Simulating Gaussian processes



Assumed audience:

ML people

How can I simulate a Gaussian Processes with a given covariance?

Lattice tricks

Basis tricks

References

Chan, G., and A. T. A. Wood. 1999. Simulation of Stationary Gaussian Vector Fields.” Statistics and Computing 9 (4): 265–68.
Dietrich, C. R., and G. N. Newsam. 1993. A Fast and Exact Method for Multidimensional Gaussian Stochastic Simulations.” Water Resources Research 29 (8): 2861–69.
———. 1997. Fast and Exact Simulation of Stationary Gaussian Processes Through Circulant Embedding of the Covariance Matrix.” SIAM Journal on Scientific Computing 18 (4): 1088–1107.
Durrande, Nicolas, Vincent Adam, Lucas Bordeaux, Stefanos Eleftheriadis, and James Hensman. 2019. Banded Matrix Operators for Gaussian Markov Models in the Automatic Differentiation Era.” In Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, 2780–89. PMLR.
Gilboa, E., Y. Saatçi, and J. P. Cunningham. 2015. Scaling Multidimensional Inference for Structured Gaussian Processes.” IEEE Transactions on Pattern Analysis and Machine Intelligence 37 (2): 424–36.
Graham, Ivan G., Frances Y. Kuo, Dirk Nuyens, Rob Scheichl, and Ian H. Sloan. 2017. Circulant Embedding with QMC – Analysis for Elliptic PDE with Lognormal Coefficients.” arXiv:1710.09254 [Math], October.
Gray, Robert M. 2006. Toeplitz and Circulant Matrices: A Review. Vol. 2.
Guinness, Joseph, and Montserrat Fuentes. 2016. Circulant Embedding of Approximate Covariances for Inference From Gaussian Data on Large Lattices.” Journal of Computational and Graphical Statistics 26 (1): 88–97.
Liu, Yang, Jingfa Li, Shuyu Sun, and Bo Yu. 2019. Advances in Gaussian Random Field Generation: A Review.” Computational Geosciences 23 (5): 1011–47.
Powell, Catherine E. 2014. “Generating Realisations of Stationary Gaussian Random Fields by Circulant Embedding.” Matrix 2 (2): 1.
Rue, Havard, and Leonhard Held. 2005. Gaussian Markov Random Fields: Theory and Applications. New York: Chapman and Hall/CRC.
Whittle, P. 1954. “On Stationary Processes in the Plane.” Biometrika 41 (3/4): 434–49.
Whittle, P. 1953. Estimation and Information in Stationary Time Series.” Arkiv För Matematik 2 (5): 423–34.

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