Generative modeling via tensor train sketching

In this paper, we introduce a sketching algorithm for constructing a tensor train representation of a probability density from its samples. Our method deviates from the standard recursive SVD-based procedure for constructing a tensor train. Instead, we formulate and solve a sequence of small linear...

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Bibliographic Details
Published in:Applied and computational harmonic analysis Vol. 67; no. C; p. 101575
Main Authors: Hur, YoonHaeng, Hoskins, Jeremy G., Lindsey, Michael, Stoudenmire, E.M., Khoo, Yuehaw
Format: Journal Article
Language:English
Published: United States Elsevier Inc 01.11.2023
Elsevier
Subjects:
Generative modeling
High-dimensional function approximation
Mathematics
Randomized algorithm
Tensor decompositions
Tensor train
High-dimensional function approximation
Generative modeling
Tensor decompositions
Tensor train
Randomized algorithm
ISSN:1063-5203, 1096-603X
Online Access:Get full text
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Summary:In this paper, we introduce a sketching algorithm for constructing a tensor train representation of a probability density from its samples. Our method deviates from the standard recursive SVD-based procedure for constructing a tensor train. Instead, we formulate and solve a sequence of small linear systems for the individual tensor train cores. This approach can avoid the curse of dimensionality that threatens both the algorithmic and sample complexities of the recovery problem. Specifically, for Markov models under natural conditions, we prove that the tensor cores can be recovered with a sample complexity that scales logarithmically in the dimensionality. Finally, we illustrate the performance of the method with several numerical experiments.
Bibliography:None
USDOE Office of Science (SC)
SC0022232
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2023.101575