Phase transitions for support recovery under local differential privacy

DOI10.4171/msl/37arXiv2011.14881MaRDI QIDQ6062699

Adrien Saumard, Cristina Butucea, Amandine Dubois

Publication date: 6 November 2023

Published in: Mathematical Statistics and Learning (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.14881

zbMATH Keywords

phase transitionvariable selectionsupport recoveryminimax rateslocal differential privacystrong log-concavity

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Cites Work

• Unnamed Item
• Unnamed Item
• Global rates of convergence of the MLEs of log-concave and \(s\)-concave densities
• Log-concavity and strong log-concavity: a review
• Log-location-scale-log-concave distributions for survival and reliability analysis
• Some applications of mass transport to Gaussian-type inequalities
• From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
• An extremal property of the normal distribution, with a discrete analog
• Variable selection with Hamming loss
• Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
• Set structured global empirical risk minimizers are rate optimal in general dimensions
• Sharp optimal recovery in the two component Gaussian mixture model
• Local differential privacy: elbow effect in optimal density estimation and adaptation over Besov ellipsoids
• Geometrizing rates of convergence under local differential privacy constraints
• Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
• Log-concave probability and its applications
• Concentration Inequalities
• Concentration phenomena in high dimensional geometry
• Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
• Our Data, Ourselves: Privacy Via Distributed Noise Generation
• The Regularity of Mappings with a Convex Potential
• Minimax Optimal Procedures for Locally Private Estimation
• Optimal Variable Selection and Adaptive Noisy Compressed Sensing
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances
• A Statistical Framework for Differential Privacy
• Testing Statistical Hypotheses
• Theoretical Guarantees for Approximate Sampling from Smooth and Log-Concave Densities
• Theory of Cryptography
• Introduction to nonparametric estimation
• Monotonicity properties of optimal transportation and the FKG and related inequalities
• Interactive versus noninteractive locally differentially private estimation: two elbows for the quadratic functional