Interpretable sparse SIR for functional data

TL;DR

This paper introduces an interpretable variable selection method for functional data that selects full intervals of predictors, enhancing interpretability and robustness against small shifts, based on an extension of Sliced Inverse Regression with a group-LASSO penalty.

Contribution

It develops a novel interval-based variable selection approach for functional regression using an extended SIR framework with a group-LASSO penalty, improving interpretability.

Findings

Effective on simulated data

Proven on real datasets

Enhanced interpretability of functional coefficients

Abstract

This work focuses on the issue of variable selection in functional regression. Unlike most work in this framework, our approach does not select isolated points in the definition domain of the predictors, nor does it rely on the expansion of the predictors in a given functional basis. It provides an approach to select full intervals made of consecutive points. This feature improves the interpretability of the estimated coefficients and is desirable in the functional framework for which small shifts are frequent when comparing one predictor (curve) to another. Our method is described in a semiparametric framework based on 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. We extend the approaches of variable selection developed for multidimensional SIR to select intervals rather than separated evaluation points in the definition domain of the functional predictors. Different and equivalent formulations of SIR are combined in a shrinkage approach with a group-LASSO-like penalty. Finally, a fully automated iterative procedure is also proposed to find the critical (interpretable) intervals. The approach is proved efficient on simulated and real data.