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Nicolas Durrande; David Ginsbourger; Olivier Roustant
Additive Covariance kernels for high-dimensional Gaussian Process modeling
Annales de la faculté des sciences de Toulouse Sér. 6, 21 no. 3 (2012), p. 481-499, doi: 10.5802/afst.1342
Article PDF | Reviews MR 3076409 | Zbl 1266.60068

Résumé - Abstract

Gaussian Process models are often used for predicting and approximating expensive experiments. However, the number of observations required for building such models may become unrealistic when the input dimension increases. In oder to avoid the curse of dimensionality, a popular approach in multivariate smoothing is to make simplifying assumptions like additivity. The ambition of the present work is to give an insight into a family of covariance kernels that allows combining the features of Gaussian Process modeling with the advantages of generalized additive models, and to describe some properties of the resulting models.

Bibliography

[1] Azaïs (J.M.) and Wschebor (M.).— Level sets and extrema of random processes and fields, Wiley Online Library (2009).  MR 2478201 |  Zbl 1168.60002
[2] Bach (F.).— Exploring large feature spaces with hierarchical multiple kernel learning, Arxiv preprint arXiv:0809.1493 (2008).
[3] Buja (A.), Hastie (T.) and Tibshirani (R.).— Linear smoothers and additive models, The Annals of Statistics, p. 453-510 (1989).  MR 994249 |  Zbl 0689.62029
[4] Chilès (J.P.) and Delfiner (P.).— Geostatistics: modeling spatial uncertainty, volume 344, Wiley-Interscience (1999).  MR 1679557 |  Zbl pre05988042
[5] Cressie (N.).— Statistics for spatial data, Terra Nova, 4(5), p. 613-617 (1992).  MR 1239641 |  Zbl 0799.62002
[6] Fang (K.).— Design and modeling for computer experiments, volume 6. CRC Press (2006).  MR 2223960 |  Zbl 1093.62117
[7] Fortet (R.M.).— Les operateurs integraux dont le noyau est une covariance, Trabajos de estadística y de investigación operativa, 36(3), p. 133-144 (1985).  Zbl 0733.47030
[8] Gaetan (C.) and Guyon (X.).— Spatial statistics and modeling, Springer Verlag (2009).  MR 2569034 |  Zbl pre05652103
[9] Ginsbourger (D.), Dupuy (D.), Badea (A.), Carraro (L.) and Roustant (O.).— A note on the choice and the estimation of kriging models for the analysis of deterministic computer experiments, Applied Stochastic Models in Business and Industry, 25(2), p. 115-131 (2009).  MR 2510851 |  Zbl 1224.62149
[10] Gunn (S.R.) and Brown (M.).— Supanova: A sparse, transparent modelling approach, In Neural Networks for Signal Processing IX, 1999, Proceedings of the 1999 IEEE Signal Processing Society Workshop, p. 21-30. IEEE (1999).
[11] Hastie (T.).— gam: Generalized Additive Models, 2011, R package version 1.04.1.
[12] Hastie (T.J.) and Tibshirani (R.J.).— Generalized additive models, Chapman & Hall/CRC (1990).  MR 1082147 |  Zbl 0747.62061
[13] Loeppky (J.L.), Sacks (J.) and Welch (W.J.).— Choosing the sample size of a computer experiment: A practical guide, Technometrics, 51(4), p. 366-376 (2009).  MR 2756473
[14] Muehlenstaedt (T.), Roustant (O.), Carraro (L.) and Kuhnt (S.).— Data-driven Kriging models based on FANOVA-decomposition, to appear in Statistics and Computing.
[15] Newey (W.K.).— Kernel estimation of partial means and a general variance estimator, Econometric Theory, 10(02), p. 1-21 (1994).  MR 1293201
[16] Rasmussen (C.E.) and Williams (C.K.I.).— Gaussian processes for machine learning (2005).  MR 2514435
[17] Roustant (O.), Ginsbourger (D.) and Deville (Y.).— DiceKriging: Kriging methods for computer experiments, 2011, R package version 1.3.
[18] Saltelli (A.), Chan (K.), Scott (E.M.) et al.— Sensitivity analysis, volume 134, Wiley New York (2000).  MR 1886391 |  Zbl 1152.62071
[19] Santner (T.J.), Williams (B.J.) and Notz (W.).— The design and analysis of computer experiments, Springer Verlag (2003).  MR 2160708 |  Zbl 1041.62068
[20] Sobol (I.M.).— Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates, Mathematics and Computers in Simulation, 55(1-3), p. 271-280, (2001).  MR 1823119 |  Zbl 1005.65004
[21] Stone (C.J.).— Additive regression and other nonparametric models, The annals of Statistics, p. 689-705 (1985).  MR 790566 |  Zbl 0605.62065
[22] R Team.— R: A language and environment for statistical computing, R Foundation for Statistical Computing Vienna Austria ISBN, 3(10) (2008).
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