A meta-model 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 (PI). Without a very complex implementation work, our model is able to complement any pre- existing 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 upper and lower quantiles of the error.
The goal of conditional quantile regression is to determine a function, d? (x), that returns the specific quantile ? of a target variable d, given an input vector x. Following Koenker [1], we implement two functional forms of d? (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 in Israel. We contrast the results with a traditional confidence intervals approach that assumes that error is normally distributed with constant (homoscedastic) variance. We apply several evaluation measures based on earlier literature and also contribute two new measures that focus on relative interval length and balance between accuracy and interval length. For the available dataset, we verified that conditional quantile regression outperforms the homoscedastic baseline in the vast majority of the indicators.


uncertainty, prediction intervals, dynamic traffic assignment, quantile regression, traffic prediction


Intelligent Transportation Systems, machine learning, traffic prediction, quantile regression


IEEE Transactions on Intelligent Transportation Systems, #99, pp. 1-13, March 2014

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