Fano's inequality for random variables
Statistics Theory
2019-06-12 v3 Information Theory
math.IT
Statistics Theory
Abstract
We extend Fano's inequality, which controls the average probability of events in terms of the average of some --divergences, to work with arbitrary events (not necessarily forming a partition) and even with arbitrary --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.
Cite
@article{arxiv.1702.05985,
title = {Fano's inequality for random variables},
author = {Sebastien Gerchinovitz and Pierre Ménard and Gilles Stoltz},
journal= {arXiv preprint arXiv:1702.05985},
year = {2019}
}