Machine Learning

, Volume 90, Issue 2, pp 231–260 | Cite as

Forecasting electricity consumption by aggregating specialized experts

A review of the sequential aggregation of specialized experts, with an application to Slovakian and French country-wide one-day-ahead (half-)hourly predictions
  • Marie Devaine
  • Pierre Gaillard
  • Yannig Goude
  • Gilles Stoltz


We consider the setting of sequential prediction of arbitrary sequences based on specialized experts. We first provide a review of the relevant literature and present two theoretical contributions: a general analysis of the specialist aggregation rule of Freund et al. (Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing (STOC), pp. 334–343, 1997) and an adaptation of fixed-share rules of Herbster and Warmuth (Mach. Learn. 32:151–178, 1998) in this setting. We then apply these rules to the sequential short-term (one-day-ahead) forecasting of electricity consumption; to do so, we consider two data sets, a Slovakian one and a French one, respectively concerned with hourly and half-hourly predictions. We follow a general methodology to perform the stated empirical studies and detail in particular tuning issues of the learning parameters. The introduced aggregation rules demonstrate an improved accuracy on the data sets at hand; the improvements lie in a reduced mean squared error but also in a more robust behavior with respect to large occasional errors.


Prediction with expert advice Specialized experts Application to real data 



We thank the anonymous reviewers and associated editor for their valuable comments and feedback, which improved drastically the exposition of our results and conclusions. Marie Devaine and Pierre Gaillard carried out this research while completing internships at EDF R&D, Clamart; this article is based on the technical reports (Devaine et al. 2009; Gaillard et al. 2011) subsequently written. Gilles Stoltz was partially supported by the French “Agence Nationale pour la Recherche” under grant JCJC06-137444 “From applications to theory in learning and adaptive statistics” and by the PASCAL Network of Excellence under EC grant no. 506778.


