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Activity Number: 203 - Emerging Statistical Methods for Big Tensor Data in Chemometrics and Related Fields
Type: Invited
Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract #321915 View Presentation
Title: SPARSE LOW-RANK TENSOR RESPONSE REGRESSION
Author(s): Will Wei Sun* and Lexin Li
Companies: University of Miami and University of California at Berkeley
Keywords: Functional connectivity analysis ; Magnetic resonance imaging ; Non-asymptotic error bound ; Non-convex optimization ; Tensor decomposition
Abstract:

Motivated by structural and functional neuroimaging analysis, we propose a new class of tensor response regression models. The model embeds two key low-dimensional structures: sparsity and low-rankness, and can handle both a general and a symmetric tensor response. We formulate parameter estimation of our model as a non-convex optimization problem, and develop an efficient alternating updating algorithm. Theoretically, we establish a non-asymptotic estimation error bound for the actual estimator obtained from our algorithm. This error bound reveals an interesting interaction between the computational efficiency and the statistical rate of convergence. Based on this general error bound, we further obtain an optimal estimation error rate when the distribution of the error tensor is Gaussian. Our technical analysis is based upon exploitation of the bi-convex structure of the objective function and a careful characterization of the impact of an intermediate sparse tensor decomposition step. Simulations and an analysis of the autism spectrum disorder imaging data further illustrate the efficacy of our method.


Authors who are presenting talks have a * after their name.

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