Journal of the American Statistical Association· 2016Q1
Parsimonious Tensor Response Regression
- 206citations
- Q1SCImago
- 2016year
Short summary
A new 'parsimonious tensor response regression' method models high-dimensional tensor data with complex structures, reducing parameters and improving interpretation by using an 'envelope method' to focus on essential information.
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Key points
- Proposes parsimonious tensor response regression for high-dimensional, structured tensor data.
- Jointly models all voxels of the tensor response, accounting for inherent structure.
- Employs an 'envelope method' to identify and focus on material information, reducing free parameters.
- The resulting estimator is shown to be asymptotically efficient with competitive finite sample performance.
AI-generated from the title and abstract; the full text is not read.
Abstract
Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include, among others, comparing tensor images across groups after adjusting for additional covariates, which is of central interest in neuroimaging analysis. We propose parsimonious tensor response regression adopting a generalized sparsity principle. It models all voxels of the tensor response jointly, while accounting for the inherent structural information among the voxels. It effectively reduces the number of free parameters, leading to feasible computation and improved interpretation. We achieve model estimation through a nascent technique called the envelope method, which identifies the immaterial information and focuses the estimation based upon the material information in the tensor response. We demonstrate that the resulting estimator is asymptotically efficient, and it enjoys a competitive finite sample performance. We also illustrate the new method on two real neuroimaging studies. Supplementary materials for this article are available online.
The authors' abstract, as published at the source. Journal of the American Statistical Association, 2016 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics