Interpretable sparse SIR for functional data

Victor Picheny (1) , Rémi Servien (2) , Nathalie Vialaneix (1)

1 MIAT INRA - Unité de Mathématiques et Informatique Appliquées de Toulouse
2 InTheRes - Innovations Thérapeutiques et Résistances

We propose a semiparametric framework based on sliced inverse regression (SIR) to address the issue of variable selection in functional regression. SIR is an effective method for dimension reduction which computes a linear projection of the predictors in a low-dimensional space, without loss of information on the regression. In order to deal with the high dimensionality of the predictors, we consider penalized versions of SIR: ridge and sparse. We extend the approaches of variable selection developed for multidimensional SIR to select intervals that form a partition of the definition domain of the functional predictors. Selecting entire intervals rather than separated evaluation points improves the interpretability of the estimated coefficients in the functional framework. A fully automated iterative procedure is proposed to find the critical (interpretable) intervals. The approach is proved efficient on simulated and real data. The method is implemented in the R package SISIR available on CRAN at https://cran.r-project.org/package=SISIR.

Mots clés: Functional regression; Lasso; Ridge regression; Interval selection; SLICED INVERSE REGRESSION; CLASSIFICATION

Mots clés: SIR; VARIABLE SELECTION; DIMENSION; MODELS; INPUTS

Domaines: Mathématiques [math]; Informatique [cs]; Sciences du Vivant [q-bio]

Victor Picheny, Rémi Servien, Nathalie Vialaneix. Interpretable sparse SIR for functional data. Statistics and Computing, 2019, 29 (2), pp.255 - 267. ⟨10.1007/s11222-018-9806-6⟩. ⟨hal-02618466⟩