论文标题
量度不平等的新颖变化，适用于Pac-Bayesian边界和Monte Carlo估计
Novel Change of Measure Inequalities with Applications to PAC-Bayesian Bounds and Monte Carlo Estimation
论文作者
论文摘要
我们引入了两个分歧家庭的几种新颖的措施不平等变化：$ f $ - diverences和$α$ - diverences。我们展示了$ f $ divergences的变异表示如何导致衡量标准不平等的新变化。我们还提出了$α$ diverences的量度不平等的多重变化，以及Hammersley-Chapman-Robbins不平等的广义版本。最后，我们介绍了措施变化不平等的几个应用，包括用于各种损失类别的Pac-bayesian界限和蒙特卡洛估计值的非反应间隔。
We introduce several novel change of measure inequalities for two families of divergences: $f$-divergences and $α$-divergences. We show how the variational representation for $f$-divergences leads to novel change of measure inequalities. We also present a multiplicative change of measure inequality for $α$-divergences and a generalized version of Hammersley-Chapman-Robbins inequality. Finally, we present several applications of our change of measure inequalities, including PAC-Bayesian bounds for various classes of losses and non-asymptotic intervals for Monte Carlo estimates.
