Scalable bayesian low-rank decomposition of incomplete multiway tensors

Piyush Rai, Yingjian Wang, Shengbo Guo, Gary Chen, David Dunson, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

41 Scopus citations

Abstract

We present a scalable Bayesian framework for low-rank decomposition of multiway tensor data with missing observations. The key issue of pre-specifying the rank of the decomposition is sidestepped in a principled manner using a multiplicative gamma process prior. Both continuous and binary data can be analyzed under the framework, in a coherent way using fully conjugate Bayesian analysis. In particular, the analysis in the non-conjugate binary case is facilitated via the use of the Pólya-Gamma sampling strategy which elicits closed-form Gibbs sampling updates. The resulting samplers are efficient and enable us to apply our framework to large-scale problems, with time-complexity that is linear in the number of observed entries in the tensor. This is especially attractive in analyzing very large but sparsely observed tensors with very few known entries. Moreover, our method admits easy extension to the supervised setting where entities in one or more tensor modes have labels. Our method outperforms several state-of-the-art tensor decomposition methods on various synthetic and benchmark real-world datasets.
Original languageEnglish (US)
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)rasmussen@ptd.net
Pages3810-3820
Number of pages11
ISBN (Print)9781634393973
StatePublished - Jan 1 2014
Externally publishedYes

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