no code implementations • 12 Oct 2023 • Alejandro Cholaquidis, Fabrice Gamboa, Leonardo Moreno
Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for this type of data.
no code implementations • 10 Oct 2023 • Marouane Il Idrissi, Nicolas Bousquet, Fabrice Gamboa, Bertrand Iooss, Jean-Michel Loubes
The elements of this decomposition can be expressed using oblique projections and allow for novel interpretability indices for evaluation and variance decomposition purposes.
1 code implementation • 23 Sep 2022 • Marouane Il Idrissi, Nicolas Bousquet, Fabrice Gamboa, Bertrand Iooss, Jean-Michel Loubes
Numerical experiments on real case studies, from the UQ and ML fields, highlight the computational feasibility of such studies and provide local and global insights on the robustness of black-box models to input perturbations.
no code implementations • 8 Sep 2020 • Yohann de Castro, Fabrice Gamboa, Didier Henrion, Jean Lasserre
The purpose of this short note is to show that the Christoffel-Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics.
Optimization and Control Statistics Theory Statistics Theory
2 code implementations • 18 Oct 2018 • François Bachoc, Fabrice Gamboa, Max Halford, Jean-Michel Loubes, Laurent Risser
In order to emphasize the impact of each input variable, this formalism uses an information theory framework that quantifies the influence of all input-output observations based on entropic projections.
1 code implementation • 8 Jun 2018 • Eustasio del Barrio, Fabrice Gamboa, Paula Gordaliza, Jean-Michel Loubes
\textit{Fairness} is generally studied in a probabilistic framework where it is assumed that there exists a protected variable, whose use as an input of the algorithm may imply discrimination.
Statistics Theory Statistics Theory 62H30, 68T01
no code implementations • 16 Mar 2018 • François Bachoc, Baptiste Broto, Fabrice Gamboa, Jean-Michel Loubes
In the framework of the supervised learning of a real function defined on a space X , the so called Kriging method stands on a real Gaussian field defined on X.
no code implementations • 2 Oct 2017 • Thomas Epelbaum, Fabrice Gamboa, Jean-Michel Loubes, Jessica Martin
In this paper, we propose deep learning architectures (FNN, CNN and LSTM) to forecast a regression model for time dependent data.
1 code implementation • 9 Jun 2017 • Yohann De Castro, Fabrice Gamboa, Didier Henrion, Roxana Hess, Jean-Bernard Lasserre
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces.
Statistics Theory Information Theory Information Theory Numerical Analysis Computation Methodology Statistics Theory 62K05, 90C25 (Primary) 41A10, 49M29, 90C90, 15A15 (secondary)
no code implementations • 31 Jan 2017 • François Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Nil Venet
We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.