Scalable Dynamic Mixture Model with Full Covariance for Probabilistic Traffic Forecasting

Seongjin Choi (), Nicolas Saunier (), Vincent Zhihao Zheng (), Martin Trépanier () and Lijun Sun ()
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Seongjin Choi: Department of Civil, Environmental, and Geo-Engineering, University of Minnesota, Minneapolis, Minnesota 55455
Nicolas Saunier: Department of Civil, Geological and Mining Engineering, Polytechnique Montreal, Montreal, Quebec H3C 3A7, Canada
Vincent Zhihao Zheng: Department of Civil Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada
Martin Trépanier: Department of Mathematical and Industrial Engineering, Polytechnique Montreal, Montreal, Quebec H3C 3A7, Canada
Lijun Sun: Department of Civil Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada

Transportation Science, 2025, vol. 59, issue 4, 708-720

Abstract: Deep-learning-based multivariate and multistep-ahead traffic forecasting models are typically trained with the mean squared error (MSE) or mean absolute error (MAE) as the loss function in a sequence-to-sequence setting, simply assuming that the errors follow an independent and isotropic Gaussian or Laplacian distributions. However, such assumptions are often unrealistic for real-world traffic forecasting tasks, where the probabilistic distribution of spatiotemporal forecasting is very complex with strong concurrent correlations across both sensors and forecasting horizons in a time-varying manner. In this paper, we model the time-varying distribution for the matrix-variate error process as a dynamic mixture of zero-mean Gaussian distributions. To achieve efficiency, flexibility, and scalability, we parameterize each mixture component using a matrix normal distribution and allow the mixture weight to change and be predictable over time. The proposed method can be seamlessly integrated into existing deep-learning frameworks with only a few additional parameters to be learned. We evaluate the performance of the proposed method on a traffic speed forecasting task and find that our method not only improves model performance but also provides interpretable spatiotemporal correlation structures.

Keywords: traffic forecasting; spatiotemporal forecasting; mixture density networks; correlated errors (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:59:y:2025:i:4:p:708-720

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