Gaussian processes 1D

By Ilias Bilionis1, Juan Camilo Lopez1, Yinuo Li

1. Purdue University

Allows the user to sample functions from a Gaussian process.

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Version 1.0 - published on 22 Jul 2015

doi:10.4231/D3WM13V45 cite this

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The choice of a function to approximate any given data, is not unique; such function can be found through different methods, in which the parameters of the model are calculated. This tool illustrates the process of sampling from a Gaussian process, to obtain a random function from a process with a given covariance and a mean of zero. Although the results are distributed around zero, this does not imply a loss of generality, since the mean can be changed by adding a function.

The Gaussian process tool takes a set of hyper parameters for a particular covariance function, which is used to calculate a covariance matrix. This matrix is positive definite and Cholesky decomposition can be used to make the sampling process computationally efficient.


  1. Rasmussen, C. E. and C. K. I. Williams (2006). Gaussian processes for machine learning. Cambridge, Mass., MIT Press.
  2. Langtangen, C.E. (2009). A primer on scientific programming with Python. Springer.

Cite this work

Researchers should cite this work as follows:

  • Ilias Bilionis, Juan Camilo Lopez, Yinuo Li (2015), "Gaussian processes 1D," (DOI: 10.4231/D3WM13V45).

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