Variance-based interaction index measuring heteroscedasticity

Abstract

This work is motivated by the need to deal with models with high-dimensional input spaces of real variables. One way to tackle high-dimensional problems is to identify interaction or non-interaction among input parameters. We propose a new variance-based sensitivity interaction index that can detect and quantify interactions among the input variables of mathematical functions and computer simulations. The computation is very similar to first-order sensitivity indices by Sobol'. The proposed interaction index can quantify the relative importance of input variables in interaction. Furthermore, detection of non-interaction for screening can be done with as low as 4n + 2 function evaluations, where n is the number of input variables. Using the interaction indices based on heteroscedasticity, the original function may be decomposed into a set of lower dimensional functions which may then be analyzed separately.

Surrogate Modelling with Sequential Design for Expensive Simulation Applications

“…Fortunately, not all input parameters contribute equally to the output variability, in fact some might not have any impact at all [3]. The surrogate models can be used directly for evaluation-based sensitivity analysis methods such as Sobol indices [4], Interaction indices [5] or gradient-based methods. For some kernel-based modelling methods, analytical computation of sensitivity measures is possibly resulting in faster and more reliable estimation schemes, even before global accuracy is achieved [6].…”