Existing deep learning-based traffic forecasting models are mainly trained with MSE (or MAE) as the loss function, assuming that residuals/errors follow independent and isotropic Gaussian (or Laplacian) distribution for simplicity. However, this assumption rarely holds for real-world traffic forecasting tasks, where the unexplained residuals are often correlated in both space and time. In this study, we propose Spatiotemporal Residual Regularization by modeling residuals with a dynamic (e.g., time-varying) mixture of zero-mean multivariate Gaussian distribution with learnable spatiotemporal covariance matrices. This approach allows us to directly capture spatiotemporally correlated residuals. For scalability, we model the spatiotemporal covariance for each mixture component using a Kronecker product structure, which significantly reduces the number of parameters and computation complexity. We evaluate the performance of the proposed method on a traffic speed forecasting task. Our results show that, by properly modeling residual distribution, the proposed method not only improves the model performance but also provides interpretable structures.

翻译：现有基于深层次学习的交通流量预测模型主要以MSE(或MAE)作为损失函数,主要以现有基于深层学习的交通流量预测模型(或MAE)为培训对象,假设残留物/载体的分布为独立和等热带高斯(或Laplacian)的简单性。然而,这一假设很少适用于现实世界的交通预测任务,因为无法解释的残余物在空间和时间上往往相互关联。在本研究中,我们建议通过模拟动态(如时间变化)混合的多位数高斯分布与可学习的中空共变矩阵的零平均值(如时间变化)混合体,来进行边际常规化。这个方法使我们能够直接捕获随机的相近剩余物。为了可扩展性,我们用Kronker产品结构来模拟每种混合物成分的跨时变共变差异性,这大大降低了参数和计算复杂性。我们评估了拟议的交通速度预测任务方法的性能。我们的结果显示,通过适当建模的剩余分布,拟议的方法不仅改进了模型性能,而且还提供了可解释的结构。