Gaussian Process (GP) regression is a well-established probabilistic meta-modeling and data analysis tool. The posterior distribution of the GP parameters can be estimated using, e.g., Markov Chain Monte Carlo (MCMC). The ability to make predictions is a key aspect of using such surrogate models. To make a GP prediction, the MCMC chain as well as the training data are required. For some applications, GP predictions can require too much computational time and/or memory, especially for many training data points. This motivates the present work to represent the GP in an equivalent polynomial (or other global functional) form called a portable GP. The portable GP inherits many benefits of the GP including feature ranking via Sobol indices, robust fitting to non-linear and high-dimensional data, accurate uncertainty estimates, etc. The framework expands the GP in a high-dimensional model representation (HDMR). After fitting each HDMR basis function with a polynomial, they are all added together to form the portable GP. A ranking of which basis functions to use in the fitting process is automatically provided via Sobol indices. The uncertainty from the fitting process can be propagated to the final GP polynomial estimate. In applications where speed and accuracy are paramount, spline fits to the basis functions give very good results. Finally, portable BHM provides an alternative set of assumptions with regards to extrapolation behavior which may be more appropriate than the assumptions inherent in GPs.
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ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 26–29, 2018
Quebec City, Quebec, Canada
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5173-9
PROCEEDINGS PAPER
Polynomial Representation of the Gaussian Process Available to Purchase
Jesper Kristensen,
Jesper Kristensen
GE Global Research, Niskayuna, NY
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Isaac Asher,
Isaac Asher
GE Global Research, Niskayuna, NY
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Liping Wang
Liping Wang
GE Global Research, Niskayuna, NY
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Jesper Kristensen
GE Global Research, Niskayuna, NY
Isaac Asher
GE Global Research, Niskayuna, NY
Liping Wang
GE Global Research, Niskayuna, NY
Paper No:
DETC2018-85145, V01BT02A044; 8 pages
Published Online:
November 2, 2018
Citation
Kristensen, J, Asher, I, & Wang, L. "Polynomial Representation of the Gaussian Process." Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1B: 38th Computers and Information in Engineering Conference. Quebec City, Quebec, Canada. August 26–29, 2018. V01BT02A044. ASME. https://doi.org/10.1115/DETC2018-85145
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