频率函数的可组合草图：超越最坏情况
Composable Sketches for Functions of Frequencies: Beyond the Worst Case
摘要：
最近，人们越来越关注使用机器学习技术来改进经典算法。在本文中，我们研究当它是可能的构造紧凑的，可组合的草图加权抽样和统计估计根据数据频率的函数。这种结构现在是大规模数据分析和机器学习管道的核心组件。然而，许多常见的功能，如阈值和p > 2的p阶频率矩，在最坏的情况下需要多项式大小的草图。我们探讨了两种不同类型的假设下的最坏情况下的性能。第一个是获得关于项目频率的嘈杂建议。这延续了Hsu et al.（ICLR 2019）的工作路线，他们假设预测是由机器学习模型提供的。第二个是在有限的一类输入频率分布上提供有保证的性能，这些分布与实践中观察到的情况更好地一致。这扩展了Charikar et al.（ICALP 2002）的开创性论文中关于Zipfian分布下的重打击者的工作。令人惊讶的是，我们的分析和经验表明，“在实践中”小多面体大小的草图提供准确的“硬”功能。
英文摘要：
Recently there has been increased interest in using machine learning techniques to improve classical algorithms. In this paper we study when it is possible to construct compact, composable sketches for weighted sampling and statistics estimation according to functions of data frequencies. Such structures are now central components of large-scale data analytics and machine learning pipelines. However, many common functions, such as thresholds and p-th frequency moments with p > 2, are known to require polynomial-size sketches in the worst case. We explore performance beyond the worst case under two different types of assumptions. The first is having access to noisy advice on item frequencies. This continues the line of work of Hsu et al. (ICLR 2019), who assume predictions are provided by a machine learning model. The second is providing guaranteed performance on a restricted class of input frequency distributions that are better aligned with what is observed in practice. This extends the work on heavy hitters under Zipfian distributions in a seminal paper of Charikar et al. (ICALP 2002). Surprisingly, we show analytically and empirically that "in practice" small polylogarithmic-size sketches provide accuracy for "hard" functions.
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