Probabilistic Traffic Forecasting with Dynamic Regression

This paper proposes a dynamic regression (DR) framework that enhances existing deep spatiotemporal models by incorporating structured learning for the error process in traffic forecasting. The framework relaxes the assumption of time independence by modeling the error series of the base model (i.e., a well-established traffic forecasting model) using a matrix-variate autoregressive (AR) model. The AR model is integrated into training by redesigning the loss function. The newly designed loss function is based on the likelihood of a nonisotropic error term, enabling the model to generate probabilistic forecasts while preserving the original outputs of the base model. Importantly, the additional parameters introduced by the DR framework can be jointly optimized alongside the base model. Evaluation on state-of-the-art traffic forecasting models using speed and flow data sets demonstrates improved performance, with interpretable AR coefficients and spatiotemporal covariance matrices enhancing the understanding of the model. History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods for Urban Passenger Mobility. Funding: Financial support from the Natural Sciences and Engineering Research Council of Canada [Discovery Grant RGPIN 2019-05950] is gratefully acknowledged. In addition, V. Z. Zheng received financial support from the FRQNT B2X Doctoral Scholarship Program.