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Graph Convolution Recurrent Denoising Diffusion Model for Multivariate Probabilistic Temporal Forecasting

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Advanced Data Mining and Applications (ADMA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14176))

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Abstract

The probabilistic estimation for multivariate time series forecasting has recently become a trend in various research fields, such as traffic, climate, and finance. The multivariate time series can be treated as an interrelated system, and it is significant to assume each variable to be independent. However, most existing methods fail to simultaneously consider spatial dependencies and probabilistic temporal dynamics. To address this gap, we introduce the Graph Convolution Recurrent Denoising Diffusion model (GCRDD), a recurrent framework for spatial-temporal forecasting that captures both spatial dependencies and temporal dynamics. Specifically, GCRDD incorporates the structural dependency into a hidden state using the graph-modified gated recurrent unit and samples from the estimated data distribution at each time step by a graph conditional diffusion model. We reveal the comparative experiment performance of state-of-the-art models in two real-world road network traffic datasets to demonstrate it as the competitive probabilistic multivariate temporal forecasting framework.

R. Li and X. Li—These authors contributed equally to this work.

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Notes

  1. 1.

    https://pytorch-geometric-temporal.readthedocs.io/en/latest/index.html.

References

  1. Afifi, H., Elmahdy, M., El Saban, M., Abu-Elkheir, M.: Probabilistic time series forecasting for unconventional oil and gas producing wells. In: The 2nd Novel Intelligent and Leading Emerging Sciences Conference, pp. 450–455 (2020)

    Google Scholar 

  2. an den Oord, A., Kalchbrenner, N., Espeholt, L., kavukcuoglu, K., Vinyals, O., Graves, A.: Conditional image generation with pixel CNN decoders. In: Advances in Neural Information Processing Systems. vol. 29, pp. 4790–4798 (2016)

    Google Scholar 

  3. Bai, J., et al.: A3t-gcn: attention temporal graph convolutional network for traffic forecasting. ISPRS Int. J. Geo Inf. 10(7), 485 (2021)

    Google Scholar 

  4. Chen, H., Rossi, R.A., Mahadik, K., Kim, S., Eldardiry, H.: Graph deep factors for probabilistic time-series forecasting. ACM Trans. Knowl. Discov. Data (2022)

    Google Scholar 

  5. Chung, F.R.: Spectral Graph Theory, vol. 92. American Mathematical Soc. (1997)

    Google Scholar 

  6. Chung, J., Gulcehre, C., Cho, K., Bengio, Y.: Empirical evaluation of gated recurrent neural networks on sequence modeling. In: Neural Information Processing Systems 2014 Workshop on Deep Learning (2014)

    Google Scholar 

  7. Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: Advances in Neural Information Processing Systems, vol. 29 (2016)

    Google Scholar 

  8. Gasthaus, J., et al.: Probabilistic forecasting with spline quantile function RNNs. In: The 22nd International Conference on Artificial Intelligence and Statistics, pp. 1901–1910 (2019)

    Google Scholar 

  9. Graves, A.: Generating sequences with recurrent neural networks. arXiv preprint arXiv:1308.0850 (2013)

  10. He, H., Zhang, Q., Bai, S., Yi, K., Niu, Z.: CATN: cross attentive tree-aware network for multivariate time series forecasting. Proc. AAAI Conf. Artif. Intell. 36(4), 4030–4038 (2022)

    Google Scholar 

  11. Hmamouche, Y., Przymus, P.M., Alouaoui, H., Casali, A., Lakhal, L.: Large multivariate time series forecasting: survey on methods and scalability. In: Utilizing Big Data Paradigms for Business Intelligence, pp. 170–197. IGI Global (2019)

    Google Scholar 

  12. Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Adv. Neural. Inf. Process. Syst. 33, 6840–6851 (2020)

    Google Scholar 

  13. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: International Conference on Learning Representations (2015)

    Google Scholar 

  14. Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: International Conference on Learning Representations (2016)

    Google Scholar 

  15. Kong, Z., Ping, W., Huang, J., Zhao, K., Catanzaro, B.: Diffwave: a versatile diffusion model for audio synthesis. In: International Conference on Learning Representations (2021)

    Google Scholar 

  16. Lai, G., Chang, W.C., Yang, Y., Liu, H.: Modeling long-and short-term temporal patterns with deep neural networks. In: The 41st International Conference on Research & Development in Information Retrieval, pp. 95–104 (2018)

    Google Scholar 

  17. Li, Y., Yu, R., Shahabi, C., Liu, Y.: Diffusion convolutional recurrent neural network: data-driven traffic forecasting. In: International Conference on Learning Representations (2017)

