Advertisement

Adaptive Design of Experiments Based on Gaussian Processes

  • Evgeny Burnaev
  • Maxim Panov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9047)

Abstract

We consider a problem of adaptive design of experiments for Gaussian process regression. We introduce a Bayesian framework, which provides theoretical justification for some well-know heuristic criteria from the literature and also gives an opportunity to derive some new criteria. We also perform testing of methods in question on a big set of multidimensional functions.

Keywords

Active learning Computer experiments Sequential design Gaussian processes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Forrester A., Sobester A., Keane A.: Engineering Design via Surrogate Modelling. A Practical Guide, pp. 238. Wiley (2008)Google Scholar
  2. 2.
    Bernstein A.V., Burnaev E.V., Kuleshov A.P.: Intellectual data analysis in metamodelling. In: Proceedings of 17th Russian Seminar “Neuroinformatics and its Applications to Data Analysis”, pp. 23–28, Krasnoyarsk (2009)Google Scholar
  3. 3.
    Giunta, A., Watson, L.T.: A comparison of approximation modeling technique: polynomial versus interpolating models. In: 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 392–404. AIAA, Reston (1998)Google Scholar
  4. 4.
    Batill, S.M., Renaud, J.E., Gu, X.: Modeling and simulation uncertainty in multidisciplinary design optimization. In: AIAA Paper, pp. 2000–4803, September 2000Google Scholar
  5. 5.
    Fedorov, V.V.: Theory of Optimal Experiments. Academic Press (1972)Google Scholar
  6. 6.
    Pukelsheim, F.: Optimal Design of Experiments. Wiley, New York (1993)zbMATHGoogle Scholar
  7. 7.
    Fedorov, V.V.: Design of spatial experiments: model fitting and prediction. In: Handbook of Statistics, pp. 515–553. Elsevier, Amsterdam (1996)Google Scholar
  8. 8.
    Zimmerman, D.L.: Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction. Environmetrics 17(6), 635–652 (2006)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Chen, R.J.W., Sudjianto, A.: On sequential sampling for global metamodeling in engineering design. In: Proceedings of DETC 2002, Montreal, Canada, September 29-October 2 (2002)Google Scholar
  10. 10.
    Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and Analysis of Computer Experiments. Statistical Science 4(4), 409–423 (1989). doi: 10.1214/ss/1177012413 CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Currin, C., Mitchell, T., Morris, M., Ylvisaker, D.: A Bayesian approach to the design and analysis of computer experiments. Journal of the American Statistical Association 86(416), 953–963 (1991)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Welch, W.J., Buck, R.J., Sacks, J., Wynn, H.P., Mitchell, T.J., Morris, M.D.: Screening, predicting and computer experiments. Technometrics 34, 15–25 (1992)CrossRefGoogle Scholar
  13. 13.
    Jones, D.R., Schonlau, M., William, J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455–492 (1998)CrossRefzbMATHGoogle Scholar
  14. 14.
    Bect, J., Ginsbourger, D., Li, L., Picheny, V., Vazquez, E.: Sequential design of computer experiments for the estimation of a probability of failure. Statistics and Computing 22(3), 773–793 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Burnaev, E., Panin, I.: Adaptive design of experiments for sobol indices estimation based on quadratic metamodel. In: Proceedings of the Third International Symposium on Learning and Data Sciences (SLDS 2015), London, England, UK, April 20–22 (to appear, 2015)Google Scholar
  16. 16.
    Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press (2006)Google Scholar
  17. 17.
    Burnaev, E., Zaytsev, A., Panov, M., Prikhodko, P., Yanovich, Yu.: Modeling of nonstationary covariance function of Gaussian process on base of expansion in dictionary of nonlinear functions. In ITaS-2011, Gelendzhik, October 2-7 (2011)Google Scholar
  18. 18.
    Belyaev, M., Burnaev, E., Kapushev, Y.: Gaussian process regression for large structured data sets. In: Proceedings of the Third International Symposium on Learning and Data Sciences (SLDS 2015), London, England, UK, April 20–22 (to appear, 2015)Google Scholar
  19. 19.
    Adler, R.J., Taylor, J.E.: Random Fields and Geometry. Springer, 2007Google Scholar
  20. 20.
    Saltelli, A., Sobol, I.M.: About the use of rank transformation in sensitivity analysis of model output. Reliab. Eng. Syst. Safety 50(3), 225–239 (1995)CrossRefGoogle Scholar
  21. 21.
    Ishigami, T., Homma, T.: An importance qualification technique in uncertainty analysis for computer models. In: Proceedings of the Isuma 1990, First International Symposium on Uncertainty Modelling and Analysis. University of Maryland (1990)Google Scholar
  22. 22.
    Rönkkönen, J., Lampinen, J.: An extended mutation concept for the local selection based differential evolution algorithm. In: Proceedings of Genetic and Evolutionary Computation Conference, GECCO 2007, London, England, UK, July 7–11 (2007)Google Scholar
  23. 23.
    Dolan, E.D., More, J.J.: Benchmarking optimization software with performance profiles. In: Mathematical Programmming, Ser. A 91, pp. 201–213 (2002)Google Scholar
  24. 24.
    Fox, R.L.: Optimization methods for engineering design. Addison-Wesley, Massachusetts (1971)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsMoscowRussia
  2. 2.DATADVANCE, LLCMoscowRussia
  3. 3.PreMoLabMIPTDolgoprudnyRussia

Personalised recommendations