  1. Antoniadis, A., Paparoditis, E., & Sapatinas, T. (2006). A functional wavelet–kernel approach for time series prediction. Journal of the Royal Statistical Society. Series B. Statistical Methodology, 68(5), 837–857. MathSciNetMATHCrossRefGoogle Scholar
  2. Antoniadis, A., Brossat, X., Cugliari, J., & Poggi, J. M. (2010). Clustering functional data using wavelets. In Proceedings of the nineteenth international conference on computational statistics (COMPSTAT). Google Scholar
  3. Auer, P., Cesa-Bianchi, N., & Gentile, C. (2002). Adaptive and self-confident on-line learning algorithms. Journal of Computer and System Sciences, 64, 48–75. MathSciNetMATHCrossRefGoogle Scholar
  4. Blum, A. (1997). Empirical support for winnow and weighted-majority algorithms: Results on a calendar scheduling domain. Machine Learning, 26, 5–23. CrossRefGoogle Scholar
  5. Blum, A., & Mansour, Y. (2007). From external to internal regret. Journal of Machine Learning Research, 8, 1307–1324. MathSciNetMATHGoogle Scholar
  6. Borodin, A., El-Yaniv, R., & Gogan, V. (2000). On the competitive theory and practice of portfolio selection. In Proceedings of the fourth Latin American symposium on theoretical informatics (LATIN’00) (pp. 173–196). Google Scholar
  7. Bruhns, A., Deurveilher, G., & Roy, J.-S. (2005). A non-linear regression model for mid-term load forecasting and improvements in seasonnality. In Proceedings of the fifteenth power systems computation conference (PSCC). Google Scholar
  8. Bunn, D. W., & Farmer, E. D. (1985). Comparative models for electrical load forecasting. New York: Wiley. Google Scholar
  9. Cesa-Bianchi, N., & Lugosi, G. (2003). Potential-based algorithms in on-line prediction and game theory. Machine Learning, 51, 239–261. MATHCrossRefGoogle Scholar
  10. Cesa-Bianchi, N., & Lugosi, G. (2006). Prediction, learning, and games. Cambridge: Cambridge University Press. MATHCrossRefGoogle Scholar
  11. Cesa-Bianchi, N., Mansour, Y., & Stoltz, G. (2007). Improved second-order inequalities for prediction under expert advice. Machine Learning, 66, 321–352. CrossRefGoogle Scholar
  12. Cover, T. M. (1991). Universal portfolios. Mathematical Finance, 1, 1–29. MathSciNetMATHCrossRefGoogle Scholar
  13. Dani, V., Madani, O., Pennock, D., Sanghai, S., & Galebach, B. (2006). An empirical comparison of algorithms for aggregating expert predictions. In Proceedings of the twenty-second conference on uncertainty in artificial intelligence (UAI). Google Scholar
  14. Dashevskiy, M., & Luo, Z. (2011). Time series prediction with performance guarantee. IET Communications, 5, 1044–1051. CrossRefGoogle Scholar
  15. de Rooij, S., & van Erven, T. (2009). Learning the switching rate by discretising Bernoulli sources online. In Proceedings of the twelfth international conference on artificial intelligence and statistics (AISTATS). Google Scholar
  16. Devaine, M., Goude, Y., & Stoltz, G. (2009). Aggregation of sleeping predictors to forecast electricity consumption (Technical report). École Normale Supérieure, Paris and EDF R&D, Clamart, July 2009. Available at
  17. Dordonnat, V., Koopman, S. J., Ooms, M., Dessertaine, A., & Collet, J. (2008). An hourly periodic state space model for modelling French national electricity load. International Journal of Forecasting, 24, 566–587. CrossRefGoogle Scholar
  18. Freund, Y., Schapire, R., Singer, Y., & Warmuth, M. (1997). Using and combining predictors that specialize. In Proceedings of the twenty-ninth annual ACM symposium on the theory of computing (STOC) (pp. 334–343). Google Scholar
  19. Gaillard, P., Goude, Y., & Stoltz, G. (2011). A further look at the forecasting of the electricity consumption by aggregation of specialized experts (Technical report). École Normale Supérieure, Paris and EDF R&D, Clamart, July 2011. Updated February 2012; available at
  20. Gerchinovitz, S., Mallet, V., & Stoltz, G. (2008). A further look at sequential aggregation rules for ozone ensemble forecasting (Technical report). Inria Paris-Rocquencourt and École Normale Supérieure Paris, September 2008. Available at
  21. Goude, Y. (2008a). Mélange de prédicteurs et application à la prévision de consommation électrique. PhD thesis, Université Paris-Sud XI, January 2008. Google Scholar
  22. Goude, Y. (2008b). Tracking the best predictor with a detection based algorithm. In Proceedings of the joint statistical meetings (JSM). See the section on Statistical Computing. Google Scholar
  23. Herbster, M., & Warmuth, M. (1998). Tracking the best expert. Machine Learning, 32, 151–178. MATHCrossRefGoogle Scholar
  24. Jacobs, A. Z. (2011). Adapting to non-stationarity with growing predictor ensembles. Master’s thesis, Northwestern University. Google Scholar
  25. Kleinberg, R. D., Niculescu-Mizil, A., & Sharma, Y. (2008). Regret bounds for sleeping experts and bandits. In Proceedings of the twenty-first annual conference on learning theory (COLT) (pp. 425–436). Google Scholar
  26. Mallet, V. (2010). Ensemble forecast of analyses: coupling data assimilation and sequential aggregation. Journal of Geophysical Research, 115, D24303. CrossRefGoogle Scholar
  27. Mallet, V., Stoltz, G., & Mauricette, B. (2009). Ozone ensemble forecast with machine learning algorithms. Journal of Geophysical Research, 114, D05307. CrossRefGoogle Scholar
  28. Monteleoni, C., & Jaakkola, T. (2003). Online learning of non-stationary sequences. In Advances in neural information processing systems (NIPS) (Vol. 16, pp. 1093–1100). Google Scholar
  29. Monteleoni, C., Schmidt, G., Saroha, S., & Asplund, E. (2011). Tracking climate models. Statistical Analysis and Data Mining, 4, 372–392. Special issue “Best of CIDU 2010”. MathSciNetCrossRefGoogle Scholar
  30. Pierrot, A., & Goude, Y. (2011). Short-term electricity load forecasting with generalized additive models. In Proceedings of the sixteenth international conference on intelligent system application to power systems (ISAP). Google Scholar
  31. Pierrot, A., Laluque, N., & Goude, Y. (2009). Short-term electricity load forecasting with generalized additive models. In Proceedings of the third international conference on computational and financial econometrics (CFE). Google Scholar
  32. Stoltz, G., & Lugosi, G. (2005). Internal regret in on-line portfolio selection. Machine Learning, 59, 125–159. MATHCrossRefGoogle Scholar
  33. Vovk, V., & Zhdanov, F. (2008). Prediction with expert advice for the Brier game. In Proceedings of the twenty-fifth international conference on machine learning (ICML). Google Scholar
  34. Wood, S. N. (2006). Generalized additive models: an introduction with R. London/Boca Raton: Chapman & Hall/CRC. MATHGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Marie Devaine
    • 1
  • Pierre Gaillard
    • 2
  • Yannig Goude
    • 3
  • Gilles Stoltz
    • 2
    • 4
  1. 1.Ecole Normale SupérieureParisFrance
  2. 2.Ecole Normale Supérieure, CNRS, INRIAParisFrance
  3. 3.EDF R&DClamartFrance
  4. 4.HEC Paris, CNRSJouy-en-JosasFrance

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