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September 2018 TPRM: Tensor partition regression models with applications in imaging biomarker detection
Michelle F. Miranda, Hongtu Zhu, Joseph G. Ibrahim
Ann. Appl. Stat. 12(3): 1422-1450 (September 2018). DOI: 10.1214/17-AOAS1116


Medical imaging studies have collected high-dimensional imaging data to identify imaging biomarkers for diagnosis, screening, and prognosis, among many others. These imaging data are often represented in the form of a multi-dimensional array, called a tensor. The aim of this paper is to develop a tensor partition regression modeling (TPRM) framework to establish a relationship between low-dimensional clinical outcomes (e.g., diagnosis) and high-dimensional tensor covariates. Our TPRM is a hierarchical model and efficiently integrates four components: (i) a partition model, (ii) a canonical polyadic decomposition model, (iii) a principal components model, and (iv) a generalized linear model with a sparse inducing normal mixture prior. This framework not only reduces ultra-high dimensionality to a manageable level, resulting in efficient estimation, but also optimizes prediction accuracy in the search for informative sub-tensors. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulation shows that TPRM outperforms several other competing methods. We apply TPRM to predict disease status (Alzheimer versus control) by using structural magnetic resonance imaging data obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study.


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Michelle F. Miranda. Hongtu Zhu. Joseph G. Ibrahim. "TPRM: Tensor partition regression models with applications in imaging biomarker detection." Ann. Appl. Stat. 12 (3) 1422 - 1450, September 2018.


Received: 1 May 2015; Revised: 1 April 2017; Published: September 2018
First available in Project Euclid: 11 September 2018

zbMATH: 06979637
MathSciNet: MR3852683
Digital Object Identifier: 10.1214/17-AOAS1116

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.12 • No. 3 • September 2018
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