Integrating Simulated Annealing and Delta Technique for Constructing Optimal Prediction Intervals

  • Abbas Khosravi
  • Saeid Nahavandi
  • Doug Creighton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5863)


This paper aims at developing a new criterion for quantitative assessment of prediction intervals. The proposed criterion is developed based on both key measures related to quality of prediction intervals: length and coverage probability. This criterion is applied as a cost function for optimizing prediction intervals constructed using delta technique for neural network model. Optimization seeks out to minimize length of prediction intervals without compromising their coverage probability. Simulated Annealing method is employed for readjusting neural network parameters for minimization of the new cost function. To further ameliorate search efficiency of the optimization method, parameters of the network trained using weight decay method are considered as the initial set in Simulated Annealing algorithm. Implementation of the proposed method for a real world case study shows length and coverage probability of constructed prediction intervals are better than those constructed using traditional techniques.


prediction interval neural network simulated annealing delta technique 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dybowski, R., Roberts, S.J.: Confidence intervals and prediction intervals for feed-forward neural networks. In: Clinical Applications of Artificial Neural Networks, Cambridge, MA (2000)Google Scholar
  2. 2.
    Hwang, J.T.G., Ding, A.A.: Prediction Intervals for Artificial Neural Networks. Journal of the American Statistical Association 92, 748–757 (1997)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Veaux, R.D.d., Schumi, J., Jason, S., Ungar, L.H.: Prediction Intervals for Neural Networks via Nonlinear Regression. Technometrics 40, 273–282 (1998)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)Google Scholar
  5. 5.
    Lu, T., Viljanen, M.: Prediction of indoor temperature and relative humidity using neural network models: model comparison. Neural Computing & Applications 18, 345–357 (2009)CrossRefGoogle Scholar
  6. 6.
    Yu, G., Qiu, H., Djurdjanovic, D., Lee, J.: Feature signature prediction of a boring process using neural network modeling with confidence bounds. The International Journal of Advanced Manufacturing Technology 30, 614–621 (2006)CrossRefGoogle Scholar
  7. 7.
    Papadopoulos, G., Edwards, P.J., Murray, A.F.: Confidence estimation methods for neural networks: a practical comparison. IEEE Transactions on Neural Networks 12, 1278–1287 (2001)CrossRefGoogle Scholar
  8. 8.
    Ho, S.L., Xie, M., Tang, L.C., Xu, K., Goh, T.N.: Neural network modeling with confidence bounds: a case study on the solder paste deposition process. IEEE Transactions on Electronics Packaging Manufacturing 24, 323–332 (2001)CrossRefGoogle Scholar
  9. 9.
    Alonso, A.M., Sipols, A.E.: A time series bootstrap procedure for interpolation intervals. Computational Statistics & Data Analysis 52, 1792–1805 (2008)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Yang, L., Kavli, T., Carlin, M., Clausen, S., de Groot, P.F.M.: An evaluation of confidence bound estimation methods for neural networks. In: Proceeding of ESIT (2000)Google Scholar
  11. 11.
    Goffe, W.L., Ferrier, G.D., Rogers, J.: Global optimization of statistical functions with simulated annealing. Journal of Econometrics 60, 65–99Google Scholar
  12. 12.
    Kirkpatrick, S., Gelatt, C., Vecchi, M.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Aarts, E., Korst, J.: Simulated Annealing and Boltzmann Machine: A Stochastic Approach to Combinatorial Optimization and Neural Computing. J. Wiley, New York (1990)Google Scholar
  14. 14.
    Khosravi, A., Nahavandi, S., Creighton, D.: Estimating performance indexes of a baggage handling system using metamodels. In: IEEE International Conference on Industrial Technology, ICIT 2009 (2009)Google Scholar
  15. 15.
    Khosravi, A., Nahavandi, S., Creighton, D.: Constructing Prediction Intervals for Neural Network Metamodels of Complex Systems. In: International Joint Conference on Neural Networks, IJCNN 2009 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Abbas Khosravi
    • 1
  • Saeid Nahavandi
    • 1
  • Doug Creighton
    • 1
  1. 1.Centre for Intelligent Systems Research (CISR)Deakin UniversityGeelongAustralia

Personalised recommendations