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High-dimensional reliability-oriented Shapley effect esti...
[Submitted on 25 Jun 2026] · 2026-06-26 · via stat updates on arXiv.org

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Abstract:This article presents a new estimation scheme for the reliability-oriented Shapley effects when there is a large number of correlated input variables in the model, using a unique sample of failure points. To do so, we first propose a new writing of the reliability-oriented closed Sobol indices involving the marginal densities conditionally to the failure, which may be high-dimensional. Then, we propose to estimate these densities with the available failing samples using Normalizing Flows, powerful tools from generative modeling that enable the estimation of complex high-dimensional densities. In addition, we provide an error estimation procedure relying on the same sample of failing points, which constitutes a new contribution for the estimation of target Shapley effects. Finally, we illustrate our methodology on numerical use-cases, discuss insightful features of our approach and provide prospects for the future.

Submission history

From: Lucas Monteiro [view email]
[v1] Thu, 25 Jun 2026 10:06:28 UTC (5,008 KB)