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.

Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue by assessing DNNs' ability to estimate conditional probabilities and propose a framework for systematic uncertainty characterization. Denoting the input sample as x and the category as y, the classification task of assigning a category y to a given input x can be reduced to the task of estimating the conditional probabilities p(y|x), as approximated by the DNN at its last layer using the softmax function. Since softmax yields a vector whose elements all fall in the interval (0, 1) and sum to 1, it suggests a probabilistic interpretation to the DNN's outcome. Using synthetic and real-world datasets, we look into the impact of various factors, e.g., probability density f(x) and inter-categorical sparsity, on the precision of DNNs' estimations of p(y|x), and find that the likelihood probability density and the inter-categorical sparsity have greater impacts than the prior probability to DNNs' classification uncertainty.

Accurate and real-time traffic forecasting plays an important role in the Intelligent Traffic System (ITS), it is of great significance for urban traffic planning, traffic management, and traffic control. However, traffic forecasting has always been a concerned open scientific issue, owing to the constraint of urban road network topological structure and the law of dynamic change with time, namely spatial dependence and temporal dependence. In order to capture the spatial and temporal dependence simultaneously, we propose a novel neural network-based traffic forecasting method, temporal graph convolutional network (T-GCN) model, which is in combination with the graph convolutional network (GCN) and gated recurrent unit (GRU). Specifically, the graph convolutional network is used to learn the complex topological structure to capture the spatial dependence and the gated recurrent unit is used to learn the dynamic change of traffic flow to capture the temporal dependence. And then, the T-GCN model is employed to realize the traffic forecasting task based on urban road network. Experiments demonstrate that our T-GCN model can obtain the spatio temporal correlation from traffic data and the prediction effects outperform state-of-art baselines on real-world traffic datasets.