Geometrizing rates of convergence under local differential privacy constraints

DOI10.1214/19-AOS1901zbMath1457.62396arXiv1805.01422MaRDI QIDQ2215754

Lukas Steinberger, Angelika Rohde

Publication date: 14 December 2020

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01422

zbMATH Keywords

data privacy protectionconstructing rate optimal privatization mechanisms and estimatorsprivate minimax risk

Mathematics Subject Classification ID

Density estimation (62G07) Functional data analysis (62R10) Nonparametric estimation (62G05) Minimax procedures in statistical decision theory (62C20)

Related Items (13)

Local differential privacy: elbow effect in optimal density estimation and adaptation over Besov ellipsoids ⋮ Multivariate density estimation from privatised data: universal consistency and minimax rates ⋮ Phase transitions for support recovery under local differential privacy ⋮ Distribution-invariant differential privacy ⋮ Goodness-of-fit testing for Hölder continuous densities under local differential privacy ⋮ The right complexity measure in locally private estimation: it is not the Fisher information ⋮ Density estimation under local differential privacy and Hellinger loss ⋮ Interactive versus noninteractive locally differentially private estimation: two elbows for the quadratic functional ⋮ On robustness and local differential privacy ⋮ On lower bounds for the bias-variance trade-off ⋮ On density estimation at a fixed point under local differential privacy ⋮ Strongly universally consistent nonparametric regression and classification with privatised data ⋮ The cost of privacy: optimal rates of convergence for parameter estimation with differential privacy

Cites Work

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• Advances in Cryptology – CRYPTO 2004
• Privacy-preserving statistical estimation with optimal convergence rates
• Testing Statistical Hypotheses
• Optimale Tests und ungünstigste Verteilungen
• Theory of Cryptography
• Introduction to nonparametric estimation
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