Parsimonious Tensor Response Regression

TL;DR

This paper introduces a parsimonious tensor response regression method that models high-dimensional tensor data efficiently, leveraging structural information and the envelope technique for improved estimation and interpretation, demonstrated on neuroimaging data.

Contribution

It proposes a novel tensor regression framework using a generalized sparsity principle and the envelope method, enhancing efficiency and interpretability in high-dimensional tensor data analysis.

Findings

The estimator is asymptotically efficient.

The method shows competitive finite sample performance.

Applied successfully to neuroimaging studies.

Abstract

Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include, among others, comparing tensor images across groups after adjusting for additional covariates, which is of central interest in neuroimaging analysis. We propose parsimonious tensor response regression adopting a generalized sparsity principle. It models all voxels of the tensor response jointly, while accounting for the inherent structural information among the voxels. It effectively reduces the number of free parameters, leading to feasible computation and improved interpretation. We achieve model estimation through a nascent technique called the envelope method, which identifies the immaterial information and focuses the estimation based upon the material information in the tensor response. We demonstrate that the resulting estimator is asymptotically efficient, and it enjoys a competitive finite sample performance. We also illustrate the new method on two real neuroimaging studies.