Discrete mixtures of kernels for Kriging-based optimization

Quality and Reliability Engineering International

Volumn 24, Issue 6, 2008, Pages 681-691

  Ginsbourger, David ^a   Helbert, Céline ^a   Carraro, Laurent ^a  

^a ECOLE DES MINES DE SAINT ETIENNE   (France)

Author keywords

Gaussian processes; Global optimization; Kernel selection; Mixtures of experts

Indexed keywords

MAXIMUM LIKELIHOOD ESTIMATION; MIXTURES; NETWORK PROTOCOLS; OPTIMIZATION; RISK PERCEPTION; SENSOR NETWORKS; STATISTICS; TRELLIS CODES;

COVARIANCE KERNELS; DATA SETS; DISCRETE MIXTURES; EFFICIENT GLOBAL OPTIMIZATION ALGORITHMS; EXPECTED IMPROVEMENTS; EXPLORATION STRATEGIES; GAUSSIAN KERNELS; GAUSSIAN PROCESSES; KERNEL SELECTION; KRIGING; KRIGING MODELS; LIKELIHOOD RATIOS; MAXIMUM-LIKELIHOOD; MIXTURES OF EXPERTS; MODEL MISSPECIFICATION; MULTIPLE KERNELS; OPTIMIZATION CRITERIONS; SIMULTANEOUS USES;

GLOBAL OPTIMIZATION;

EID: 54949126356     PISSN: 07488017     EISSN: 10991638     Source Type: Journal    
DOI: 10.1002/qre.945     Document Type: Conference Paper

References (27)

1. Koehler JR, Owen AB. Computer experiments. Technical Report, Department of Statistics, Stanford University, 1996.
2. Santner TJ, Williams BJ, Notz WJ. The Design and Analysis of Computer Experiments. Springer: Berlin, 2003.
3. Jones DR, Schonlau M, Welch WJ. Efficient global optimization of expensive black-box functions. Journal of Global Optimization 1998; 13:455-492.
4. Journel A. Fundamentals of geostatistics in five lessons. Technical Report, Stanford Center for Reservoir Forecasting, 1988.
5. Cressie NAC. Statistics for Spatial Data (Wiley Series in Probability and Mathematical Statistics). Wiley: New York, 1993.
6. Rasmussen CE, Williams KI. Gaussian Processes for Machine Learning. MIT Press: Cambridge, MA, 2006.
7. Robert CP. L'analyse Statistique Bayesienne. Economica: Paris, 1992.
8. Mebane WR Jr, Sekhon JS. Genetic optimization using derivatives: theory and application to non-linear models. Political Analysis 1998; 7:187-210.
9. Sweeting TJ. Uniform asymptotic normality of the maximum likelihood estimator. The Annals of Statistics 1980; 8(6): 1375-1381.
10. Mardia KV, Marshall RJ. Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 1984; 71:135-146.
11. Abt M, Welch WJ. Fisher information and maximum-likelihood estimation of covariance parameters in Gaussian stochastic processes. The Canadian Journal of Statistics 1998; 26:127-137.
12. Ginsbourger D, Dupuy D, Badea A, Roustant O, Carraro L. On the selection and the estimation of Kriging models for deterministic computer experiments. Joint ENBIS-DEINDE Conference, 2007.
13. Li R, Sudjianto A. Analysis of computer experiments using penalized likelihood in Gaussian Kriging models. Technometrics 2005; 47(47): 111-120.
14. O'Hagan A. Bayesian analysis of computer code outputs: a tutorial. Reliability Engineering and System Safety 2006; 91(91):1290-1300.
15. Martin JD, Simpson TW. A Monte Carlo simulation of the Kriging model. In Proceedings of the Tenth AIAA/ISSMO MultidiscipHnary Analysis and Optimization Conference, 30 August-2 September, Albany, NJ, AIAA-2004-4324, 2004.
16. Jones DR. A taxonomy of global optimization methods based on response surfaces. Journal of Global Optimization 2001; 2 (21):345-383.
17. Sasena MJ, Papalambros P, Goovaerts P. Exploration of metamodeling sampling criteria for constrained global optimization. Engineering Optimization 2001.
18. Kracker H. Methoden zur analyse von computerexperimenten mit anwendung auf die hochdruckblechumformung. Master's Thesis, Dortmund University, 2006.
19. Henkenjohann N, Göbel R, Kleiner M, Kunert J. An adaptive sequential procedure for efficient optimization of the sheet metal spinning process. Quality and Reliability Engineering International 2005; 21:439-455.
20. Schlather M. Simulation and analysis of random fields. R News 2001; 1(2): 18-20.
21. Vert JP. Double mixture and universal inference. Technical Report DMA-00-15, Ecole Normale Supérieure, 2000.
22. Goel T, Haftka R, Shyy W, Queipo N. Simultaneous use of multiple surrogates. In Proceedings of the Eleventh AIAA-ISSMO MultidiscipHnary Analysis and Optimization, 6-8 September 2006, Portsmouth, Virginia, 2006.
23. Paciorek CJ. Nonstationary Gaussian processes for regression and spatial modelling. PhD Thesis, Carnegie Mellon University, 2003.
24. Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning. Springer: Berlin, 2001.
25. McLachlan GJ, Krishnan T. The EM Algorithm and. Extensions (Wiley Series in Probability and. Statistics). Wiley: New York, 1997.
26. Jordan MI, Jacobs RA. Hierarchical mixture of experts and the EM algorithm. Technical Report, Massachusetts Institute of Technology, 1993.
27. Burnham KP, Anderson DR. Model Selection and Multimodel Inference. Springer: Berlin, 1998.