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Minimax density estimation in the adversarial framework under local differential privacy

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  • معلومة اضافية
    • Contributors:
      Institut de Mathématiques de Toulouse UMR5219 (IMT); Université Toulouse Capitole (UT Capitole); Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse); Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J); Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3); Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS); Institut National des Sciences Appliquées - Toulouse (INSA Toulouse); Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT); Université Paris Nanterre (UPN); Modélisation aléatoire de Paris X (MODAL'X); Université Paris Nanterre (UPN)-Centre National de la Recherche Scientifique (CNRS); ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011); ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019)
    • بيانات النشر:
      HAL CCSD
    • الموضوع:
      2024
    • Collection:
      Université Toulouse 2 - Jean Jaurès: HAL
    • نبذة مختصرة :
      We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates under local differential privacy over Sobolev spaces. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates.
    • Relation:
      hal-04522328; https://hal.science/hal-04522328; https://hal.science/hal-04522328/document; https://hal.science/hal-04522328/file/PrivateDensityEstim_HAL.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.661F1884