An Explainable Stacked Ensemble Model for Static Route-Free Estimation of Time of Arrival

TL;DR

This work tackles static route-free ETA prediction for taxi trips by introducing a novel stacked ensemble that combines heterogeneous first-level models. It couples this predictive framework with three novel joining methods to produce explanations that fuse first- and second-level model contributions, enabling local post-hoc interpretability. Empirical results on NYC and Washington DC taxi data show the stacked ensemble can outperform baselines and single-level models, while the explanations reveal how features like distance, time-bin, and weather-related factors influence predictions. The approach demonstrates the feasibility of achieving higher prediction accuracy without sacrificing transparency, offering practical benefits for drivers and passengers and a path toward broader explainable route-free ETA applications.

Abstract

To compare alternative taxi schedules and to compute them, as well as to provide insights into an upcoming taxi trip to drivers and passengers, the duration of a trip or its Estimated Time of Arrival (ETA) is predicted. To reach a high prediction precision, machine learning models for ETA are state of the art. One yet unexploited option to further increase prediction precision is to combine multiple ETA models into an ensemble. While an increase of prediction precision is likely, the main drawback is that the predictions made by such an ensemble become less transparent due to the sophisticated ensemble architecture. One option to remedy this drawback is to apply eXplainable Artificial Intelligence (XAI). The contribution of this paper is three-fold. First, we combine multiple machine learning models from our previous work for ETA into a two-level ensemble model - a stacked ensemble model - which on its own is novel; therefore, we can outperform previous state-of-the-art static route-free ETA approaches. Second, we apply existing XAI methods to explain the first- and second-level models of the ensemble. Third, we propose three joining methods for combining the first-level explanations with the second-level ones. Those joining methods enable us to explain stacked ensembles for regression tasks. An experimental evaluation shows that the ETA models correctly learned the importance of those input features driving the prediction.

Figures (13)

• Figure 1: Motivating scenario about ETA for the planning of taxi schedules.
• Figure 2: Architecture of a stacked ensemble with two levels--the models $\psi_1, \psi_2, \ldots, \psi_{|\Psi|}$ build the first level and the model $\zeta$ the second level.
• Figure 3: Distribution of the average duration in minutes over the week in the New York City data set (darker blue) and in the Washington DC data set (lighter blue).
• Figure 4: Distribution of the pickup (a) and dropoff (b) locations for randomly selected trips from the training data of the New York City data set.
• Figure 5: Local feature importance via LIME per feature of the samples in the scenarios for the first-level models; each plot refers to one scenario, (a) for SC1, (b) for SC2, (c) for SC3, and (d) for SC4; the ten trips with an expected lower influence are marked with lighter triangles--the ones with an expected higher influence with less light triangles; each line connects the feature importances for one trip along the various features used by the corresponding model.