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.
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BibTeX
@misc{monteiro2026highdimensional,
title = {{High-dimensional reliability-oriented Shapley effects estimation}},
author = {Lucas Monteiro and Jérôme Morio and Julien Demange-Chryst and François Bachoc},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.26826},
eprint = {2606.26826},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26826},
}
RIS
TY - UNPB
TI - High-dimensional reliability-oriented Shapley effects estimation
AU - Lucas Monteiro
AU - Jérôme Morio
AU - Julien Demange-Chryst
AU - François Bachoc
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2606.26826
UR - https://arxiv.org/abs/2606.26826
AB - 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.
ER -