A New Class of Skewed Tensor Distributions

• Activity Number: 62 - High-Dimensional Regression Methods
• Type: Contributed
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Inkoo Lee* and Debajyoti Sinha and Qing Mai and Dipankar Bandyopadhyay
• Companies: Rice University and Florida State University and Florida State University and Virginia Commonwealth University
• Keywords: Heavy tailed error distribution; Markov chain Monte Carlo; Skewness; Tensor elliptical class

Abstract

To tackle the challenges in tensor data analysis, we propose a general class of skewed elliptical distributions for random tensors. We leverage the tensor structure to reduce the number of parameters and achieve parsimony. Any linear combinations of tensor elliptically distributed variables are still tensor elliptical variables. Moreover, the proposed class of skewed elliptical distributions is closed under marginalization and the marginal distribution has the same form as the skewed tensor elliptical density as well as conditional density. We demonstrate some of the properties of our proposal by studying the skewed tensor-t and skewed tensor normal distributions. Practical applications of this new distribution class are provided via Bayesian tensor response regression analysis with tensor spike-and-slab lasso prior for tensor regression coefficients. We illustrate the practical advantages of tensor spike-and-slab Lasso prior to detecting fast decaying teeth types and sites in a periodontal disease study.