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arXiv · 1702.05985

Fano's inequality for random variables

Sebastien Gerchinovitz·Pierre Ménard·Gilles Stoltz
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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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Sebastien Gerchinovitz, Pierre Ménard, Gilles Stoltz. 2017-02-20. Fano's inequality for random variables. https://arxiv.org/abs/1702.05985

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