Alternating linear scheme in a bayesian framework for low-rank tensor approximation

Alternating linear scheme in a bayesian framework for low-rank tensor approximation

Menzen, C.M. (TU Delft Team Manon Kok)
Kok, M. (TU Delft Team Manon Kok)
Batselier, K. (TU Delft Team Kim Batselier)

2022

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets can be facilitated. In this paper, we find a low-rank representation for a given tensor by solving a Bayesian inference problem. This is achieved by dividing the overall inference problem into subproblems where we sequentially infer the posterior distribution of one tensor decomposition component at a time. This leads to a probabilistic interpretation of the well-known iterative algorithm alternating linear scheme (ALS). In this way, the consideration of measurement noise is enabled, as well as the incorporation of application-specific prior knowledge and the uncertainty quantification of the low-rank tensor estimate. To compute the low-rank tensor estimate from the posterior distributions of the tensor decomposition components, we present an algorithm that performs the unscented transform in tensor train format.

alternating linear scheme
Bayesian inference
low-rank approximation
tensor decomposition
tensor train

http://resolver.tudelft.nl/uuid:e7560971-5833-46b5-8be4-618221feac65

https://doi.org/10.1137/20M1386414

1064-8275

SIAM Journal on Scientific Computing, 44 (3), A1116-A1144

Institutional Repository

journal article

© 2022 C.M. Menzen, M. Kok, K. Batselier