## 2 Related Work  
Machine learning has been widely applied to predict the travel time of buses. Multiple machine learning-based prediction methods have been proposed in the previous literature, including linear regression (LR) [24; 25], support vector regression (SVR) [3; 7; 26; 27], artificial neural network (ANN) [3; 24; 28], random forest (RF) [6; 29], the Kalman filter (KF) [30; 31], and deep learning prediction models [4; 21; 32; 33; 34]. Among them, the LR models are only used for comparison with other models in most studies [33]. SVR and ANN have become the most widely used models because of their strong nonlinear fitting ability and ability to map complex nonlinear relationships. For example, in [7], the authors demonstrated for the first time the feasibility of applying SVR to predict travel time and demonstrated that SVR is suitable for traffic data analysis. [PERSON] et al. [11] used support vector machines and V-vector regression with linear kernel functions for prediction. In [35], the authors proposed a bus travel time prediction model with a forgetting factor based on SVM. In [29], the authors used three different algorithms, namely random forest, projection pursuit regression, and support vector machine, to carry out extensive experiments on each route in the study. In [27], the authors proposed a new road segment-based method for predicting bus travel time, selecting the basic prediction model by comparing the performance of SVM, ANN, and k-NN. In [6], the authors proposed the neighbor-based random forest (RFNN) method to predict bus travel time, which has been calibrated and validated with real-world data. Although the results of RFNN show high accuracy, its long computation time is currently not suitable for real-time prediction. To improve the prediction accuracy of travel time and avoid the disadvantage of using a single model, many studies have tried to use hybrid models to predict the travel time of buses. For example, reference [36; 37; 38; 39] added the KF algorithm to machine learning-based methods. In [23], the authors proposed a new model combining queuing theory and machine learning to predict bus travel time. Compared to a single model, the results of mixed models indicate that they can provide better performance. The above machine learning-based methods are all based on shallow learning architectures, but they struggle to handle the correlation between spatiotemporal data factors, and the relationships between these factors are more complex and nonlinear [21]. In recent years, researchers have proposed some research based on deep neural networks. In [32], the authors proposed using recurrent neural networks (RNNs) to predict the arrival time of buses by utilizing long-range correlations between multiple time steps. [PERSON] et al. [33] utilized the nonstationary spatiotemporal correlations present in urban public transportation networks to propose a multi-output, multi-time-step, deep neural network that utilizes a combination of convolutional and long short-term memory (LSTM) layers to discover complex patterns that traditional methods cannot capture. In [4], the authors proposed a method (TP-SCF) to automatically learn the different traffic conditions of different bus routes and train a separate prediction model (LSTM) for each different traffic mode to improve prediction accuracy. In [34], the authors developed a Geo-conv LSTM model that can extract the subsequent spatial features of the entire bus travel sequence through a 1D convolutional neural network (CNN) while also capturing the temporal dependencies between sub-sequences through the LSTM network. [PERSON] et al. [21] proposed using the NMF algorithm to group route links with similar traffic patterns into different groups and training separate CNN models for each group to improve the accuracy of model predictions. Unfortunately, although all of the above studies strive to improve the accuracy of bus travel time prediction, these studies cannot provide information about travel time such as confidence level.