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A review on quantile regression for stochastic computer experiments

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  • Torossian, Léonard
  • Picheny, Victor
  • Faivre, Robert
  • Garivier, Aurélien

Abstract

We report on an empirical study of the main strategies for quantile regression in the context of stochastic computer experiments. To ensure adequate diversity, six metamodels are presented, divided into three categories based on order statistics, functional approaches, and those of Bayesian inspiration. The metamodels are tested on several problems characterized by the size of the training set, the input dimension, the signal-to-noise ratio and the value of the probability density function at the targeted quantile. The metamodels studied reveal good contrasts in our set of experiments, enabling several patterns to be extracted. Based on our results, guidelines are proposed to allow users to select the best method for a given problem.

Suggested Citation

  • Torossian, Léonard & Picheny, Victor & Faivre, Robert & Garivier, Aurélien, 2020. "A review on quantile regression for stochastic computer experiments," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:reensy:v:201:y:2020:i:c:s0951832019300638
    DOI: 10.1016/j.ress.2020.106858
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    1. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    2. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Description of techniques," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 28-54.
    3. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    4. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Example results," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 55-77.
    5. Andreas Christmann & Ingo Steinwart, 2008. "Consistency of kernel‐based quantile regression," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(2), pages 171-183, March.
    6. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    7. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    8. Janis Janusevskis & Rodolphe Le Riche, 2013. "Simultaneous kriging-based estimation and optimization of mean response," Journal of Global Optimization, Springer, vol. 55(2), pages 313-336, February.
    9. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    11. Efromovich, Sam, 2010. "Dimension Reduction and Adaptation in Conditional Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 761-774.
    12. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    13. Taddy, Matthew A. & Kottas, Athanasios, 2010. "A Bayesian Nonparametric Approach to Inference for Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 357-369.
    14. Victor Picheny & Ronan Trépos & Pierre Casadebaig, 2017. "Optimization of black-box models with uncertain climatic inputs—Application to sunflower ideotype design," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-15, May.
    15. Marzena Rostek, 2010. "Quantile Maximization in Decision Theory ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 339-371.
    16. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    1. Song, Bing & Zhang, Zhipeng & Qin, Yong & Liu, Xiang & Hu, Hao, 2022. "Quantitative analysis of freight train derailment severity with structured and unstructured data," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. Manon Costa & Sébastien Gadat, 2021. "Non-asymptotic study of a recursive superquantile estimation algorithm," Post-Print hal-03610477, HAL.
    3. Gadat, Sébastien & Costa, Manon, 2020. "Non asymptotic controls on a stochastic algorithm for superquantile approximation," TSE Working Papers 20-1149, Toulouse School of Economics (TSE).

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