Projection pursuit emulation for many-input computer experiments

References

• Aldrin, M. 1996. Moderate projection pursuit regression for multivariate response data. Computational Statistics & Data Analysis 21:501–31.
   Web of Science ®Google Scholar
• Aldrin, M., E. Bolviken, and T. Schweder. 1993. Projection pursuit regression for moderate non-linearities. Computational Statistics & Data Analysis 16:379–403.
   Web of Science ®Google Scholar
• Boukouvalas, A., J. P. Gosling, and H. Maruri-Aguilar. 2014. An efficient screening method for computer experiments. Technometrics 56 (4):422–31. doi:10.1080/00401706.2013.866599.
   Web of Science ®Google Scholar
• Carnell, R. 2020. lhs: Latin hypercube samples. R package version 1.1.1.
   Google Scholar
• Chang, J., and H. K. Lee. 2015. Variable selection via a multi-stage strategy. Journal of Applied Statistics 42 (4):762–74. doi:10.1080/02664763.2014.985640.
   Web of Science ®Google Scholar
• Choi, T., J. Q. Shi, and B. Wang. 2011. A Gaussian process regression approach to a single-index model. Journal of Nonparametric Statistics 23 (1):21–36. doi:10.1080/10485251003768019.
   Web of Science ®Google Scholar
• Clarke, J. A. 2001. Energy simulation in building design (2nd ed.). Oxford: Butterworth-Heinemann.
   Google Scholar
• Dancik, G. M. 2013. mlegp: Maximum likelihood estimates of gaussian processes. R package version 3.1.4.
   Google Scholar
• Delbridge, I. A., D. S. Bindel, and A. G. Wilson. 2019. Randomly projected additive Gaussian processes for regression. arXiv:1912.12834.
   Google Scholar
• Demmel, J. W. 1997. Applied numerical linear algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics.
   Google Scholar
• Fan, J. 1993. Local linear regression smoothers and their minimax efficiencies. The Annals of Statistics 21 (1):196–216. doi:10.1214/aos/1176349022.
   Web of Science ®Google Scholar
• Fan, J., and I. Gijbels. 1992. Variable bandwidth and local linear regression smoothers. The Annals of Statistics 20 (4):2008–36. doi:10.1214/aos/1176348900.
   Web of Science ®Google Scholar
• Ferraty, F., A. Goia, E. Salinelli, and P. Vieu. 2013. Functional projection pursuit regression. Test 22 (2):293–320. doi:10.1007/s11749-012-0306-2.
   Web of Science ®Google Scholar
• Friedman, J. H., and W. Stuetzle. 1981. Projection pursuit regression. Journal of the American Statistical Association 76 (376):817–23. doi:10.1080/01621459.1981.10477729.
   Web of Science ®Google Scholar
• Gilboa, E., Y. Saatci, and J. Cunningham. 2013. Scaling multidimensional Gaussian processes using projected additive approximations. In International Conference on Machine Learning, Atlanta, GA, 454–61.
   Google Scholar
• Gramacy, R. B., and H. Lian. 2012. Gaussian process single index models as emulators for computer experiments. Technometrics 54 (1):30–41. doi:10.1080/00401706.2012.650527.
   Web of Science ®Google Scholar
• Hall, P., and B. A. Turlach. 1997. Interpolation methods for adapting to sparse design in nonparametric regression. Journal of the American Statistical Association 92 (438):466–72. doi:10.1080/01621459.1997.10473998.
   Web of Science ®Google Scholar
• Hardle, W., P. Hall, and H. Ichimura. 1993. Optimal smoothing in single-index models. The Annals of Statistics 21 (1):157–78. doi:10.1214/aos/1176349020.
   Web of Science ®Google Scholar
• Jeffrey, S. R., and H. Tristen. 2020. np: Nonparametric kernel smoothing methods for mixed data types. R package version 0.60-10.
   Google Scholar
• Joseph, V. R., and L. Kang. 2011. Regression-based inverse distance weighting with applications to computer experiments. Technometrics 53 (3):254–65. doi:10.1198/TECH.2011.09154.
   Web of Science ®Google Scholar
• Kang, L., and V. R. Joseph. 2016. Kernel approximation: From regression to interpolation. SIAM/ASA Journal on Uncertainty Quantification 4 (1):112–29. doi:10.1137/130948112.
   Web of Science ®Google Scholar
• Linkletter, C. D., D. Bingham, N. W. Hengartner, D. Higdon, and K. Ye. 2006. Variable selection for Gaussian process models in computer experiments. Technometrics 48 (4):478–90. doi:10.1198/004017006000000228.
   Web of Science ®Google Scholar
• Liu, X., and S. Guillas. 2017. Dimension reduction for Gaussian process emulation: An application to the influence of bathymetry on tsunami heights. SIAM/ASA Journal on Uncertainty Quantification 5 (1):787–812. doi:10.1137/16M1090648.
   Web of Science ®Google Scholar
• Ma, Y., and L. Zhu. 2012. A semiparametric approach to dimension reduction. Journal of the American Statistical Association 107 (497):168–79. doi:10.1080/01621459.2011.646925.
   PubMed Web of Science ®Google Scholar
• Morris, M. D. 1991. Factorial sampling plans for preliminary computational experiments. Technometrics 33 (2):161–74. doi:10.1080/00401706.1991.10484804.
   Web of Science ®Google Scholar
• Morris, M. D., and T. J. Mitchell. 1995. Exploratory designs for computational experiments. Journal of Statistical Planning and Inference 43 (3):381–402. doi:10.1016/0378-3758(94)00035-T.
   Web of Science ®Google Scholar
• Reich, B. J., C. B. Storlie, and H. D. Bondell. 2009. Variable selection in Bayesian smoothing spline ANOVA models: Application to deterministic computer codes. Technometrics 51 (2):110–20. doi:10.1198/TECH.2009.0013.
   PubMed Web of Science ®Google Scholar
• Roosen, C. B., and T. J. Hastie. 1994. Automatic smoothing spline projection pursuit. Journal of Computational and Graphical Statistics 3:235–48.
   Google Scholar
• Runarsson, T. P., and X. Yao. 2005. Search biases in constrained evolutionary optimization. IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews) 35 (2):233–43. doi:10.1109/TSMCC.2004.841906.
   Web of Science ®Google Scholar
• Sacks, J., W. Welch, T. J. Mitchell, and H. P. Wynn. 1989. Design and analysis of computer experiments. Statistical Science 4 (4):409–23. doi:10.1214/ss/1177012413.
   Google Scholar
• Santner, T. J., B. J. Williams, and W. I. Notz. 2018. The design and analysis of computer experiments. New York: Springer.
   Google Scholar
• Shepard, D. 1968. A two-dimensional interpolation function for irregularly-spaced data. Proc. 23rd ACM National Conference, Association for Computing Machinery, New York, 517–24. doi:10.1145/800186.810616.
   Google Scholar
• Steven, G. J. 2016. nlopt: Nonlinear-optimization Package. R package version 1.1.0.
   Google Scholar
• Sung, C.-L., W. J. Wang, M. Plumlee, and B. Haaland. 2020. Multi-resolution functional ANOVA for large-scale, many-input computer experiments. Journal of the American Statistical Association 115 (530):908–19. doi:10.1080/01621459.2019.1595630.
   Web of Science ®Google Scholar
• Yang, X. 2010. Firefly algorithm, stochastic test functions and design optimization. International Journal of Bio-Inspired Computation 2 (2):78–84. doi:10.1504/IJBIC.2010.032124.
   Web of Science ®Google Scholar