Tensor Regression with Applications in Neuroimaging Data Analysis

TL;DR

This paper introduces a novel tensor regression framework that effectively handles high-dimensional, structured tensor covariates in neuroimaging data, enabling efficient estimation and prediction.

Contribution

It proposes a new family of tensor regression models that exploit tensor structure, reducing dimensionality and improving computational efficiency in neuroimaging analysis.

Findings

Demonstrates effectiveness on synthetic data

Shows improved prediction on MRI data

Provides scalable estimation algorithm

Abstract

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.