Covariance functions for Gaussian Process Models

Vesna Tanko (2009) Covariance functions for Gaussian Process Models. EngD thesis.

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Abstract

The main topic of this thesis are Gaussian processes for machine learning, more precisely the selection of covariance function, which represents one of the most important issues of GP modeling. To understand covariance function, it is necessary to know GP modeling basics, thus they are included in the thesis. Besides GP modeling basics, the most popular covariance functions are described. Their selection and use are presented on two particular cases of GP modeling. The first case was used to study covariance functions and provide us with guidelines for similar data modeling and recommendations to determine appropriate covariance function. Finally, we used the experiences gained through the experiments and made predictions for the second case of data. We realized, that selection of covariance function depends on data structure and primarily purpose of modeling, by which we mean individuals expectations and background knowledge of GP model output. In other words: selection of covariance function for smooth function modeling differs from selection of covariance function for linear line.

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