# Joint Tracking of Multiple Quantiles Through Conditional Quantiles

## TL;DR

This paper introduces a novel approach for jointly estimating multiple quantiles in real-time data streams using conditional quantiles, addressing the limitations of existing methods in maintaining quantile monotonicity and improving adaptability.

## Contribution

The paper proposes the concept of conditional quantiles and develops two new estimators for joint quantile tracking, enhancing performance over existing algorithms.

## Key findings

- Outperforms existing joint quantile tracking algorithms
- Achieves faster adaptation in dynamic data streams
- Works effectively on synthetic and real-world data

## Abstract

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.