Multivariate functional responses low rank regression with an application to brain imaging data

TL;DR

This paper introduces a low rank regression model for multivariate functional responses with high-dimensional data, utilizing nuclear norm regularization, and demonstrates its effectiveness through simulations and neuroimaging data analysis.

Contribution

It develops a novel low rank regression approach for high-dimensional multivariate functional data using sieve basis expansion and nuclear norm regularization.

Findings

The method achieves accurate estimation with derived error bounds.

Simulation studies validate the effectiveness of the approach.

Application to neuroimaging data demonstrates practical utility.

Abstract

We propose a multivariate functional responses low rank regression model with possible high dimensional functional responses and scalar covariates. By expanding the slope functions on a set of sieve basis, we reconstruct the basis coefficients as a matrix. To estimate these coefficients, we propose an efficient procedure using nuclear norm regularization. We also derive error bounds for our estimates and evaluate our method using simulations. We further apply our method to the Human Connectome Project neuroimaging data to predict cortical surface motor task-evoked functional magnetic resonance imaging signals using various clinical covariates to illustrate the usefulness of our results.