HyperLogLog草图的基数估计新算法
New cardinality estimation algorithms for HyperLogLog sketches
摘要：
本文提出了一种新的方法来估计由HyperLogLog草图记录的数据集的基数。一个理论上有动机的扩展到原来的估计，消除了小和大基数的偏见。基于极大似然原理，导出了二次无偏估计方法，并给出了一种稳健有效的数值算法。最大似然方法也可以应用于多个HyperLogLog草图。特别是，它表明，它给出了更精确的基数估计工会，交集，或两个集，都是由HyperLogLog草图表示的传统技术相比，使用的包括-排除原则的相对互补。所有的新方法都通过大量的仿真验证。
英文摘要：
This paper presents new methods to estimate the cardinalities of data sets recorded by HyperLogLog sketches. A theoretically motivated extension to the original estimator is presented that eliminates the bias for small and large cardinalities. Based on the maximum likelihood principle a second unbiased method is derived together with a robust and efficient numerical algorithm to calculate the estimate. The maximum likelihood approach can also be applied to more than a single HyperLogLog sketch. In particular, it is shown that it gives more precise cardinality estimates for union, intersection, or relative complements of two sets that are both represented by HyperLogLog sketches compared to the conventional technique using the inclusion-exclusion principle. All the new methods are demonstrated and verified by extensive simulations.
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