{"paper":{"title":"High-dimensional reliability-oriented Shapley effect estimation with Normalizing Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Bachoc Fran\\c{c}ois, Demange-Chryst Julien, Monteiro Lucas, Morio J\\'er\\^ome","submitted_at":"2026-06-25T10:06:28Z","abstract_excerpt":"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. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26826","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26826/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}