Interval sparsity for functional inverse regression
Résumé
In the present work, we focus on the functional regression model in which a real random variable has to be predicted from functional predictors. We use the semiparametric framework of Sliced Inverse Regression (SIR). SIR is an effective method for dimension reduction of high-dimensional data which computes a linear projection of the predictors in a low-dimensional space, without loss on regression information. The present work addresses the issue of variable selection in functional SIR in order to improve the interpretability of the components. We extend the approaches of variable selection developped for multidimensional SIR to select intervals rather than separated evaluation points in the definition domain of functional predictors. SIR is formulated in different and equivalent ways which are alternatively used to produce ridge estimates of the components which are shrinked afterwards with a group-LASSO like penalty. An iterative procedure which automatically defines the relevant intervals is also introduced to provide a priori information to the sparse model. The approach is proved efficient on simulated data.