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Doctoral thesis
Open access
English

Tensor Train Approximations: Riemannian Methods, Randomized Linear Algebra and Applications to Machine Learning

ContributorsVoorhaar, Rik
Number of pages117
Imprimatur date2022-12-19
Defense date2022-12-15
Abstract

This thesis concerns the optimization and application of low-rank methods, with a special focus on tensor trains (TTs). In particular, we develop methods for computing TT approximations of a given tensor in a variety of low-rank formats and we show how to solve the tensor completion problem for TTs using Riemannian methods. This is then applied to train a machine learning (ML) estimator based on discretized functions. We also study randomized methods for obtaining low-rank approximations of matrices and tensors. Finally, we consider how such randomized methods can be used to solve general linear matrix and tensor equations.

eng
Keywords
  • Tensors
  • Tensor trains
  • Numerical Analysis
  • Numerical Linear Algebra
  • Matrix Product State
  • Randomized Linear Algebra
  • Machine Learning
Research group
Citation (ISO format)
VOORHAAR, Rik. Tensor Train Approximations: Riemannian Methods, Randomized Linear Algebra and Applications to Machine Learning. 2022. doi: 10.13097/archive-ouverte/unige:166308
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Technical informations

Creation12/26/2022 10:20:00 AM
First validation12/26/2022 10:20:00 AM
Update time03/16/2023 10:28:10 AM
Status update03/16/2023 10:28:08 AM
Last indexation02/01/2024 9:27:12 AM
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