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Brief Report A note on construction of covariance functions of multiple Gaussian processes
Received date: 2013-09-25
Revised date: 2014-01-15
Supported by
Supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201107123), Central Support Local Projects (PXM 2013-014210-000173), Projects for Talents from Beijing Organization Department (2013D005017000016), and National Natural Science Foundation of China (11271355)
We provide a simple but general method to construct covariance functions of dependent Gaussian processes with multiple outputs. Our method relies only on existing covariance functions of Gaussian processes with single output. Several examples in computer experiments are given.
MU Weiyan , XIONG Shifeng . Brief Report A note on construction of covariance functions of multiple Gaussian processes[J]. Journal of University of Chinese Academy of Sciences, 2014 , 31(6) : 843 -845 . DOI: 10.7523/j.issn.2095-6134.2014.06.017
[1] Cressie N. Statistics for spatial data[M]. New York: Wiley, 1993.
[2] Rasmussen C E, Williams C K I. Gaussian processes for machine learning[M]. Cambridge: MIT Press, 2006.
[3] Santner T J, Williams B J, Notz W I. The design and analysis of computer experiments[M]. New York: Springer, 2003.
[4] Boyle P K, Frean M R. Dependent Gaussian processes[C]//Advances in Neural Information Processing Systems. Cambrige, MIT Press, 2004: 17.
[5] Andriluka M, Weizsäcker L, Hofmann T. Multi-class classification with dependent Gaussian processes: technical report[R/OL]. 2008[2013-07-15].http://www.gkmm.informatik.tu-darmstadt.de/publications/files/andriluka07asmda.pdf.
[6] Kennedy M C, O’Hagan A. Predicting the output from a complex computer code when fast approximations are available[J]. Biometrika, 2000, 87: 1-13.
[7] Qian P Z G, Wu C F J. Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments[J]. Technometrics, 2008, 50: 192-204.
[8] Higdon D, Gattiker J, Williams B, et al. Computer model calibration using high-dimensional output[J]. Journal of the American Statistical Association, 2008, 103: 570-583.
[9] Qian P Z G, Wu H, Wu C F J. Gaussian process models for computer experiments with qualitative and quantitative factors[J]. Technometrics, 2008, 50: 383-396.
[10] Han G, Santner T J, Notz W I, et al. Prediction for computer experiments having quantitative and qualitative input variables[J]. Technometrics, 2009, 51: 278-288.
[11] Zhou Q, Qian P Z G, Zhou S. A simple approach to emulation for computer models with qualitative and quantitative factors[J]. Technometrics, 2011, 53: 266-273.
[12] Bayarri M J, Berger J O, Cafeo J, et al. Computer model validation with functional output[J]. Annals of Statistics, 2007, 35: 1 874-1 906.
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