Bayesian factorizations of big sparse tensors.

Published

Journal Article

It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics. The most common low rank tensor factorization relies on parallel factor analysis (PARAFAC), which expresses a rank k tensor as a sum of rank one tensors. When observations are only available for a tiny subset of the cells of a big tensor, the low rank assumption is not sufficient and PARAFAC has poor performance. We induce an additional layer of dimension reduction by allowing the effective rank to vary across dimensions of the table. For concreteness, we focus on a contingency table application. Taking a Bayesian approach, we place priors on terms in the factorization and develop an efficient Gibbs sampler for posterior computation. Theory is provided showing posterior concentration rates in high-dimensional settings, and the methods are shown to have excellent performance in simulations and several real data applications.

Full Text

Duke Authors

Cited Authors

  • Zhou, J; Bhattacharya, A; Herring, A; Dunson, D

Published Date

  • January 2015

Published In

Volume / Issue

  • 110 / 512

Start / End Page

  • 1562 - 1576

PubMed ID

  • 31210707

Pubmed Central ID

  • 31210707

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2014.983233

Language

  • eng