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Scalable bayesian low-rank decomposition of incomplete multiway tensors

Publication ,  Conference
Rai, P; Wang, Y; Guo, S; Chen, G; Dunson, D; Carin, L
Published in: 31st International Conference on Machine Learning, ICML 2014
January 1, 2014

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.

Duke Scholars

Published In

31st International Conference on Machine Learning, ICML 2014

Publication Date

January 1, 2014

Volume

5

Start / End Page

3810 / 3820
 

Citation

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Rai, P., Wang, Y., Guo, S., Chen, G., Dunson, D., & Carin, L. (2014). Scalable bayesian low-rank decomposition of incomplete multiway tensors. In 31st International Conference on Machine Learning, ICML 2014 (Vol. 5, pp. 3810–3820).
Rai, P., Y. Wang, S. Guo, G. Chen, D. Dunson, and L. Carin. “Scalable bayesian low-rank decomposition of incomplete multiway tensors.” In 31st International Conference on Machine Learning, ICML 2014, 5:3810–20, 2014.
Rai P, Wang Y, Guo S, Chen G, Dunson D, Carin L. Scalable bayesian low-rank decomposition of incomplete multiway tensors. In: 31st International Conference on Machine Learning, ICML 2014. 2014. p. 3810–20.
Rai, P., et al. “Scalable bayesian low-rank decomposition of incomplete multiway tensors.” 31st International Conference on Machine Learning, ICML 2014, vol. 5, 2014, pp. 3810–20.
Rai P, Wang Y, Guo S, Chen G, Dunson D, Carin L. Scalable bayesian low-rank decomposition of incomplete multiway tensors. 31st International Conference on Machine Learning, ICML 2014. 2014. p. 3810–3820.

Published In

31st International Conference on Machine Learning, ICML 2014

Publication Date

January 1, 2014

Volume

5

Start / End Page

3810 / 3820