Nonparametric Matrix Response Regression with Application to Brain Imaging Data Analysis

TL;DR

This paper introduces a nonparametric matrix response regression model tailored for neuroimaging data, effectively capturing nonlinear relationships and low-rank structures in dynamic brain images, with demonstrated superior performance in real studies.

Contribution

It proposes a novel nuclear norm regularization approach for matrix response regression, specifically designed for dynamic neuroimaging data analysis, with efficient algorithms and theoretical guarantees.

Findings

Outperforms existing methods in simulations.

Improves prediction accuracy in calcium imaging data.

Enhances dynamic connectivity analysis in EEG studies.

Abstract

With the rapid growth of neuroimaging technologies, a great effort has been dedicated recently to investigate the dynamic changes in brain activity. Examples include time course calcium imaging and dynamic brain functional connectivity. In this paper, we propose a novel nonparametric matrix response regression model to characterize the nonlinear association between 2D image outcomes and predictors such as time and patient information. Our estimation procedure can be formulated as a nuclear norm regularization problem, which can capture the underlying low-rank structure of the dynamic 2D images. We present a computationally efficient algorithm, derive the asymptotic theory and show that the method outperforms other existing approaches in simulations. We then apply the proposed method to a calcium imaging study for estimating the change of fluorescent intensities of neurons, and an electroencephalography study for a comparison in the dynamic connectivity covariance matrices between alcoholic and control individuals. For both studies, the method leads to a substantial improvement in prediction error.