High-dimensional reliability-oriented Shapley effects estimation

Abstract

This article presents a new estimation scheme for the reliability-oriented Shapley effects when there is a large number of correlated input variables, using a unique sample of failure points. First, we propose a new reformulation of the reliability-oriented closed Sobol indices. This reformulation circumvents the estimation issues associated with existing methods in the literature, but requires estimating densities in potentially high dimensions. Once the reliability-oriented closed Sobol indices have been estimated through these densities, the reliability-oriented Shapley effects are estimated through permutation aggregation to circumvent the issue related to the dimension. In addition, we provide an error estimation procedure relying on the same sample of failing points resulting in a probabilistic error bound, and avoiding any additional call to the model. We illustrate our methodology on numerical use-cases where we compare several density estimators and we propose an application to the monitoring of adaptive importance sampling.

arXiv comment30 pages, 18 figures