利用丢弃样本对多集合聚集的紧估计
Leveraging Discarded Samples for Tighter Estimation of Multiple-Set Aggregates
摘要：
许多数据集，如购物篮数据，文本或超文本文档，以及在不同位置或时间段记录的传感器观察，被建模为一组集合在一个基础集的键。我们感兴趣的是基本的聚合，如权重或选择性的键，满足一些选择谓词定义的键的属性和成员在特定的集合。这个一般公式包括基本的聚合，如Jaccard系数，汉明距离和关联规则。在海量数据集上，精确计算可能效率低下或不可行。基于协调随机样本的草图是支持近似查询处理的经典摘要。通过从这些集合的草图中生成谓词中使用的集合的并集的草图（样本），然后将估计器应用于该并集草图来解决问题。我们得到新的更紧密（无偏）估计，利用抽样的关键是目前在联盟的适用草图，但排除在联盟草图。我们建立分析，我们的估计占主导地位的估计适用于联盟草图{ \em所有查询和数据集}。对合成数据和真实数据的经验评估表明，在典型应用中，我们可以预期估计误差减少25%-4倍。
英文摘要：
Many datasets such as market basket data, text or hypertext documents, and sensor observations recorded in different locations or time periods, are modeled as a collection of sets over a ground set of keys. We are interested in basic aggregates such as the weight or selectivity of keys that satisfy some selection predicate defined over keys' attributes and membership in particular sets. This general formulation includes basic aggregates such as the Jaccard coefficient, Hamming distance, and association rules. On massive data sets, exact computation can be inefficient or infeasible. Sketches based on coordinated random samples are classic summaries that support approximate query processing. Queries are resolved by generating a sketch (sample) of the union of sets used in the predicate from the sketches these sets and then applying an estimator to this union-sketch. We derive novel tighter (unbiased) estimators that leverage sampled keys that are present in the union of applicable sketches but excluded from the union sketch. We establish analytically that our estimators dominate estimators applied to the union-sketch for {\em all queries and data sets}. Empirical evaluation on synthetic and real data reveals that on typical applications we can expect a 25%-4 fold reduction in estimation error.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
