Probabilistic Block Term Decomposition for the Modelling of Higher-order Arrays
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Probabilistic Block Term Decomposition for the Modelling of Higher-order Arrays. / Hinrich, Jesper Love; Morup, Morten.
I: Computing in Science and Engineering, 2024.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Probabilistic Block Term Decomposition for the Modelling of Higher-order Arrays
AU - Hinrich, Jesper Love
AU - Morup, Morten
N1 - Publisher Copyright: IEEE
PY - 2024
Y1 - 2024
N2 - Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools. This paper explores the use of Bayesian modeling in the context of tensor factorization and presents a probabilistic extension of the so-called Block-Term Decomposition (BTD) model and show how it can interpolate between two common decomposition models - the Canonical Polyadic Decomposition (CPD) and the Tucker decomposition. This probabilistic extension is obtained by applying Bayesian inference to the BTD model, allowing for uncertainty quantification, robustness to corruption by noise and model miss-specification. The novelty of this model is its applicability to Nth-order tensors, incorporating mode specific orthogonality within each block, and priors that penalizing complexity of the core arrays. On synthetic and two real datasets, we highlight the benefits of probabilistic tensor factorization considering the BTD, demonstrating that the probabilistic BTD can successfully quantify multi-linear structures and is robust to noise.
AB - Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools. This paper explores the use of Bayesian modeling in the context of tensor factorization and presents a probabilistic extension of the so-called Block-Term Decomposition (BTD) model and show how it can interpolate between two common decomposition models - the Canonical Polyadic Decomposition (CPD) and the Tucker decomposition. This probabilistic extension is obtained by applying Bayesian inference to the BTD model, allowing for uncertainty quantification, robustness to corruption by noise and model miss-specification. The novelty of this model is its applicability to Nth-order tensors, incorporating mode specific orthogonality within each block, and priors that penalizing complexity of the core arrays. On synthetic and two real datasets, we highlight the benefits of probabilistic tensor factorization considering the BTD, demonstrating that the probabilistic BTD can successfully quantify multi-linear structures and is robust to noise.
KW - Bayes methods
KW - Computational modeling
KW - Data models
KW - Maximum likelihood estimation
KW - Noise
KW - Probabilistic logic
KW - Tensors
U2 - 10.1109/MCSE.2024.3398054
DO - 10.1109/MCSE.2024.3398054
M3 - Journal article
AN - SCOPUS:85192766710
JO - Computing in Science and Engineering
JF - Computing in Science and Engineering
SN - 1521-9615
ER -
ID: 393271451