Multivariate functional group sparse regression: functional predictor selection

TL;DR

This paper introduces new methods for selecting relevant functional predictors and estimating their coefficients in high-dimensional multivariate functional data, with proven theoretical properties and practical applications to brain imaging.

Contribution

It develops two novel functional group-sparse regression methods with convergence and consistency guarantees in infinite-dimensional Hilbert spaces.

Findings

Effective in selecting relevant functional predictors

Accurate estimation of functional coefficients

Successful application to fMRI data revealing brain regions

Abstract

In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under high-dimensional multivariate functional data setting. In particular, we develop two methods for functional group-sparse regression under a generic Hilbert space of infinite dimension. We show the convergence of algorithms and the consistency of the estimation and the selection (oracle property) under infinite-dimensional Hilbert spaces. Simulation studies show the effectiveness of the methods in both the selection and the estimation of functional coefficients. The applications to the functional magnetic resonance imaging (fMRI) reveal the regions of the human brain related to ADHD and IQ.