# Highway Speed Prediction Using Gated Recurrent Unit Neural Networks
## 2 Background  
A considerable amount of literature has been published on traffic forecasting. The traffic prediction methods can be broadly categorized into a parametric approach, a non-parametric approach, and a hybrid approach, based on parametric and non-parametric methods [7, 8]. Parametric methods are based on statistical models. For example, the traffic speed can be calculated using analytical equations. These equations are based on a variety of parameters, such as demand, capacity, or weather. However, it is not easy to estimate the parameters accurately under dynamic traffic conditions. Among parametric approaches, the auto-regressive integrated moving average model (ARIMA) has been widely utilized for traffic forecasting [9]. The ARIMA model assumes that the time series data are stationary when mean and variance are constant. Although the ARIMA model presents an acceptable performance in predicting short-term traffic speed, it is unlikely to accurately conduct traffic forecasting due to the nonlinearity and randomness of traffic data [8, 10]. Moreover, the Kalman filter model also has been applied to traffic forecasting [11, 12]. The Kalman filter model is a recursive estimation algorithm that continuously updates the travel-time state variable using new observations. The state transition model performs prediction and estimation, and error covariance is minimized. It has the advantage of using only the information from the previous time period and has excellent accuracy in real-time prediction. However, the prediction accuracy is dependent on the state transition model, and a time-lag problem may occur if the travel time changes rapidly at each time interval [13]. The stochastic and nonlinear features negatively impact the parametric approach in traffic data. Therefore, recent studies have concentrated on non-parametric approaches. Mainly, machine learning algorithms have been applied to predict traffic speed and flow. For example, the support vector machine (SVM) model has been applied to highway travel time prediction. The SVM is a supervised learning-based linear classification model that can find the spatial boundaries of the given data [14]. Even though the SVM is suitable for binary classification, it has a disadvantage of sensitivity to parameter and kernel selection [15, 16]. Further, the k-nearest neighbors (k-NN) model predicts highway travel time using similar patterns based on large-capacity historical data. For similarity measurement, a Euclidean distance function is generally used, and matching with past historical data is conducted according to the similarity of distance. In this model, each step's parameter setting (historical data smoothing, similarity function, k-number, or prediction function) plays a vital role in the prediction accuracy. The k-NN model has shown higher accuracy than the ARIMA and Kalman filter models by matching similar history data through trend reflection [17]. However, it is still a challenge to perform accurate traffic forecasting due to the shallow structure of the model mentioned above. Data-driven approaches, such as deep learning, have launched a new era of traffic prediction. Deep learning is a sub-field of machine learning, which uses an artificial neural network (ANN) to learn representations from data. The ANN's deep learning model automatically obtains the weight parameters' optimal values from the training data. The goal of learning is to find the weight parameters that minimize the loss function, representing better complex non-linear relationships from data accurately [18; 19]. With the development of deep learning, the convolutional neural network (CNN) has been utilized to predict traffic flow [20]. The traffic flow information over the traffic network is converted to a series of images. These images are fed into a CNN. Although this approach has merit in terms of spatial dependency, it cannot represent various traffic information, including speed, density, or weather within the images.