Scalable Dynamic Mixture Model with Full Covariance for Probabilistic Traffic Forecasting

• URL: http://arxiv.org/abs/2212.06653v3
• Date: Sat, 19 Aug 2023 23:12:05 GMT
• Title: Scalable Dynamic Mixture Model with Full Covariance for Probabilistic Traffic Forecasting
• Authors: Seongjin Choi, Nicolas Saunier, Vincent Zhihao Zheng, Martin Trepanier, Lijun Sun
• Abstract summary: We propose a dynamic mixture of zero-mean Gaussian distributions for the time-varying error process. The proposed method can be seamlessly integrated into existing deep-learning frameworks with only a few additional parameters to be learned. We evaluate the proposed method on a traffic speed forecasting task and find that our method not only improves model horizons but also provides interpretabletemporal correlation structures.
• Score: 16.04029885574568
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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