Gaussian Process Regression for Structured Data Sets
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation — Gaussian Process regression — can hardly be applied due to its computational complexity. In this paper a new approach for a Gaussian Process regression in case of a factorial design of experiments is proposed. It allows to efficiently compute exact inference and handle large multidimensional and anisotropic data sets.
KeywordsGaussian process Structured data Regularization
Unable to display preview. Download preview PDF.
- 1.Abdel-Gawad, A.H., Minka, T.P., et al.: Sparse-posterior gaussian processes for general likelihoods. arXiv preprint arXiv:1203.3507 (2012)
- 2.Armand, S.C.: Structural Optimization Methodology for Rotating Disks of Aircraft Engines. NASA technical memorandum, National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program (1995)Google Scholar
- 5.Evoluationary computation pages – the function testbed: Laappeenranta University of Technology. http://www.it.lut.fi/ip/evo/functions/functions.html
- 6.Forrester, A.I.J., Sobester, A., Keane, A.J.: Engineering Design via Surrogate Modelling - A Practical Guide. J. Wiley (2008)Google Scholar
- 7.Friedman, J.H.: Multivariate adaptive regression splines. The Annals of Statistics, 1–67 (1991)Google Scholar
- 10.Montgomery, D.C.: Design and Analysis of Experiments. John Wiley & Sons (2006)Google Scholar
- 11.Neal, R.M.: Monte carlo implementation of gaussian process models for bayesian regression and classification. arXiv preprint physics/9701026 (1997)
- 13.Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. MIT Press (2006)Google Scholar
- 14.Rasmussen, C.E., Ghahramani, Z.: Infinite mixtures of gaussian process experts. In: Advances in Neural Information Processing Systems 14, pp. 881–888. MIT Press (2001)Google Scholar
- 15.Rendall, T., Allen, C.: Multi-dimensional aircraft surface pressure interpolation using radial basis functions. Proc. IMechE Part G: Aerospace Engineering 222, 483–495 (2008)Google Scholar
- 16.Snelson, E., Ghahramani, Z.: Sparse gaussian processes using pseudo-inputs. In: Advances in Neural Information Processing Systems 18, pp. 1257–1264 (2005)Google Scholar
- 18.Swiss International Institute of Technology. http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/