 Bayesian Factorizations of Big Sparse TensorsJing Zhou, Anirban Bhattacharya, Amy H. Herring and David B. Dunson Journal of the American Statistical Association, 2015, vol. 110, issue 512, 1562-1576 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. Date: 2015 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1562-1576 Ordering information: This journal article can be ordered from DOI: 10.1080/01621459.2014.983233 Access Statistics for this article Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson More articles in Journal of the American Statistical Association from Taylor & Francis Journals |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.