TY - GEN
T1 - Kriging in tensor train data format
AU - Dolgov, Sergey
AU - Litvinenko, Alexander
AU - Liu, Dishi
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Circulant
KW - FFT
KW - Geostatistical estimation
KW - Geostatistical optimal design
KW - Kriging
KW - Low-rank tensor approximation
KW - Tensor train
KW - Toeplitz
UR - http://www.scopus.com/inward/record.url?scp=85079319960&partnerID=8YFLogxK
U2 - 10.7712/120219.6343.18651
DO - 10.7712/120219.6343.18651
M3 - Chapter in a published conference proceeding
AN - SCOPUS:85079319960
SN - 9786188284494
T3 - Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
SP - 309
EP - 329
BT - Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
A2 - Papadrakakis, M.
A2 - Papadopoulos, V.
A2 - Stefanou, G.
PB - National Technical University of Athens
CY - Athens, Greece
T2 - 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
Y2 - 24 June 2019 through 26 June 2019
ER -