Computing Shapley Effects for Sensitivity Analysis

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 new algorithms that offer 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. These algorithms work in the presence of input dependencies. With these new algorithms, one may estimate all generalized (Shapley–Owen) effects for interactions.