STORE: Sparse Tensor Response Regression and Neuroimaging Analysis
This is an incremental improvement for neuroimaging analysis, enabling more efficient handling of high-dimensional tensor data.
The authors tackled the problem of regression with tensor responses in neuroimaging by proposing STORE, a model incorporating element-wise sparsity and low-rankness, which achieved a fast estimation error rate allowing tensor dimensions to grow exponentially with sample size in Gaussian cases.
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.