A0254
Title: Elliptically-contoured tensor-variate distributions with application to improved image learning
Authors: Carlos Llosa - Sandia National Laboratories (United States) [presenting]
Ranjan Maitra - Iowa State University (United States)
Abstract: Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution, which may be inadequate when data comes from distributions with heavier or lighter tails. A general family of elliptically contoured (EC) tensor-variate distributions is studied, and its characterizations, moments, marginal and conditional distributions are derived. Procedures are described 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, where Tyler's robust estimator is extended. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. Tensor-variate classification rules are developed 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 tensor-variate analysis of variance (TANOVA) framework under EC errors are 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.
