Probabilistic Tensor Train Decomposition

Jesper Løve Hinrich, Morten Mørup

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


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
Publication date2019
ISBN (Print)978-9-0827-9703-9
Publication statusPublished - 2019
Event2019 27th European Signal Processing Conference - PALEXCO, Muelle de Transatlánticos, A Coruña, Spain
Duration: 2 Sep 20196 Sep 2019


Conference2019 27th European Signal Processing Conference
LocationPALEXCO, Muelle de Transatlánticos
CityA Coruña
Internet address


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

Fingerprint Dive into the research topics of 'Probabilistic Tensor Train Decomposition'. Together they form a unique fingerprint.

Cite this