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Bayesian Factorizations of Big Sparse Tensors

Citation

Zhou, Jing; Bhattacharya, Anirban; Herring, Amy H.; & Dunson, David B. (2015). Bayesian Factorizations of Big Sparse Tensors. Journal of the American Statistical Association, 110(512), 1562-1576. PMCID: PMC6579540

Abstract

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. In contingency table applications in which the sample size is massively less than the number of cells in the table, 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. 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.

URL

http://dx.doi.org/10.1080/01621459.2014.983233

Reference Type

Journal Article

Year Published

2015

Journal Title

Journal of the American Statistical Association

Author(s)

Zhou, Jing
Bhattacharya, Anirban
Herring, Amy H.
Dunson, David B.

PMCID

PMC6579540