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Fano's inequality for random variables

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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); Laboratoire de Mathématiques d'Orsay (LMO); Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS); Statistique mathématique et apprentissage (CELESTE); Inria Saclay - Ile de France; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO); Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
    • بيانات النشر:
      HAL CCSD
      Institute of Mathematical Statistics (IMS)
    • الموضوع:
      2020
    • Collection:
      Université Toulouse 2 - Jean Jaurès: HAL
    • نبذة مختصرة :
      International audience ; We extend Fano's inequality, which controls the average probability of events in terms of the average of some f--divergences, to work with arbitrary events (not necessarily forming a partition) and even with arbitrary [0,1]--valued random variables, possibly in continuously infinite number. We provide two applications of these extensions, in which the consideration of random variables is particularly handy: we offer new and elegant proofs for existing lower bounds, on Bayesian posterior concentration (minimax or distribution-dependent) rates and on the regret in non-stochastic sequential learning.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/1702.05985; hal-01470862; https://hal.science/hal-01470862; https://hal.science/hal-01470862v3/document; https://hal.science/hal-01470862v3/file/Fano-HAL-final.pdf; ARXIV: 1702.05985
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.E4F99145