Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors

Piyush Rai, Yingjian Wang, Shengbo Guo, Gary Chen, David Dunson, Lawrence Carin
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1800-1808, 2014.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-rai14, title = {Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors}, author = {Rai, Piyush and Wang, Yingjian and Guo, Shengbo and Chen, Gary and Dunson, David and Carin, Lawrence}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1800--1808}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/rai14.pdf}, url = {https://proceedings.mlr.press/v32/rai14.html}, 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.} }
Endnote
%0 Conference Paper %T Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors %A Piyush Rai %A Yingjian Wang %A Shengbo Guo %A Gary Chen %A David Dunson %A Lawrence Carin %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-rai14 %I PMLR %P 1800--1808 %U https://proceedings.mlr.press/v32/rai14.html %V 32 %N 2 %X 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.
RIS
TY - CPAPER TI - Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors AU - Piyush Rai AU - Yingjian Wang AU - Shengbo Guo AU - Gary Chen AU - David Dunson AU - Lawrence Carin BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-rai14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1800 EP - 1808 L1 - http://proceedings.mlr.press/v32/rai14.pdf UR - https://proceedings.mlr.press/v32/rai14.html AB - 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. ER -
APA
Rai, P., Wang, Y., Guo, S., Chen, G., Dunson, D. & Carin, L.. (2014). Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1800-1808 Available from https://proceedings.mlr.press/v32/rai14.html.

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