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math.ST2025
Non-asymptotic confidence regions on RKHS. The Paley-Wiener and standard Sobolev space cases
Fabrice Gamboa, Olivier Roustant
We consider the problem of constructing a global, probabilistic, and non-asymptotic confidence region for an unknown function observed on a random design. The unknown function is a…
math.ST2025
General reproducing properties in RKHS with application to derivative and integral operators
Fatima-Zahrae El-Boukkouri, Josselin Garnier, Olivier Roustant
In this paper, we consider the reproducing property in Reproducing Kernel Hilbert Spaces (RKHS). We establish a reproducing property for the closure of the class of combinations of…
math.ST2024
Fast pick-freeze estimation of Sobol' sensitivity maps using basis expansions
Yuri Sao, Olivier Roustant, Geraldo de Freitas Maciel
Global sensitivity analysis (GSA) aims at quantifying the contribution of input variables over the variability of model outputs. In the frame of functional outputs, a common goal i…