Importing Uncertainty Estimates from One Surrogate to Another

In adaptive sampling and optimization methods, the uncertainty estimators are used to guide the selection of the next sampling point(s). These algorithms often limit themselves to surrogates such as kriging and polynomial response surface because of the lack of uncertainty estimates in the implementation of other surrogates. We propose the importation (borrowing) of uncertainty estimates from one surrogate to another. This would allow the use of support vector regression models together with kriging uncertainty estimates, for example. When multiple surrogates are available, we also propose using crossvalidation to aid in the decision of which surrogate to import from. The approach was tested on two algebraic examples for ten basic surrogates including different instances of kriging, polynomial response surface, radial basis neural networks and support vector regression surrogates. For these examples we found that (i) the statistically based uncertainty estimates do not always correlate well to the errors; (ii) importation of uncertainty structure can offer a reasonable solution; and (iii) cross-validation successfully selects the surrogate according to the quality of the uncertainty structure and therefore it is useful in choosing which surrogate to import the uncertainty estimate from.