🤖 AI Summary
Existing deep spatiotemporal models for traffic flow forecasting assume temporally independent prediction errors, leading to inaccurate uncertainty quantification. To address this, we propose a dynamic error modeling framework that explicitly captures the spatiotemporal dependencies of forecast errors via a Matrix-Autoregressive (MAR) model—relaxing the independence assumption. We introduce, for the first time, an anisotropic error likelihood into the loss function, enabling joint optimization of the primary forecasting model and the error dynamics. Our approach further incorporates interpretable autoregressive coefficients and a structured spatiotemporal covariance matrix. Evaluated on diverse real-world speed and flow datasets, the method significantly outperforms state-of-the-art baselines: it improves point forecast accuracy while delivering well-calibrated, physically interpretable quantile forecasts and rigorous uncertainty quantification.
📝 Abstract
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 non-isotropic 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 (SOTA) traffic forecasting models using speed and flow datasets demonstrates improved performance, with interpretable AR coefficients and spatiotemporal covariance matrices enhancing the understanding of the model.