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

arXiv: https://arxiv.org/abs/2203.09438 · HTML: https://mlsanity.com/paper/2203.09438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Principles and Practice of Explainable Machine Learning](https://mlsanity.com/paper/2009.11698/) (2020)
- [DeepPool: Distributed Model-free Algorithm for Ride-sharing using Deep Reinforcement Learning](https://mlsanity.com/paper/1903.03882/) (2019)
- [Interpreting Tree Ensembles with inTrees](https://mlsanity.com/paper/1408.5456/) (2014)
- [A Simple Baseline for Travel Time Estimation using Large-Scale Trip Data](https://mlsanity.com/paper/1512.08580/) (2015)
- [The Shapley Value of Classifiers in Ensemble Games](https://mlsanity.com/paper/2101.02153/) (2021)
- [A Distributed Model-Free Ride-Sharing Approach for Joint Matching, Pricing, and Dispatching using Deep Reinforcement Learning](https://mlsanity.com/paper/2010.01755/) (2020)
- [Optimizing Taxi Carpool Policies via Reinforcement Learning and Spatio-Temporal Mining](https://mlsanity.com/paper/1811.04345/) (2018)
- [Ensembles of Random SHAPs](https://mlsanity.com/paper/2103.03302/) (2021)

## Built on by (most cited first, 1 of 1)

- [Traffic4cast at NeurIPS 2022 -- Predict Dynamics along Graph Edges from Sparse Node Data: Whole City Traffic and ETA from Stationary Vehicle Detectors](https://mlsanity.com/paper/2303.07758/) (2023)

## Abstract (arXiv)

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.