随机变量的Fano不等式
Fano's inequality for random variables
摘要：
我们延长法诺的不等式，它控制的平均概率的事件的平均一些$f$ -发散，工作与任意事件（不一定形成一个分区），甚至与任意$[0,1]$ -值随机变量，可能在连续无穷多。我们提供了两个应用这些扩展，其中考虑随机变量是特别方便：我们提供了新的和优雅的证明现有的下界，贝叶斯后验浓度（极大极小或分布依赖）率和非随机顺序学习的遗憾。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
