturing industry
Upper bound
Upper bounds
van Trees inequ- ality
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Summary:We consider a discrete distribution estimation problem under the local differential privacy and the one-bit communication constraints. A fundamental privacy-utility tradeoff in this problem is formulated as the minimax squared loss. We show a tighter lower bound on the minimax squared loss, which has exactly the same form with the upper bound by the recursive Hadamard response by Chen et al. up to a constant factor of 4 for arbitrary LDP constraint and arbitrary finite data space. To derive the lower bound, we modify the van Trees inequality to involve a symmetrized Fisher information, which is invariant under the choice of the coordinate system on the probability simplex. We further characterize the maximum of the symmetrized Fisher information by considering the joint effect of the privacy and the communication constraints.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2022.3205276