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

Diplôme Thèse Tensor Train Approximations: Riemannian Methods, Randomized Linear Algebra and Applications to Machine Learning eng 2022-12-15 2022-12-19 author Voorhaar Rik 856797 director Vandereycken Bart 829601 117 10.13097/archive-ouverte/unige:166308 urn:nbn:ch:unige-1663086 Sc. 5707 <p>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.</p> Tensors Tensor trains Numerical Analysis Numerical Linear Algebra Matrix Product State Randomized Linear Algebra Machine Learning Dewey 510 Swiss National Science Foundation Analysis and implementation of low-rank tensor algorithms 192363 CH Projects 25 Section de mathématiques 11 false 847 Analyse numérique 422f298d-d674-4128-890a-d7a1483ee01a Thesis Public thesis.pdf 7216765 application/pdf CC0 d0b999d2-710c-4080-b8cb-a99d0a862f2c Imprimatur Public imprimatur.pdf 1588922 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Tensor Train Approximations: Riemannian Methods, Randomized Linear Algebra and Applications to Machine Learning				2022	649	621

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