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                            Library & Multimedia
 Reduced-Rank Tensor-on-Tensor Regression and Tensor-Variate Analysis of Variance
NCJ Number
              306082
Journal

*Ieee Transactions on Pattern Analysis and Machine Intelligence* Volume: 45 Issue: 2 Dated: 01 February 2023 Pages: 2282-2296
Author(s)
          Carlos Llosa-Vite;
                        Ranjan Maitra
Date Published

February 2023
Length
              15 pages
Annotation
              Since fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have tensor-variate structure, the authors extend the classical multivariate regression model to exploit such structure in two ways.
Abstract
              First, they impose four types of low-rank tensor formats on the regression coefficients. Second, they model the errors using the tensor-variate normal distribution that imposes a Kronecker separable format on the covariance matrix. They obtain maximum likelihood estimators via block-relaxation algorithms and derive their computational complexity and asymptotic distributions. Their regression framework enables them to formulate tensor-variate analysis of variance (TANOVA) methodology. This methodology, when applied in a one-way TANOVA layout, enables them to identify cerebral regions significantly associated with the interaction of suicide attempters or non-attempter ideators and positive-, negative- or death-connoting words in a functional Magnetic Resonance Imaging study. Another application uses three-way TANOVA on the Labeled Faces in the Wild image dataset to distinguish facial characteristics related to ethnic origin, age group, and gender. A R package totr implements the methodology. (Published abstract provided)
      
  
          Additional Details
Grant Number(s)
        2015-DN-BX-K056
                                2018-R2-CX-0034
                                15PNIJ-21-GG-04141-RESS


  
  
        
  Agencies
        NIJ-Sponsored


  
  
        
  Publication Type
        Research (Applied/Empirical)


  
  
        
  Award
        Quantitative Tools for Examination of Microscopic Fracture Surface Topology and Degradation for Physical Match Analysis of Evidence
                                Physics and Statistical Models for Physical Match Analysis Utilizing 3D Microscopy of Fracture Surfaces
                                Physics and Mathematical Models for Error Quantifications in Comparative 3D Microscopy for Physical Match Analysis
    
  
  
Date Published: February 1, 2023
    
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                Ethnic groups
        Regression Analysis
        Magnetic resonance imaging (MRI)



  
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