Post by Felipe Chegury Viana on Aug 6, 2008 20:16:42 GMT -5
Dear all,
Here it is a reference on use of multiple surrogates for minimal RMS error in prediction:
F. A. C. Viana and R. T. Haftka, "USING MULTIPLE SURROGATES FOR MINIMIZATION OF THE RMS ERROR IN META-MODELING," in: Proceedings of the ASME 2008 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference - IDETC/CIE 2008, Brooklyn, USA, August 3-6, 2008.
Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. Previous work has shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross validation errors may also be used to create a weighted surrogate. In this paper, we discuss whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We propose the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We find that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We find that the cross validation error vectors provide an excellent estimate of the RMS errors when the number of data points is high. Hence the use of cross validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions. However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions.
You can find more about it on:
fchegury.110mb.com/publications.html
All the best,
Felipe
Here it is a reference on use of multiple surrogates for minimal RMS error in prediction:
F. A. C. Viana and R. T. Haftka, "USING MULTIPLE SURROGATES FOR MINIMIZATION OF THE RMS ERROR IN META-MODELING," in: Proceedings of the ASME 2008 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference - IDETC/CIE 2008, Brooklyn, USA, August 3-6, 2008.
Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. Previous work has shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross validation errors may also be used to create a weighted surrogate. In this paper, we discuss whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We propose the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We find that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We find that the cross validation error vectors provide an excellent estimate of the RMS errors when the number of data points is high. Hence the use of cross validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions. However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions.
You can find more about it on:
fchegury.110mb.com/publications.html
All the best,
Felipe