Advertisement

Machine Learning

, Volume 108, Issue 8–9, pp 1287–1306 | Cite as

Grouped Gaussian processes for solar power prediction

  • Astrid DahlEmail author
  • Edwin V. Bonilla
Article
Part of the following topical collections:
  1. Special Issue of the ECML PKDD 2019 Journal Track

Abstract

We consider multi-task regression models where the observations are assumed to be a linear combination of several latent node functions and weight functions, which are both drawn from Gaussian process priors. Driven by the problem of developing scalable methods for forecasting distributed solar and other renewable power generation, we propose coupled priors over groups of (node or weight) processes to exploit spatial dependence between functions. We estimate forecast models for solar power at multiple distributed sites and ground wind speed at multiple proximate weather stations. Our results show that our approach maintains or improves point-prediction accuracy relative to competing solar benchmarks and improves over wind forecast benchmark models on all measures. Our approach consistently dominates the equivalent model without coupled priors, achieving faster gains in forecast accuracy. At the same time our approach provides better quantification of predictive uncertainties.

Keywords

Gaussian processes multi-task learning Bayesian nonparametric methods scalable inference solar power prediction 

Notes

Acknowledgements

This research was conducted with support from the Cooperative Research Centre for Low-Carbon Living in collaboration with the University of New South Wales and Solar Analytics Pty Ltd.

