STORE: Sparse tensor response regression and neuroimaging analysis

Wei Sun, Lexin Li

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
Volume18
StatePublished - Nov 1 2017

Fingerprint

Neuroimaging
Tensors
Tensor
Regression
Estimation Error
Error analysis
Error Bounds
Functional neuroimaging
Nonconvex Optimization
Nonconvex Problems
Computational efficiency
Sparsity
Computational Efficiency
Parameter estimation
Updating
Error Rate
Parameter Estimation
Efficacy
Disorder
Predictors

Keywords

  • Functional connectivity analysis
  • High-dimensional statistical learning
  • Magnetic resonance imaging
  • Non-asymptotic error bound
  • Tensor decomposition

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

Cite this

STORE : Sparse tensor response regression and neuroimaging analysis. / Sun, Wei; Li, Lexin.

In: Journal of Machine Learning Research, Vol. 18, 01.11.2017.

Research output: Contribution to journalArticle

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