数据放大：实例最优属性估计
Data Amplification: Instance-Optimal Property Estimation
摘要：
最著名和最常用的分布属性估计技术使用插件估计器，用经验频率代替基础分布。我们提出了新的线性时间可计算的估计，显着“放大”的有效数据量。对于各种各样的分布特性，包括四个最流行的分布特性和每个底层分布，它们实现了使用一个随机因子更多样本的频率插件估计器所能达到的精度。具体来说，对于香农熵和一个非常广泛的类的属性，包括$\ell_1$距离，新的估计使用$n$样本，以达到准确性的经验估计与$n\log n$样本。对于支持大小和覆盖率，新的估计器使用$n$样本来实现经验频率的性能，样本量$n$乘以属性值的对数。显着加强了传统的最小最大公式，这些结果不仅适用于最差的分布，但对每一个潜在的分布。此外，对数放大因子是最佳的。各种分布的实验表明，新的估计优于以前的国家的最先进的估计设计的每个特定的属性。
英文摘要：
The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly "amplify" the effective amount of data available. For a large variety of distribution properties including four of the most popular ones and for every underlying distribution, they achieve the accuracy that the empirical-frequency plug-in estimators would attain using a logarithmic-factor more samples. Specifically, for Shannon entropy and a very broad class of properties including $\ell_1$-distance, the new estimators use $n$ samples to achieve the accuracy attained by the empirical estimators with $n\log n$ samples. For support-size and coverage, the new estimators use $n$ samples to achieve the performance of empirical frequency with sample size $n$ times the logarithm of the property value. Significantly strengthening the traditional min-max formulation, these results hold not only for the worst distributions, but for each and every underlying distribution. Furthermore, the logarithmic amplification factors are optimal. Experiments on a wide variety of distributions show that the new estimators outperform the previous state-of-the-art estimators designed for each specific property.
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