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Num. Meth. Prog., 2017, Volume 18, Issue 3, Pages 214–220 (Mi vmp874)  

This article is cited in 1 scientific paper (total in 1 paper)

Application of block low-rank matrices in Gaussian processes for regression

D. A. Sushnikova

Skolkovo Institute of Science and Technology

Abstract: The Gaussian processes for regression are considered. During simulation of correlated noises using the Gaussian processes, the main difficulty is the computation of the posterior mean and dispersion of the prediction. This computation requires the inversion of the dense covariance matrix of order $n$, where $n$ is the sample size. In addition, for the likelihood evaluation we need to compute the logarithm of the determinant of the dense covariance matrix, which is also a time-consuming problem. A new method for the fast computation of the covariance matrix logarithm is proposed. This method is based on the approximation of this matrix by a sparse matrix. The proposed method appears to be time efficient compared to the HODLR (Hierarchically Off-Diagonal Low-Rank) method and the traditional dense method.

Keywords: Gaussian processes, $\mathcal{H}^2$ matrix, sparse matrix, Cholesky factorization.

Funding Agency Grant Number
Russian Science Foundation 17-11-01376
Russian Foundation for Basic Research 17-01-00854


Full text: PDF file (496 kB)
UDC: 519.65; 519.613; 519.246
Received: 17.05.2017

Citation: D. A. Sushnikova, “Application of block low-rank matrices in Gaussian processes for regression”, Num. Meth. Prog., 18:3 (2017), 214–220

Citation in format AMSBIB
\Bibitem{Sus17}
\by D.~A.~Sushnikova
\paper Application of block low-rank matrices in Gaussian processes for regression
\jour Num. Meth. Prog.
\yr 2017
\vol 18
\issue 3
\pages 214--220
\mathnet{http://mi.mathnet.ru/vmp874}


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    This publication is cited in the following articles:
    1. A. V. Panyukov, Kh. Z. Chalub, Ya. A. Mezal, “Approksimatsiya matritsy s polozhitelnymi elementami matritsei edinichnogo ranga”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:2 (2018), 28–36  mathnet  crossref  elib
  • Numerical methods and programming
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