The estimation of quantiles is one of the most fundamental data mining tasks. As most real-time data streams vary dynamically over time, there is a quest for adaptive quantile estimators. The most well-known type of adaptive quantile estimators is the incremental one which documents the state-of-the art performance in tracking quantiles. However, the absolute vast majority of incremental quantile estimators fail to jointly estimate multiple quantiles in a consistent manner without violating the monotone property of quantiles. In this paper, first we introduce the concept of conditional quantiles that can be used to extend incremental estimators to jointly track multiple quantiles. Second, we resort to the concept of conditional quantiles to propose two new estimators. Extensive experimental results, based on both synthetic and real-life data, show that the proposed estimators clearly outperform legacy state-of-the-art joint quantile tracking algorithms in terms of accuracy while achieving faster adaptivity in the face of dynamically varying data streams.

分位数的估计是最基本的数据挖掘任务之一。由于大多数实时数据流会随着时间动态变化，因此需要自适应分位数估计器。最著名的自适应分位数估计器类型是增量式，它记录了跟踪分位数的最新性能。但是，绝大部分增量分位数估计器都不能以一致的方式共同估计多个分位数而不违反分位数的单调性质。在本文中，我们首先介绍条件分位数的概念可用于扩展增量估算器以共同跟踪多个分位数。其次，我们采用条件分位数的概念来提出两个新的估计量。基于合成数据和实际数据的大量实验结果表明，在动态变化的数据流中，所提出的估计器在准确性方面明显优于传统的最新联合分位数跟踪算法，同时实现了更快的适应性。