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.
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Contributor : Gilles Stoltz <>
Submitted on : Tuesday, September 18, 2018 - 9:38:12 AM
Last modification on : Friday, April 12, 2019 - 4:22:51 PM
Document(s) archivé(s) le : Wednesday, December 19, 2018 - 1:13:32 PM


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  • HAL Id : hal-01470862, version 2
  • ARXIV : 1702.05985


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



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