eprintid: 50353 rev_number: 10 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/05/03/53 datestamp: 2025-02-03 08:46:00 lastmod: 2025-02-11 15:03:28 status_changed: 2025-02-11 15:03:28 type: article metadata_visibility: show creators_name: Gadat, Sébastien creators_name: Lalanne, Clément creators_id: sebastien.gadat@tse-fr.eu creators_idrefppn: 080889433 creators_idrefppn: 272832871 creators_halaffid: 1002422 title: Privately learning smooth distribution on the hypercube by projections ispublished: pub subjects: subjects_ECO 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. date: 2024 date_type: published publisher: JMLR official_url: http://tse-fr.eu/pub/130279 faculty: tse divisions: tse language: en has_fulltext: FALSE view_date_year: 2024 full_text_status: none publication: Proceedings of Machine Learning Research volume: Vol. 235 place_of_pub: Cambridge pagerange: 25936 - 25975 refereed: TRUE issn: 2640-3498 oai_identifier: oai:tse-fr.eu:130279 harvester_local_overwrite: volume harvester_local_overwrite: pending harvester_local_overwrite: creators_idrefppn harvester_local_overwrite: creators_halaffid harvester_local_overwrite: publisher harvester_local_overwrite: place_of_pub harvester_local_overwrite: hal_id harvester_local_overwrite: hal_version harvester_local_overwrite: hal_url harvester_local_overwrite: hal_passwd harvester_local_overwrite: creators_id oai_lastmod: 2025-02-10T07:59:08Z oai_set: tse site: ut1 hal_id: hal-04926471 hal_passwd: as#pxlr hal_version: 1 hal_url: https://hal.science/hal-04926471 citation: Gadat, Sébastien and Lalanne, Clément (2024) Privately learning smooth distribution on the hypercube by projections. Proceedings of Machine Learning Research, Vol. 235. 25936 - 25975.