References

  1. Álvarez, M., & Lawrence, N. D. (2009). Sparse convolved Gaussian processes for multi-output regression. In Neural Information Processing Systems.Google Scholar
  2. Álvarez, M. A., & Lawrence, N. D. (2011). Computationally efficient convolved multiple output Gaussian processes. Journal of Machine Learning Research, 12(5), 1459–1500.MathSciNetzbMATHGoogle Scholar
  3. Álvarez, M. A., Luengo, D., Titsias, M. K., & Lawrence, N. D. (2010). Efficient multioutput Gaussian processes through variational inducing kernels. In Artificial Intelligence and Statistics.Google Scholar
  4. Álvarez, M. A., Rosasco, L., & Lawrence, N. D. (2012). Kernels for vector-valued functions: A review. Foundations and Trends in Machine Learning, 4(3), 195–266.CrossRefzbMATHGoogle Scholar
  5. Antonanzas, J., Osorio, N., Escobar, R., Urraca, R., de Pison, F. M., & Antonanzas-Torres, F. (2016). Review of photovoltaic power forecasting. Solar Energy, 136, 78–111.CrossRefGoogle Scholar
  6. Bilionis, I., Constantinescu, E. M., & Anitescu, M. (2014). Data-driven model for solar irradiation based on satellite observations. Solar Energy, 110, 22–38.CrossRefGoogle Scholar
  7. Bonilla, E. V., Chai, K. M. A., & Williams, C. K. I. (2008). Multi-task Gaussian process prediction. In Neural Information Processing Systems.Google Scholar
  8. Bonilla, E. V., Krauth, K., & Dezfouli, A. (2016). Generic inference in latent Gaussian process models. arxiv:1609.00577.
  9. Cressie, N., & Wikle, C. K. (2011). Statistics for spatio-temporal data. Hoboken: Wiley.zbMATHGoogle Scholar
  10. Dahl, A. & Bonilla, E. (2017). Scalable Gaussian process models for solar power forecasting. In W. L. Woon, Z. Aung, O. Kramer, & S. Madnick (Eds.), Data analytics for renewable energy integration: Informing the generation and distribution of renewable energy (pp. 94–106). Springer International Publishing.Google Scholar
  11. Dezfouli, A., & Bonilla, E. V. (2015). Scalable inference for Gaussian process models with black-box likelihoods. In Neural Information Processing Systems.Google Scholar
  12. Gardner, J. R., Pleiss, G., Wu, R., Weinberger, K. Q., & Wilson, A. G. (2018). Product kernel interpolation for scalable Gaussian processes. arXiv:1802.08903.
  13. Goovaerts, P. (1997). Geostatistics for natural resources evaluation. Oxford: Oxford University Press.Google Scholar
  14. Hensman, J., Matthews, A., & Ghahramani, Z. (2015). Scalable variational Gaussian process classification. In AISTATS.Google Scholar
  15. Hensman, J., Rattray, M., & Lawrence, N. D. (2014). Fast nonparametric clustering of structured time-series. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(2), 383–393.CrossRefGoogle Scholar
  16. Inman, R. H., Pedro, H. T., & Coimbra, C. F. (2013). Solar forecasting methods for renewable energy integration. Progress in Energy and Combustion Science, 39(6), 535–576.CrossRefGoogle Scholar
  17. Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1998). An introduction to variational methods for graphical models. Berlin: Springer.CrossRefzbMATHGoogle Scholar
  18. Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. CoRR. arXiv:1412.6980.
  19. Kingma, D. P., & Welling, M. (2014). Auto-encoding variational Bayes. International Conference on Learning Representations.Google Scholar
  20. Krauth, K., Bonilla, E. V., Cutajar, K., & Filippone, M. (2017). AutoGP: Exploring the capabilities and limitations of Gaussian process models. In Uncertainty in Artificial Intelligence.Google Scholar
  21. Matthews, A. G. de G., van der Wilk, M., Nickson, T., Fujii, K., Boukouvalas, A., León-Villagrá, P., et al. (2017). GPflow: A Gaussian process library using TensorFlow. Journal of Machine Learning Research, 18(40), 1–6.Google Scholar
  22. Nguyen, T. V. & Bonilla, E. V. (2014). Automated variational inference for Gaussian process models. In Neural Information Processing Systems.Google Scholar
  23. Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. Cambridge: The MIT Press.zbMATHGoogle Scholar
  24. Remes, S., Heinonen, M., & Kaski, S. (2017). A mutually-dependent Hadamard kernel for modelling latent variable couplings. In M.-L. Zhang & Y.-K. Noh (Eds.), Proceedings of the Ninth Asian Conference on Machine Learning, vol. 77 of Proceedings of Machine Learning Research, (pp. 455–470).Google Scholar
  25. Rezende, D. J., Mohamed, S., & Wierstra, D. (2014). Stochastic backpropagation and approximate inference in deep generative models. In International Conference on Machine Learning.Google Scholar
  26. Sampson, P. D., & Guttorp, P. (1992). Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association, 87(417), 108–119.CrossRefGoogle Scholar
  27. Shinozaki, K., Yamakawa, N., Sasaki, T., & Inoue, T. (2016). Areal solar irradiance estimated by sparsely distributed observations of solar radiation. IEEE Transactions on Power Systems, 31(1), 35–42.CrossRefGoogle Scholar
  28. Teh, Y. W., Seeger, M., & Jordan, M. I. (2005). Semiparametric latent factor models. In Artificial Intelligence and Statistics.Google Scholar
  29. Titsias, M. (2009). Variational learning of inducing variables in sparse Gaussian processes. In AISTATS.Google Scholar
  30. Voyant, C., Notton, G., Kalogirou, S., Nivet, M.-L., Paoli, C., Motte, F., et al. (2017). Machine learning methods for solar radiation forecasting: A review. Renewable Energy, 105, 569–582.CrossRefGoogle Scholar
  31. Widén, J., Carpman, N., Castellucci, V., Lingfors, D., Olauson, J., Remouit, F., et al. (2015). Variability assessment and forecasting of renewables: A review for solar, wind, wave and tidal resources. Renewable and Sustainable Energy Reviews, 44, 356–375.CrossRefGoogle Scholar
  32. Wilson, A. G., Knowles, D. A., & Ghahramani, Z. (2012). Gaussian process regression networks. In International Conference on Machine Learning.Google Scholar
  33. Yang, D., Gu, C., Dong, Z., Jirutitijaroen, P., Chen, N., & Walsh, W. M. (2013). Solar irradiance forecasting using spatial-temporal covariance structures and time-forward kriging. Renewable Energy, 60, 235–245.CrossRefGoogle Scholar
  34. Yang, D., Kleissl, J., Gueymard, C. A., Pedro, H. T., & Coimbra, C. F. (2018). History and trends in solar irradiance and PV power forecasting: A preliminary assessment and review using text mining. Solar Energy, 168, 60–101.CrossRefGoogle Scholar
  35. Yang, D., Ye, Z., Lim, L. H. I., & Dong, Z. (2015). Very short term irradiance forecasting using the lasso. Solar Energy, 114, 314–326.CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Data61SydneyAustralia

Personalised recommendations