A new quantile tracking algorithm using a generalized exponentially weighted average of observations

Abstract

The Exponentially Weighted Average (EWA) of observations is known to be state-of-art estimator for tracking expectations of dynamically varying data stream distributions. However, how to devise an EWA estimator to rather track quantiles of data stream distributions is not obvious. In this paper, we present a lightweight quantile estimator using a generalized form of the EWA. To the best of our knowledge, this work represents the first reported quantile estimator of this form in the literature. An appealing property of the estimator is that the update step size is adjusted online proportionally to the difference between current observation and the current quantile estimate. Thus, if the estimator is off-track compared to the data stream, large steps will be taken to promptly get the estimator back on-track. The convergence of the estimator to the true quantile is proven using the theory of stochastic learning. Extensive experimental results using both synthetic and real-life data show that our estimator clearly outperforms legacy state-of-the-art quantile tracking estimators and achieves faster adaptivity in dynamic environments. The quantile estimator was further tested on real-life data where the objective is efficient online control of indoor climate. We show that the estimator can be incorporated into a concept drift detector for efficiently decide when a machine learning model used to predict future indoor temperature should be retrained/updated.