Active subspace methods and derivative-based Shapley effects for functions with non-independent variables

M. Lamboni and S. Kucherenko

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 247, issue C, 137-154

Abstract: Lower-dimensional subspaces that impact estimates of uncertainty are often described by Linear combinations of input variables, leading to active variables. This paper extends the derivative-based active subspace methods and derivative-based Shapley effects to cope with functions with non-independent variables, and it introduces sensitivity-based active subspaces. While derivative-based subspace methods focus on directions along which the function exhibits significant variation, sensitivity-based subspace methods seek a reduced set of active variables that enables a reduction in the function’s variance. We propose both theoretical results using the recent development of gradients of functions with non-independent variables and practical settings by making use of optimal computations of gradients, which admit dimension-free upper-bounds of the biases and the parametric rate of convergence. Simulations show that the relative performance of derivative-based and sensitivity-based active subspaces methods varies across different functions.

Keywords: Active subspaces; Dependent variables; Derivative-free methods; DGSMs; Shapley effects (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:247:y:2026:i:c:p:137-154

DOI: 10.1016/j.matcom.2026.03.020

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