Gaussian processes 2D

By Ilias Bilionis1, Yinuo Li1, Juan Camilo Lopez1

1. Purdue University

Gaussian Process 2D Sampling

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Version 1.0 - published on 03 Aug 2015

doi:10.4231/D3M61BR05 cite this

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Abstract

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.

References

  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; Yinuo Li; Juan Camilo Lopez (2015), "Gaussian processes 2D," https://nanohub.org/resources/gp2d. (DOI: 10.4231/D3M61BR05).

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