Kriging in tensor train data format

Sergey Dolgov, Alexander Litvinenko, Dishi Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as Kriging, computing conditional covariance, geostatistical optimal de-sign, and others. However, the approximation of a full tensor by its low-rank format can be computationally formidable. In this work, we incorporate the robust Tensor Train (TT) approximation of covariance matrices and the efficient TT-Cross algorithm into the FFT-based Kriging. It is shown that here the computational complexity of Kriging is reduced to O(dr3n), where n is the mode size of the estimation grid, d is the number of variables (the dimension), and r is the rank of the TT approximation of the covariance matrix. For many popular covariance functions the TT rank r remains stable for increasing n and d. The advantages of this approach against those using plain FFT are demonstrated in synthetic and real data examples.

Original languageEnglish
Title of host publicationProceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
EditorsM. Papadrakakis, V. Papadopoulos, G. Stefanou
Place of PublicationAthens, Greece
PublisherNational Technical University of Athens
Pages309-329
Number of pages21
ISBN (Print)9786188284494
DOIs
Publication statusPublished - 1 Jan 2019
Event3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019 - Crete, Greece
Duration: 24 Jun 201926 Jun 2019

Publication series

NameProceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019

Conference

Conference3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
CountryGreece
CityCrete
Period24/06/1926/06/19

Keywords

  • Circulant
  • FFT
  • Geostatistical estimation
  • Geostatistical optimal design
  • Kriging
  • Low-rank tensor approximation
  • Tensor train
  • Toeplitz

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Theoretical Computer Science

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