Sparse logistic regression on functional data

TL;DR

This paper introduces a Sparse Functional Logistic Regression model that estimates a locally sparse coefficient function for functional data, effectively identifying relevant regions and improving interpretability in medical monitoring applications.

Contribution

It proposes a novel doubly-penalized likelihood approach with B-splines for estimating locally sparse coefficient functions in functional logistic regression.

Findings

Successfully identifies null and non-null regions of the coefficient function.

Achieves smooth and accurate estimation of relevant functional regions.

Effectively applied to dialysis spectral data to pinpoint key chemical regions.

Abstract

Motivated by a hemodialysis monitoring study, we propose a logistic model with a functional predictor, called the Sparse Functional Logistic Regression (SFLR), where the corresponding coefficient function is {\it locally sparse}, that is, it is completely zero on some subregions of its domain. The coefficient function, together with the intercept parameter, are estimated through a doubly-penalized likelihood approach with a B-splines expansion. One penalty is for controlling the roughness of the coefficient function estimate and the other penalty, in the form of the $L_1$ norm, enforces the local sparsity. A Newton-Raphson procedure is designed for the optimization of the penalized likelihood. Our simulations show that SFLR is capable of generating a smooth and reasonably good estimate of the coefficient function on the non-null region(s) while recognizing the null region(s). Application of the method to the Raman spectral data generated from the heomdialysis study pinpoint the wavenumber regions for identifying key chemicals contributing to the dialysis progress.