Fano's inequality for random variables

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01470862
Contributeur : Gilles Stoltz <>
Soumis le : mardi 18 septembre 2018 - 09:38:12
Dernière modification le : samedi 27 octobre 2018 - 01:26:15

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Fano-Statistical-Science--R1.p...
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  • HAL Id : hal-01470862, version 2
  • ARXIV : 1702.05985

Citation

Sebastien Gerchinovitz, Pierre Ménard, Gilles Stoltz. Fano's inequality for random variables. 2018. 〈hal-01470862v2〉

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