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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, June 4, 2019 - 10:43:02 AM
Last modification on : Wednesday, October 14, 2020 - 4:09:55 AM


  • HAL Id : hal-01470862, version 3
  • ARXIV : 1702.05985


Sebastien Gerchinovitz, Pierre Ménard, Gilles Stoltz. Fano's inequality for random variables. Statistical Science, Institute of Mathematical Statistics (IMS), In press. ⟨hal-01470862v3⟩



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