Kriging in tensor train data format

Sergey Dolgov; Alexander Litvinenko; Dishi Liu

doi:10.7712/120219.6343.18651

Kriging in tensor train data format

Sergey Dolgov, Alexander Litvinenko, Dishi Liu

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

3 Citations (SciVal)

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 language	English
Title of host publication	Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
Editors	M. Papadrakakis, V. Papadopoulos, G. Stefanou
Place of Publication	Athens, Greece
Publisher	National Technical University of Athens
Pages	309-329
Number of pages	21
ISBN (Print)	9786188284494
DOIs	https://doi.org/10.7712/120219.6343.18651
Publication status	Published - 1 Jan 2019
Event	3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019 - Crete, Greece Duration: 24 Jun 2019 → 26 Jun 2019

Publication series

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

Conference

Conference	3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
Country/Territory	Greece
City	Crete
Period	24/06/19 → 26/06/19

Funding

The research reported in this publication was supported by funding from the Alexander von Humboldt Foundation. We also would like to thank Wolfgang Nowak for sharing his Matlab code.

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

Access to Document

10.7712/120219.6343.18651

https://arxiv.org/abs/1904.09668

Cite this

Dolgov, S., Litvinenko, A., & Liu, D. (2019). Kriging in tensor train data format. In M. Papadrakakis, V. Papadopoulos, & G. Stefanou (Eds.), Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019 (pp. 309-329). (Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019). National Technical University of Athens. https://doi.org/10.7712/120219.6343.18651

Kriging in tensor train data format. / Dolgov, Sergey; Litvinenko, Alexander; Liu, Dishi.
Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019. ed. / M. Papadrakakis; V. Papadopoulos; G. Stefanou. Athens, Greece: National Technical University of Athens, 2019. p. 309-329 (Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Dolgov, S, Litvinenko, A & Liu, D 2019, Kriging in tensor train data format. in M Papadrakakis, V Papadopoulos & G Stefanou (eds), Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019. Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019, National Technical University of Athens, Athens, Greece, pp. 309-329, 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019, Crete, Greece, 24/06/19. https://doi.org/10.7712/120219.6343.18651

Dolgov S, Litvinenko A, Liu D. Kriging in tensor train data format. In Papadrakakis M, Papadopoulos V, Stefanou G, editors, Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019. Athens, Greece: National Technical University of Athens. 2019. p. 309-329. (Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019). doi: 10.7712/120219.6343.18651

Dolgov, Sergey ; Litvinenko, Alexander ; Liu, Dishi. / Kriging in tensor train data format. Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019. editor / M. Papadrakakis ; V. Papadopoulos ; G. Stefanou. Athens, Greece : National Technical University of Athens, 2019. pp. 309-329 (Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019).

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Kriging in tensor train data format

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