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Abstract:
Gaussian Processes are powerful regression models specified
by parametrized mean and covariance functions. Standard approaches
to estimate these parameters (known by the name Hyperparameters)
are Maximum Likelihood (ML) and Maximum APosterior (MAP)
approaches. In this paper, we propose and investigate predictive
approaches, namely, maximization of Geisser's Surrogate Predictive
Probability (GPP) and minimization of mean square error with
respect to GPP (referred to as Geisser's Predictive mean square
Error (GPE)) to estimate the hyperparameters. We also derive
results for the standard Cross-Validation (CV) error and make a
comparison. These approaches are tested on a number of problems and
experimental results show that these approaches are strongly
competitive to existing approaches.
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