Kernel-based sensivity analysis for (excursion) sets - IFPEN - IFP Energies nouvelles Access content directly
Preprints, Working Papers, ... (Preprint) Year : 2023

Kernel-based sensivity analysis for (excursion) sets


This work is motivated by goal-oriented sensitivity analysis of inputs/outputs of complex simulators. More precisely we are interested in the ranking of the uncertain input variables that impact the most a feasible design domain. Most sensitivity analysis methods deal with scalar outputs. In this paper, we propose a way to perform sensitivity analysis when dealing with set-valued outputs. Our new methodology is driven by sensitivity analysis on excursion sets but can also be applied to setvalued simulators as in viability field, or when dealing with maps such as pollutant concentration maps or flooding zone maps. We propose a method based on the Hilbert Schmidt Independence Criterion (HSIC) with a kernel tailored to sets as outputs. A first contribution is the proof that this kernel is characteristic (i.e injectivity of the embedding in the associated Reproducing Kernel Hilbert Space), a required property for the HSIC interpretation in a sensitivity analysis context. We propose then to compute the HSIC-ANOVA indices which allow a decomposition of the input contributions. Using these indices, we can identify which inputs should be neglected (screening) and we can rank the others by influence (ranking). The estimation of these indices is also adapted to the set-valued outputs. Finally we test the proposed method on two test cases of excursion sets.
Fichier principal
Vignette du fichier
article_final_KbSAoS.pdf (324.73 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04094561 , version 1 (11-05-2023)
hal-04094561 , version 2 (15-05-2023)
hal-04094561 , version 3 (26-05-2023)



Noé Fellmann, Christophette Blanchet-Scalliet, Céline Helbert, Adrien Spagnol, Delphine Sinoquet. Kernel-based sensivity analysis for (excursion) sets. 2023. ⟨hal-04094561v2⟩
96 View
15 Download



Gmail Facebook Twitter LinkedIn More