TY  - JOUR
CY  - Cambridge
ID  - publications50353
UR  - http://tse-fr.eu/pub/130279
A1  - Gadat, Sébastien
A1  - Lalanne, Clément
Y1  - 2024///
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  - JMLR
JF  - Proceedings of Machine Learning Research
VL  - Vol. 235
SN  - 2640-3498
TI  - Privately learning smooth distribution on the hypercube by projections
SP  - 25936 
AV  - none
EP  -  25975
ER  -