Probabilistic Tensor Train Decomposition

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

The tensor train decomposition (TTD) has become an attractive decomposition approach due to its ease of inference by use of the singular value decomposition and flexible yet compact representations enabling efficient computations and reduced memory usage using the TTD representation for further analyses. Unfortunately, the level of complexity to use and the order in which modes should be decomposed using the TTD is unclear. We advance TTD to a fully probabilistic TTD (PTTD)
using variational Bayesian inference to account for parameter uncertainty and noise. In particular, we exploit that the PTTD enables model comparisons by use of the evidence lower bound (ELBO) of the variational approximation. On synthetic data with ground truth structure and a real 3-way fluorescence spectroscopy dataset, we demonstrate how the ELBO admits quantification of model specification not only in terms of numbers of components for each factor in the TTD, but also a suitable
order of the modes in which the TTD should be employed. The proposed PTTD provides a principled framework for the characterization of model uncertainty, complexity, and modeland mode-order when compressing tensor data using the TTD
Original languageEnglish
Title of host publicationProceedings of 2019 27th European Signal Processing Conference
Number of pages5
PublisherIEEE
Publication date2019
ISBN (Print)978-9-0827-9703-9
DOIs
Publication statusPublished - 2019
Event2019 27th European Signal Processing Conference - PALEXCO, Muelle de Transatlánticos, A Coruña, Spain
Duration: 2 Sep 20196 Sep 2019
http://eusipco2019.org

Conference

Conference2019 27th European Signal Processing Conference
LocationPALEXCO, Muelle de Transatlánticos
CountrySpain
CityA Coruña
Period02/09/201906/09/2019
Internet address

Keywords

  • Bayesian inference
  • Tensor train decomposition
  • Matrix product state
  • Multi-modal data

Cite this

Hinrich, J. L., & Mørup, M. (2019). Probabilistic Tensor Train Decomposition. In Proceedings of 2019 27th European Signal Processing Conference IEEE. https://doi.org/10.23919/EUSIPCO.2019.8903177
Hinrich, Jesper Løve ; Mørup, Morten. / Probabilistic Tensor Train Decomposition. Proceedings of 2019 27th European Signal Processing Conference. IEEE, 2019.
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Hinrich, JL & Mørup, M 2019, Probabilistic Tensor Train Decomposition. in Proceedings of 2019 27th European Signal Processing Conference. IEEE, 2019 27th European Signal Processing Conference, A Coruña, Spain, 02/09/2019. https://doi.org/10.23919/EUSIPCO.2019.8903177

Probabilistic Tensor Train Decomposition. / Hinrich, Jesper Løve; Mørup, Morten.

Proceedings of 2019 27th European Signal Processing Conference. IEEE, 2019.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Hinrich JL, Mørup M. Probabilistic Tensor Train Decomposition. In Proceedings of 2019 27th European Signal Processing Conference. IEEE. 2019 https://doi.org/10.23919/EUSIPCO.2019.8903177