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