RT Journal Article
SR 00
A1 Gadat, Sébastien
A1 Lalanne, Clément
T1 Privately learning smooth distribution on the hypercube by projections
JF Proceedings of Machine Learning Research
YR 2024
FD 2024
VO Vol. 235
SP 25936 
OP  25975
AB 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.
PB JMLR
SN 2640-3498
LK https://publications.ut-capitole.fr/id/eprint/50353/
UL http://tse-fr.eu/pub/130279