Abstract
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 language | English |
|---|---|
| Title of host publication | Proceedings of 2019 27th European Signal Processing Conference |
| Number of pages | 5 |
| Publisher | IEEE |
| Publication date | 2019 |
| ISBN (Print) | 978-9-0827-9703-9 |
| DOIs | |
| Publication status | Published - 2019 |
| Event | 2019 27th European Signal Processing Conference - PALEXCO, Muelle de Transatlánticos, A Coruña, Spain Duration: 2 Sep 2019 → 6 Sep 2019 http://eusipco2019.org |
Conference
| Conference | 2019 27th European Signal Processing Conference |
|---|---|
| Location | PALEXCO, Muelle de Transatlánticos |
| Country | Spain |
| City | A Coruña |
| Period | 02/09/2019 → 06/09/2019 |
| Internet address |
Keywords
- Bayesian inference
- Tensor train decomposition
- Matrix product state
- Multi-modal data
Cite this
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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 proceeding › Article in proceedings › Research › peer-review
TY - GEN
T1 - Probabilistic Tensor Train Decomposition
AU - Hinrich, Jesper Løve
AU - Mørup, Morten
PY - 2019
Y1 - 2019
N2 - 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 suitableorder 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
AB - 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 suitableorder 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
KW - Bayesian inference
KW - Tensor train decomposition
KW - Matrix product state
KW - Multi-modal data
U2 - 10.23919/EUSIPCO.2019.8903177
DO - 10.23919/EUSIPCO.2019.8903177
M3 - Article in proceedings
SN - 978-9-0827-9703-9
BT - Proceedings of 2019 27th European Signal Processing Conference
PB - IEEE
ER -