A metamodel for estimating error bounds in real-time traffic prediction systems

This paper presents a methodology for estimating the upper and lower bounds of a real-time traffic prediction system, i.e., its prediction interval. Without a very complex implementation work, our model is able to complement any preexisting prediction system with extra uncertainty information such as the 5% and 95% quantiles. We treat the traffic prediction system as a black box that provides a feed of predictions. Having this feed together with observed values, we then train conditional quantile regression methods that estimate the upper and lower quantiles of the error. The goal of conditional quantile regression is to determine a function, i.e., d^τ (x), that returns the specific quantile τ of a target variable d, given an input vector x. Following Koenker, we implement two functional forms of d^τ (x): locally weighted linear, which relies on value on the neighborhood of x, and splines, a piecewise defined smooth polynomial function. We demonstrate this methodology with three different traffic prediction models applied to two freeway data sets from Irvine, CA, and Tel Aviv, Israel. We contrast the results with a traditional confidence intervals approach that assumes that the error is normally distributed with constant (homoscedastic) variance. We apply several evaluation measures based on earlier literature and contribute two new measures that focus on relative interval length and balance between accuracy and interval length. For the available data set, we verified that conditional quantile regression outperforms the homoscedastic baseline in the vast majority of the indicators.