Computing Shapley Effects for Sensitivity Analysis

Abstract

Shapley effects are attracting increasing attention as sensitivity measures. When the value function is the conditional variance, they account for the individual and higher order effects of a model input. They are also well defined under model input dependence. However, one of the issues associated with their use is computational cost. We present a new algorithm that offers major improvements for the computation of Shapley effects, reducing computational burden by several orders of magnitude (from k! • k to 2 k , where k is the number of inputs) with respect to currently available implementations. The algorithm works in the presence of input dependencies. The algorithm also makes it possible to estimate all generalized (Shapley-Owen) effects for interactions.

Kernel-based ANOVA decomposition and Shapley effects -- Application to global sensitivity analysis

“…For a given input all interactions and correlations with other ones are mixed up, but the interpretation as parts of the output variance is kept and input rankings are still sensible. For these reasons Shapley effects are now commonly thought as central importance measures in GSA for dealing with dependence, and their estimation has been thoroughly investigated recently (Song et al, 2016;Iooss and Prieur, 2019;Broto et al, 2020;Plischke et al, 2020).…”