# Short-Term Traffic Flow Forecasting via Multi-Regime Modeling and Ensemble Learning
## 1 Introduction  
Traffic congestion brings substantial negative impacts on humanity, such as high travel costs, increased anxiety, and polluted air. To alleviate traffic congestion problems, researchers and authorities all over the world have explored a wide number of feasible solutions. Among them, intelligent transportation system (ITS) has become the most popular and effective one. By effectively and efficiently collecting, processing, and disseminating traffic data, ITS helps traffic researchers and practitioners make reasonable and reliable decisions, and has achieved great success during the past decade [1; 2; 3; 4; 5].  
Traffic flow describes the traffic conditions over certain time intervals using representative measures, for example, flow rate, speed, and density. As the values of the measures are continuous over time, traffic flow is commonly recorded and described with a time series format. Short-term traffic flow forecasting, the forecasted time scale of which is no more than 30 min (e.g., 5, 10, or 15 min) is a fundamental function in ITS. One key issue in traffic flow forecasting is how to properly define and capture the temporal patterns of traffic flow [6]. To solve this issue, two categories of coping strategiesare commonly adopted. The first is a detrending strategy, which is to build forecasting models by separating the trends of the traffic flow time series from the remaining fluctuations and developing distinct models to describe the trends and fluctuations, respectively. The second is a multi-regime strategy, which assumes that different patterns are contained in traffic flow dynamics. Based on the assumption, different regimes are first identified according to the distinct patterns. After that, the pattern of each regime is characterized and captured by a separate model. A comprehensive comparison study with the two strategies was conducted by [PERSON] et al. [6]. They concluded that the models based on the multi-regime strategy are capable of identifying the local trends in the vehicle count time series and describing its fluctuations more effectively. However, the overall forecasting errors of the multi-regime models cannot be notably reduced in their experiments because of the introduced errors by the regime identification model.  
As the above analyses show, the forecasting performance of a multi-regime model is closely related to two major aspects. First, a proper regime identification model needs to be built in order to assign the correct regime to each traffic flow observation. Second, an accurate multi-regime forecasting model to capture the patterns of different regimes of traffic flow is required. Inspired by these two facts, this paper presents an effective approach to forecasting short-term traffic flow based on multi-regime modeling and ensemble learning, which includes two key procedures. First, to properly capture the different patterns of traffic flow dynamics, a regime identification model based on a probabilistic approach is developed. Each regime represents a specific and homogeneous traffic condition. The probabilistic approach builds on the concepts of the Markov Process and Markov Chain. Second, a forecasting model using an ensemble learning strategy is developed, which integrates the outputs of multiple individual learners to produce the final forecasts. The ensemble learning strategy introduced can effectively improve the accuracy of the forecasting model.  
The organization of this paper is as follows. The next section provides a comprehensive review on the existing studies associated with traffic flow forecasting. Subsequently, the details of the proposed approach are given. After that, the evaluated data sets are described. The following experiments are carried out to evaluate the proposed approach. Lastly, the conclusions and future work are discussed.