4.9. References

[Everitt2002]
    1. Everitt. The Cambridge Dictionary of Statistics. Cambridge University Press, 2002.
[Tetko1995]
    1. Tetko, D. J. Livingstone, and A. I. Luik. Neural network studies. 1. comparison of overfitting and overtraining. J. Chem. Inf. Comput. Sci., 35(5):826-833, 1995.
[Bernstein2011]
  1. Bernstein, M. Belyaev, E. Burnaev, and Y. Yanovich. Smoothing of surrogate models. In Proceedings of the conference “Information Technology and Systems - 2011”, pages 423-432, Gelendzhik, Russia, 2011.
[Arlot2010]
  1. Arlot and A. Celisse. A survey of cross-validation procedures for model selection. Statistics Surveys, 4:40-79, 2010.
[Geisser1993]
  1. Geisser. Predictive Inference. New York: Chapman and Hall, 1993.
[Rasmussen2005]
    1. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). The MIT Press, 2005.
[Runge1901]
  1. Runge. Uber empirische Funktionen und die Interpolation zwischen aquidistanten Ordinaten. Zeitschrift fur Mathematik und Physik, 46:224-243, 1901.
[Hastie2008]
  1. Hastie, R. Tibshirani, and J. Friedman. The elements of statistical learning: data mining, inference, and prediction. Springer, 2008.
[Hyman1983]
    1. Hyman. Accurate monotonicity preserving cubic interpolation. SIAM J. Sci. Stat. Comput., 4(4):645-654, 1983.
[Renka1987]
    1. Renka. Interpolatory tension splines with automatic selection of tension factors. Society for Industrial and Applied Mathematics, Journal for Scientific and Statistical Computing, 8:393-415, 1987.
[Rentrop1980]
  1. Rentrop. An algorithm for the computation of the exponential spline. Numerische Mathematik, 35:81-93, 1980.
[Belyaev2013]
  1. Belyaev and E. Burnaev. Approximation of a multidimensional dependency based on a linear expansion in a dictionary of parametric functions. Informatics and its Applications, 7(3), 2013.
[Cressie1993]
      1. Cressie. Statistics for Spatial Data. Wiley, 1993.
[Burnaev2011]
  1. Burnaev, A. Zaytsev, M. Panov, P. Prihodko, and Y. Yanovich. Modeling of non-stationary covariance function of gaussian process using decomposition in dictionary of nonlinear functions. In Proceedings of the conference “Information Technology and Systems - 2011”, pages 357-362, Gelendzhik, Russia, 2011.
[Foster2009]
  1. Foster, A. Waagen, and N. Aijaz. Stable and efficient gaussian process calculations. Journal of machine learning, 10:857-882, 2009.
[Bettebghor2011]
  1. Bettebghor, N. Bartoli, S. Grihon, J. Morlier, and M. Samuelides. Surrogate modeling approximation using a mixture of experts based on EM joint estimation. Structural and Multidisciplinary Optimization, 43:243-259, 2011.
[Grihon2012]
  1. Grihon, E. Burnaev, M. Belyaev and P. Prikhodko. Surrogate Modeling of Stability Constraints for Optimization of Composite Structures, Third International Workshop on Surrogate Modelling and Space Mapping For Engineering Optimization (SMSMEO 2012), Reykjavik, Iceland; Aug 9-11, 2012.
[Belyaev2013b]
  1. Belyaev. Approximation problem for cartesian product based data. Proceedings of MIPT, 5(3):11-23, 2013.
[Belyaev2013c]
  1. Belyaev. Approximation problem for factorized data. Artificial intelligence and decision theory, 3:95-110, 2013.
[Belyaev2011]
  1. Belyaev, E. Burnaev, and A. Lyubin. Parametric dictionary selection for approximation of multidimensional dependency. In Proceedings of All-Russian conference “Mathematical methods of pattern recognition (MMPR-15)”, pages 146-150, Petrozavodsk, Russia, 11-17 September 2011.
[Panov2011]
    1. Panov, E. V. Burnaev, and A. A. Zaytsev. Bayesian regularization for regression based on gaussian processes. In Proceedings of All-Russian conference “Mathematical methods of pattern recognition (MMPR-15)”, pages 142-146, Petrozavodsk, Russia, 11-17 September 2011.
[Forrester2008]
  1. Forrester, A. S’obester, and A. Keane. Engineering design via surrogate modelling: a practical guide. Progress in astronautics and aeronautics. J. Wiley, 2008.