Model Selection and Adaptation of Hyperparameters

C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006,ISBN 2006 Massachusetts Institute of 5 Model Selection andAdaptation ofHyperparametersIn chapters 2 and 3 we have seen how to do regression and classification usinga Gaussian process with a given fixed covariance function. However, in manypractical applications, it may not be easy to specify all aspects of the covari-ance function with confidence. While some properties such as stationarity ofthe covariance function may be easy to determine from the context, we typicallyhave only rather vague information about other properties, such as the valueof free (hyper-) parameters, length-scales. In chapter 4 several examplesof covariance functions were presented, many of which have large numbers ofparameters. In addition, the exact form and possible free parameters of thelikelihood function may also not be known in advance.

C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. 2006 Massachusetts Institute of Technology.c www ...

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