TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS.

Published

Journal Article

Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Full Text

Duke Authors

Cited Authors

  • Johndrow, JE; Bhattacharya, A; Dunson, DB

Published Date

  • January 2017

Published In

Volume / Issue

  • 45 / 1

Start / End Page

  • 1 - 38

PubMed ID

  • 29332971

Pubmed Central ID

  • 29332971

Electronic International Standard Serial Number (EISSN)

  • 2168-8966

International Standard Serial Number (ISSN)

  • 0090-5364

Digital Object Identifier (DOI)

  • 10.1214/15-aos1414

Language

  • eng