Efficient Quantile Tracking Using an Oracle

Concept drift is a well-known issue that arises when working with data streams. In this paper, we present a procedure that allows a quantile tracking procedure to cope with concept drift. We suggest using expected quantile loss, a popular loss function in quantile regression, to monitor the quantile tracking error, which, in turn, is used to efficiently adapt to concept drift. The suggested procedures adapt efficiently to concept drift, and the tracking performance is close to theoretically optimal. The procedures were further applied to three real-life streaming data sets related to Twitter event detection, activity recognition, and stock trading. The results show that the procedures are efficient at adapting to concept drift, thereby documenting the real-world applicability of the procedures. We further used asymptotic theory from statistics to show the appealing theoretical property that, if the data stream distribution is stationary over time, the procedures converge to the true quantile.