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Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Journal Article · · ACM Transactions on Probabilistic Machine Learning
DOI:https://doi.org/10.1145/3675161· OSTI ID:2502155
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Iowa State Univ., Ames, IA (United States)
+ Show Author Affiliations
Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
National Institute of Justice (NIJ); National Institutes of Health (NIH); USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
NA0003525
OSTI ID:
2502155
Report Number(s):
SAND2025--00372J
Journal Information:
ACM Transactions on Probabilistic Machine Learning, Journal Name: ACM Transactions on Probabilistic Machine Learning Journal Issue: 1 Vol. 1; ISSN 2836-8924
Publisher:
Association for Computing Machinery (ACM)Copyright Statement
Country of Publication:
United States
Language:
English

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97 MATHEMATICS AND COMPUTING
Kronecker-separable covariance
multilinear statistics
random tensors
robust statistics
scale mixtures
tensor covariance
tensor decompositions
tensor regression and classification
tensor-variate analysis of variance
tensor-variate discriminant analysis