The self-improving sorter proposed by Ailon et al. consists of two phases: a relatively long training phase and rapid operation phase. In this study, we have developed an efficient way to further improve this sorter by approximating its training phase to be faster but not sacrificing much performance in the operation phase. It is very necessary to ensure the accuracy of the estimated entropy when we test the performance of this approximated sorter. Thus we further developed a useful formula to calculate an upper bound for the 'error' of the estimated entropy derived from the input data with unknown distributions. Our work will contribute to the better use of this self-improving sorter for huge data in a quicker way.

中文翻译：

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近似自改进排序器的改进及其估计熵的误差分析

Ailon 等人提出的自我改进型分拣机。包括两个阶段：相对较长的训练阶段和快速操作阶段。在这项研究中，我们开发了一种有效的方法来进一步改进这种分拣机，通过将其训练阶段近似为更快但不牺牲操作阶段的太多性能。我们在测试这个近似排序器的性能时，非常有必要保证估计熵的准确性。因此，我们进一步开发了一个有用的公式来计算从具有未知分布的输入数据导出的估计熵的“误差”的上限。我们的工作将有助于更好地使用这种自我改进的分类器以更快的方式处理大量数据。