The Annals of Applied Statistics

TPRM: Tensor partition regression models with applications in imaging biomarker detection

Michelle F. Miranda, Hongtu Zhu, and Joseph G. Ibrahim

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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.

Article information

Ann. Appl. Stat., Volume 12, Number 3 (2018), 1422-1450.

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

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Zentralblatt MATH identifier

Bayesian hierarchical model big data MCMC tensor decomposition tensor regression


Miranda, Michelle F.; Zhu, Hongtu; Ibrahim, Joseph G. TPRM: Tensor partition regression models with applications in imaging biomarker detection. Ann. Appl. Stat. 12 (2018), no. 3, 1422--1450. doi:10.1214/17-AOAS1116.

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Supplemental materials

  • Matlab functions. We provide the Matlab code to run the simulation study of Section 3.1 and the real data in Section 4.
  • How to obtain the required Matlab toolboxes. We provide the details on how to run the simulation and on how to run TPRM for your own dataset. In addition, we provide information on how to obtain the toolboxes necessary to run the matlab code.