Private Quantiles Estimation in the Presence of Atoms - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Private Quantiles Estimation in the Presence of Atoms

Résumé

We address the differentially private estimation of multiple quantiles (MQ) of a dataset, a key building block in modern data analysis. We apply the recent non-smoothed Inverse Sensitivity (IS) mechanism to this specific problem and establish that the resulting method is closely related to the current state-ofthe-art, the JointExp algorithm, sharing in particular the same computational complexity and a similar efficiency. However, we demonstrate both theoretically and empirically that (non-smoothed) JointExp suffers from an important lack of performance in the case of peaked distributions, with a potentially catastrophic impact in the presence of atoms. While its smoothed version would allow to leverage the performance guarantees of IS, it remains an open challenge to implement. As a proxy to fix the problem we propose a simple and numerically efficient method called Heuristically Smoothed JointExp (HSJointExp), which is endowed with performance guarantees for a broad class of distributions and achieves results that are orders of magnitude better on problematic datasets.
Fichier principal
Vignette du fichier
hal.pdf (993.88 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03572701 , version 1 (14-02-2022)
hal-03572701 , version 2 (08-02-2023)

Identifiants

  • HAL Id : hal-03572701 , version 1

Citer

Clément Sébastien Lalanne, Clément Gastaud, Nicolas Grislain, Aurélien Garivier, Rémi Gribonval. Private Quantiles Estimation in the Presence of Atoms. 2022. ⟨hal-03572701v1⟩

Collections

INSERM
149 Consultations
117 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More