Gadat, Sébastien and Lalanne, Clément (2024) Privately learning smooth distribution on the hypercube by projections. Proceedings of Machine Learning Research, Vol. 235. 25936 - 25975.

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Abstract

Fueled by the ever-increasing need for statistics that guarantee the privacy of their training sets, this article studies the centrally-private estimation of Sobolev-smooth densities of probability over the hypercube in dimension d. The contributions of this article are two-fold : Firstly, it generalizes the one-dimensional results of (Lalanne et al., 2023b) to non-integer levels of smoothness and to a high-dimensional setting, which is important for two reasons : it is more suited for modern learning tasks, and it allows understanding the relations between privacy, dimensionality and smoothness, which is a central question with differential privacy. Secondly, this article presents a private strategy of estimation that is data-driven (usually referred to as adaptive in Statistics) in order to privately choose an estimator that achieves a good bias-variance trade-off among a finite family of private projection estimators without prior knowledge of the ground-truth smoothness β. This is achieved by adapting the Lepskii method for private selection, by adding a new penalization term that makes the estimation privacy-aware.

Item Type: Article
Language: English
Date: 2024
Refereed: Yes
Place of Publication: Cambridge
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 03 Feb 2025 08:46
Last Modified: 11 Feb 2025 15:03
OAI Identifier: oai:tse-fr.eu:130279
URI: https://publications.ut-capitole.fr/id/eprint/50353
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