Sharp uniform convergence bounds through empirical centralization
Sharp uniform convergence bounds through empirical centralization
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发表时间：
2020
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通讯作者：
Cyrus Cousins;Matteo Riondato
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作者：
Cyrus Cousins;Matteo Riondato
我们介绍了经验集中式的使用，以从他们的期望中获得新的实用，概率，样本依赖性界限，以使家庭功能的经验手段的上偏差（SD）。我们的边界对最大（即w弱）方差和函数范围具有最佳依赖性，并且对样本数量与现有SD边界的依赖性相同。为了计算实践中的边界，我们开发了经验中心化家族的经验拉德马赫平均值的新型紧密浓缩的蒙特 - 卡洛估计量，并且我们显示了经验w弱方差的新浓度结果。我们的实验评估表明，我们的界限极高的非中央化界限，即使在小样本量下也非常实用。
We introduce the use of empirical centralization to derive novel practical, probabilistic, sample-dependent bounds to the Supremum Deviation (SD) of empirical means of functions in a family from their expectations. Our bounds have optimal dependence on the maximum (i.e., wimpy) variance and the function ranges, and the same dependence on the number of samples as existing SD bounds. To compute the bounds in practice, we develop novel tightly-concentrated Monte-Carlo estimators of the empirical Rademacher average of the empirically-centralized family, and we show novel concentration results for the empirical wimpy variance. Our experimental evaluation shows that our bounds greatly outperform non-centralized bounds and are extremely practical even at small sample sizes.