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

• URL: http://arxiv.org/abs/2012.11228v1
• Date: Mon, 21 Dec 2020 10:15:30 GMT
• Title: Alternating linear scheme in a Bayesian framework for low-rank tensor approximation
• Authors: Clara Menzen, Manon Kok, Kim Batselier
• Abstract summary: We find a low-rank representation for a given tensor by solving a Bayesian inference problem. We present an algorithm that performs the unscented transform in tensor train format.
• Score: 5.833272638548154
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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 sub-problems 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.

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