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Journal of Machine Learning for Modeling and Computing

每年出版 4 

ISSN 打印: 2689-3967

ISSN 在线: 2689-3975

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CONSTRAINED GAUSSIAN PROCESS REGRESSION: AN ADAPTIVE APPROACH FOR THE ESTIMATION OF HYPERPARAMETERS AND THE VERIFICATION OF CONSTRAINTS WITH HIGH PROBABILITY

卷 2, 册 2, 2021, pp. 55-76
DOI: 10.1615/JMachLearnModelComput.2021039837
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摘要

This paper focuses on the Gaussian process regression (GPR) of nonlinear functions subject to multiple linear constraints such as boundedness, monotonicity or convexity. It presents an algorithm allowing for the optimization, in a concerted way, of the statistical moments of the Gaussian process used for the regression and the position of a reduced number of points where the constraints are required to hold, such that the constraints are verified in the whole input space, with high probability, at a reasonable computational cost. After having presented the theoretical bases and the numerical implementation of this algorithm, this paper illustrates its efficiency through the analysis of several test functions of increasing dimensions.

参考文献
  1. Agrell, C., Gaussian Processes with Linear Operator Inequality Constraints, J. Mach. Learn. Res., vol. 20, pp. 1-36,2019.

  2. Auffray, Y., Barbillon, P., and Marin, J., Maximin Design on Non Hypercube Domains and Kernel Interpolation, Stat. Comput., vol. 22, no. 3, pp. 703-712,2012.

  3. Bachoc, F., Lagnoux, A., and Lopera, A.L., Maximum Likelihood Estimation for Gaussian Processes under Inequality Constraints, Electr. J. Stat., vol. 13, pp. 2921-2969,2019.

  4. Botev, Z.I., The Normal Law under Linear Restrictions: Simulation and Estimation via Minimax Tilting, J. R. Stat. Soc.: Ser. B, vol. 79, no. 1, pp. 125-148,2017.

  5. Damblin, G., Couplet, M., andIooss, B., Numerical Studies of Space Filing Designs: Optimization of Latin Hypercube Samples and SubprojectionProperties, J. Simul., vol. 7, pp. 276-289,2013.

  6. Fang, K., Wrap-Around 12-Discrepancy of Random Sampling, Latin Hypercube and Uniform Designs, J. Complex, vol. 17, pp. 608-624,2001.

  7. Fang, K., Li, R., and Sudjianto, A., Design and Modeling for Computer Experiments, London, UK: Chapman and Hall, 2006.

  8. Fang, K. and Lin, D., Uniform Experimental Designs and Their Applications in Industry, Handbook Stat., vol. 22, pp. 131-178,2003.

  9. Golshtein, E., An Iterative Linear Programming Algorithm Based on an Augmented Lagrangian, in Proc. of the Nonlinear Programming Symp. 4, Madison, WI, pp. 131-146, July 14-16,1981.

  10. Joseph, V.R., Gul, E., and Ba, S., Maximum Projection Designs for Computer Experiments, Biometrika, vol. 102, no. 2, pp. 371-380,2015.

  11. Kennedy, M.C. and O'Hagan, A., Bayesian Calibration of Computer Models, J. R. Stat. Soc, vol. 63, pp. 425-464,2001.

  12. Kotecha, J.H. and Djuric, P.M., Gibbs Sampling Approach for Generation of Truncated Multivariate Gaussian Random Variables, in Proc. of the Acoustics, Speech, and Signal Processing, 1999, on 1999 IEEE Int. Conf. Volume 03, ICASSP '99, IEEE Computer Society, Phoenix, AZ, pp. 1757-1760,1999. DOI: 10.1109/ICASSP. 1999.756335.

  13. Lopez-Lopera, A., Bachoc, F., Durrande, N., and Roustant, O., Finite Dimensional Gaussian Approximation with Linear Inequality Constraints, SIAM/ASA J. Uncert. Quantif., vol. 6, no. 3, pp. 1224-1255, 2018.

  14. Maatouk, H. and Bay, X., Gaussian Process Emulators for Computer Experiments with Inequality Constraints, Math. Geosci, vol. 49, no. 5, pp. 557-582,2017.

  15. Pensoneault, A., Yang, X., and Zhu, X., Nonnegativity-Enforced Gaussian Process Regression, Theor. Appl. Mech. Lett., vol. 10, no. 3, pp. 182-187,2020.

  16. Perrin, G., Point Process-Based Approaches for the Reliability Analysis of Systems Modeled by Costly Simulators, Reliab. Eng. Sys. Safety, vol. 214,2021.

  17. Perrin, G. and Cannamela, C., A Repulsion-Based Method for the Definition and the Enrichment of Opotimized Space Filing Designs in Constrained Input Spaces, J. Soc. Frangaise Stat., vol. 158, no. 1, pp. 37-67,2017.

  18. Riihimki, J. and Vehtari, A., Gaussian Processes with Monotonicity Information, J. Mach. Learn. Res.- Proc. Track, vol. 9, pp. 645-652,2010.

  19. Sacks, J., Welch, W., Mitchell, T., and Wynn, H., Design and Analysis of Computer Experiments, Stat. Sci., vol. 4, pp. 409-435,1989.

  20. Santner, T.J., Williams, B., and Notz, W., The Design and Analysis of Computer Experiments, New York, NY: Springer, 2003.

  21. Swiler, L., Gulian, M., Frankel, A., Safta, C., and Jakeman, J., A Survey of Constrained Gaussian Process Regression: Approahces and Implementation Challenges, J. Mach. Learn. Model. Comput., vol. 1, no. 2, pp. 119-156,2020.

  22. Veiga, S.D. and Marrel, A., Gaussian Process Modeling with Inequality Constraints, Ann. Faculte Sci. Toulouse: Math, vol. 21, no. 3, pp. 529-555,2012.

  23. Veiga, S.D. and Marrel, A., Gaussian Process Regression with Linear Inequality Constraints, Reliab. Eng. Sys. Safety, vol. 195, p. 106732,2020.

  24. Wang, X. and Berger, J.O., Estimating Shape Constrained Functions Using Gaussian Processes, SIAM/ASA J. Uncert. Quantif., vol. 4, pp. 1-25,2016.

  25. Zhan, D. and Xing, H., Expected Improvement for Expensive Optimization: A Review, J. Global Optim., vol. 78, p. 507-544, 2020.

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