TY  - RPRT
CY  - Toulouse
ID  - publications48670
UR  - http://tse-fr.eu/pub/129117
A1  - Lalanne, Clément
A1  - Gadat, Sébastien
Y1  - 2024/02//
N2  - 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  - TSE Working Paper
T3  - TSE Working Paper
M1  - working_paper
TI  - Privately Learning Smooth Distributions on the Hypercube by Projections
AV  - public
EP  - 46
ER  -