Scalable Dynamic Mixture Model with Full Covariance for Probabilistic Traffic Forecasting
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910001228939264 |
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| author | Choi, Seongjin Saunier, Nicolas Zheng, Vincent Zhihao Trepanier, Martin Sun, Lijun |
| author_facet | Choi, Seongjin Saunier, Nicolas Zheng, Vincent Zhihao Trepanier, Martin Sun, Lijun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06653 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Scalable Dynamic Mixture Model with Full Covariance for Probabilistic Traffic Forecasting Choi, Seongjin Saunier, Nicolas Zheng, Vincent Zhihao Trepanier, Martin Sun, Lijun Machine Learning 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. |
| title | Scalable Dynamic Mixture Model with Full Covariance for Probabilistic Traffic Forecasting |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2212.06653 |