Extremum Global Sensitivity Analysis with Least Squares Polynomials and their Ridges
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Global sensitivity analysis is a powerful set of ideas and computational heuristics for understanding the importance and interplay between different parameters in a data-set. Such a data-set is characterized by a set of vector-valued input parameters and a set of scalar-valued output quantities of interest, where we typically assume that the inputs are independent and information on their joint density can be obtained. Alternatively, if the inputs are correlated, one requires information on the marginals and their correlations. In either case, if the output quantities of interest are smooth and continuous, polynomial least squares approximations can be used to extract Sobol' indices. In this paper, we build on these previously well-known ideas by studying two different aspects of this paradigm. First, we study whether sensitivity indices can be computed efficiently if one leverages a polynomial ridge approximation---a polynomial least squares fit over a subspace. We discuss a recipe that utilizes this special dependence structure to reduce the number of model evaluations required for this process. Second, we discuss two heuristics for evaluating input sensitivities when constrained near output extrema: skewness-based sensitivity indices and Monte Carlo filtering. We provide algorithms that implement the ideas discussed in this paper, codes for which are available online.
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