Tensor completion via Gaussian process-based initialization

Yermek Kapushev, Ivan Oseledets, Evgeny Burnaev

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that the tensor is of high order, and tensor values are generated by an unknown smooth function. The assumption allows us to develop an efficient initialization scheme based on Gaussian process regression and the TT-cross approximation technique. The proposed approach can be used in conjunction with any optimization algorithm that is usually utilized in tensor completion problems. We empirically justify that in this case the reconstruction error improves compared to the tensor completion with random initialization. As an additional benefit, our technique automatically selects rank thanks to using the TT-cross approximation technique.

Original languageEnglish
Pages (from-to)A3812-A3824
JournalSIAM Journal on Scientific Computing
Volume42
Issue number6
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Cross-approximation
  • Gaussian processes
  • Tensor completion
  • Tensor train

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