Joint Tracking of Multiple Quantiles Through Conditional Quantiles

Estimation of quantiles is one of the most fundamental real-time analysis tasks. Most real-time data streams vary dynamically with time and incremental quantile estimators document state-of-the art performance to track quantiles of such data streams. However, most are not able to make joint estimates of multiple quantiles in a consistent manner, and estimates may violate the monotone property of quantiles. In this paper we propose the general concept of conditional quantiles that can extend incremental estimators to jointly track multiple quantiles. We apply the concept to propose two new estimators. Extensive experimental results, on both synthetic and real-life data, show that the new estimators clearly outperform legacy state-of-the-art joint quantile tracking algorithm and achieve faster adaptivity in dynamically varying data streams.