Random forest based estimation of quantile oriented global sensitivity analysis measure

This thesis is devoted to the estimation and application of Quantile-Oriented Sensitivity
Analysis (QOSA) measures, including the first-order QOSA indices, the total QOSA indices, and the
Quantile-Oriented Shapley Effects (QOSE) indices, which provide a natural and interpretable extension
when input variables are dependent. Compared with variance-based measures, QOSA indices are both
more robust and more informative, as they capture distributional features beyond variance. Our first
contribution is the development of a new quantile-oriented random forest, which achieves performance
comparable to other state-of-the-art random forest approaches for quantile regression. Building on this
tool, we integrate the projected algorithm to estimate conditional quantiles given a subset of inputs.
This enables the estimation of QOSA indices through a straightforward plug-in procedure. We establish
consistency results for the conditional quantile estimators and three type QOSA indices. The final part
of the thesis focuses on the application of QOSE in meteorology. We demonstrate that QOSE indices can
effectively identify and rank the most influential input variables, thereby offering practical guidance for
model simplification and for allocating computational resources more efficiently.

Directeurs:

• PR Véronique MAUME-DESCHAMPS (Université Claude Bernard Lyon 1 )
• PR Clémentine PRIEUR (Université Grenoble Alpes )

Rapporteur·e·s:

• PR Agnès LAGNOUX (Institut de Mathématiques de Toulouse )
• Bertrand IOOSS (EDF R&D )

Examinateur·trice·s:

• Anne-Laure FOUGERES (Université Claude Bernard Lyon 1 )
• Bertrand MICHEL (Ecole Centrale de Nantes )
• Maxime TAILLARDAT (Météo-France )