Fusion regression methods with repeated functional data

TL;DR

This paper introduces two fusion regression methods for repeated functional data that leverage neighborhood structures to identify common regression coefficients, demonstrated through simulations and EEG data analysis.

Contribution

It proposes novel fusion penalties for functional data regression, extending variable fusion and group fusion lasso techniques to account for dependence structures.

Findings

Methods effectively identify shared regression functions among close conditions.

Numerical simulations validate the methods' performance.

Application to EEG data illustrates practical utility.

Abstract

Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood structure (spatial, group, etc.). Two regression methods based on fusion penalties are proposed to consider the dependence induced by this structure. These methods aim to obtain parsimonious coefficient regression functions, by determining if close conditions are associated with common regression coefficient functions. The first method is a generalization to functional data of the variable fusion methodology based on the 1-nearest neighbor. The second one relies on the group fusion lasso penalty which assumes some grouping structure of conditions and allows for homogeneity among the regression coefficient functions within groups. Numerical simulations and an application of electroencephalography data are presented.