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- Title
STORE: Sparse Tensor Response Regression and Neuroimaging Analysis.
- Authors
Wei Sun, Will; Lexin Li
- 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 predic- tor. 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 estima- tion 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 illus- trate the efficacy of our model through intensive simulations and an analysis of the Autism spectrum disorder neuroimaging data.
- Subjects
BRAIN imaging; DIAGNOSTIC imaging; REGRESSION analysis; PARAMETER estimation; MATHEMATICAL optimization; AUTISM spectrum disorders
- Publication
Journal of Machine Learning Research, 2017, Vol 18, Issue 124/149, p1
- ISSN
1532-4435
- Publication type
Article