    Google Scholar 

  18. Lim, B., Zohren, S.: Time-series forecasting with deep learning: a survey. Phil. Trans. R. Soc. A 379(2194), 20200209 (2021)

    Article  MathSciNet  Google Scholar 

  19. Patton, A.: Copula methods for forecasting multivariate time series. Handb. Econ. Forecast. 2, 899–960 (2013)

    Article  Google Scholar 

  20. Rangapuram, S.S., Seeger, M.W., Gasthaus, J., Stella, L., Wang, Y., Januschowski, T.: Deep state space models for time series forecasting. In: Advances in Neural Information Processing Systems, vol. 31 (2018)

    Google Scholar 

  21. Rasul, K., Seward, C., Schuster, I., Vollgraf, R.: Autoregressive denoising diffusion models for multivariate probabilistic time series forecasting. In: International Conference on Machine Learning, pp. 8857–8868 (2021)

    Google Scholar 

  22. Rozemberczki, B., et al.: PyTorch geometric temporal: spatiotemporal signal processing with neural machine learning models. In: Proceedings of the 30th International Conference on Information and Knowledge Management, pp. 4564–4573 (2021)

    Google Scholar 

  23. Seo, Y., Defferrard, M., Vandergheynst, P., Bresson, X.: Structured sequence modeling with graph convolutional recurrent networks. In: Cheng, L., Leung, A.C.S., Ozawa, S. (eds.) ICONIP 2018. LNCS, vol. 11301, pp. 362–373. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-04167-0_33

  24. Shang, C., Chen, J., Bi, J.: Discrete graph structure learning for forecasting multiple time series. arXiv preprint arXiv:2101.06861 (2021)

  25. Shih, S.Y., Sun, F.K., Lee, H.Y.: Temporal pattern attention for multivariate time series forecasting. Mach. Learn. 108(8), 1421–1441 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  26. Shuman, D.I., Narang, S.K., Frossard, P., Ortega, A., Vandergheynst, P.: The emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Process. Mag. 30(3), 83–98 (2013)

    Article  Google Scholar 

  27. Song, Y., Ermon, S.: Improved techniques for training score-based generative models. Adv. Neural. Inf. Process. Syst. 33, 12438–12448 (2020)

    Google Scholar 

  28. Sutskever, I., Vinyals, O., Le, Q.V.: Sequence to sequence learning with neural networks. In: Advances in Neural Information Processing Systems, vol. 27 (2014)

    Google Scholar 

  29. Tashiro, Y., Song, J., Song, Y., Ermon, S.: CSDI: conditional score-based diffusion models for probabilistic time series imputation. Adv. Neural. Inf. Process. Syst. 34, 24804–24816 (2021)

    Google Scholar 

  30. Wu, Z., Pan, S., Long, G., Jiang, J., Zhang, C.: Graph wavenet for deep spatial-temporal graph modeling. In: The 28th International Joint Conference on Artificial Intelligence (IJCAI). International Joint Conferences on Artificial Intelligence Organization (2019)

    Google Scholar 

  31. Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., Philip, S.Y.: A comprehensive survey on graph neural networks. IEEE Trans. Neural Netw. Learn. Syst. 32(1), 4–24 (2020)

    Article  MathSciNet  Google Scholar 

  32. Wu, Z., Pan, S., Long, G., Jiang, J., Chang, X., Zhang, C.: Connecting the dots: multivariate time series forecasting with graph neural networks. In: The 26th ACM International Conference on Knowledge Discovery & Data Mining, pp. 753–763 (2020)

    Google Scholar 

  33. Yang, L., et al.: Diffusion models: a comprehensive survey of methods and applications. arXiv preprint arXiv:2209.00796 (2022)

  34. Zhao, L., et al.: T-GCN: a temporal graph convolutional network for traffic prediction. IEEE Trans. Intell. Transp. Syst. 21(9), 3848–3858 (2019)

    Google Scholar 

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Correspondence to Junbin Gao .

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Li, R., Li, X., Gao, S., Choy, S.T.B., Gao, J. (2023). Graph Convolution Recurrent Denoising Diffusion Model for Multivariate Probabilistic Temporal Forecasting. In: Yang, X., et al. Advanced Data Mining and Applications. ADMA 2023. Lecture Notes in Computer Science(), vol 14176. Springer, Cham. https://doi.org/10.1007/978-3-031-46661-8_44

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  • DOI: https://doi.org/10.1007/978-3-031-46661-8_44

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