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• W3116724564 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 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." @default.
• W3116724564 created "2021-01-05" @default.
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• W3116724564 date "2022-05-05" @default.
• W3116724564 modified "2023-09-26" @default.
• W3116724564 title "Alternating Linear Scheme in a Bayesian Framework for Low-Rank Tensor Approximation" @default.
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• W3116724564 doi "https://doi.org/10.1137/20m1386414" @default.
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