STORE: Sparse Tensor Response Regression and Neuroimaging Analysis

TL;DR

This paper introduces STORE, a novel sparse tensor response regression model tailored for neuroimaging data, capable of handling symmetric and non-symmetric tensors with theoretical guarantees and practical validation.

Contribution

STORE is the first model to incorporate element-wise sparsity and low-rankness for tensor responses in neuroimaging, with an efficient algorithm and non-asymptotic error bounds.

Findings

Effective in simulations and real neuroimaging data analysis.

Achieves fast estimation rates with high-dimensional tensors.

Handles both structural and functional neuroimaging data.

Abstract

Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor response, and thus is applicable to both structural and functional neuroimaging data. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating updating algorithm. We establish a non-asymptotic estimation error bound for the actual estimator obtained from the proposed algorithm. This error bound reveals an interesting interaction between the computational efficiency and the statistical rate of convergence. When the distribution of the error tensor is Gaussian, we further obtain a fast estimation error rate which allows the tensor dimension to grow exponentially with the sample size. We illustrate the efficacy of our model through intensive simulations and an analysis of the Autism spectrum disorder neuroimaging data.