4 papers
Minimax Additive Regression under Unknown Dependent Designs
Baptiste Ferrere, Fabrice Gamboa, Jean-Michel Loubes
We study additive regression under an unknown and potentially non product design distribution, allowing the number of covariates to grow with the sample size. We consider a coupled…
Generalized Functional ANOVA: A Complete Theoretical Framework
Baptiste Ferrere, Nicolas Bousquet, Fabrice Gamboa +1
The functional ANOVA provides a fundamental representation of square-integrable multivariate functions into main effects and higher-order interactions. For independent inputs, the…
Exact Functional ANOVA Decomposition for Categorical Inputs Models
Baptiste Ferrere, Nicolas Bousquet, Fabrice Gamboa +2
Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, t…
Fourier Analysis on the Boolean Hypercube via Hoeffding Functional Decomposition
Baptiste Ferrere, Nicolas Bousquet, Fabrice Gamboa +2
Fourier analysis on the Boolean hypercube is fundamentally defined as the orthogonal decomposition of the space of pseudo-Boolean functions with respect to the uniform probability…