Computationally efficient algorithm for Gaussian Process regression in case of structured samples

M. Belyaev, E. Burnaev, Y. Kapushev

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Surrogate modeling is widely used in many engineering problems. Data sets often have Cartesian product structure (for instance factorial design of experiments with missing points). In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation–Gaussian Process regression–can be hardly applied due to its computational complexity. In this paper a computationally efficient approach for constructing Gaussian Process regression in case of data sets with Cartesian product structure is presented. Efficiency is achieved by using a special structure of the data set and operations with tensors. Proposed algorithm has low computational as well as memory complexity compared to existing algorithms. In this work we also introduce a regularization procedure allowing to take into account anisotropy of the data set and avoid degeneracy of regression model.

Original languageEnglish
Pages (from-to)499-513
Number of pages15
JournalComputational Mathematics and Mathematical Physics
Issue number4
Publication statusPublished - 2016
Externally publishedYes


  • factorial design of experiments
  • Gaussian processes
  • incomplete factorial design of experiments
  • operations with tensors
  • regularization


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