Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reduced-Rank Tensor-on-Tensor Regression and Tensor-variate Analysis of
  Variance   Fitting regression models with many multivariate responses and covariates can
be challenging, but such responses and covariates sometimes have tensor-variate
structure. We extend the classical multivariate regression model to exploit
such structure in two ways: first, we impose four types of low-rank tensor
formats on the regression coefficients. Second, we model the errors using the
tensor-variate normal distribution that imposes a Kronecker separable format on
the covariance matrix. We obtain maximum likelihood estimators via
block-relaxation algorithms and derive their computational complexity and
asymptotic distributions. Our regression framework enables us to formulate
tensor-variate analysis of variance (TANOVA) methodology. This methodology,
when applied in a one-way TANOVA layout, enables us to identify cerebral
regions significantly associated with the interaction of suicide attempters or
non-attemptor 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.

19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc