Using multiple surrogates for minimization of the RMS error in meta-modeling

[fche...@gmail.com]

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:
http://fchegury.110mb.com/publications.html


All the best,
Felipe