Part of Advances in Neural Information Processing Systems 12 (NIPS 1999)
S. Sundararajan, S. Keerthi
Gaussian Processes are powerful regression models specified by parametrized mean and covariance functions. Standard approaches to estimate these parameters (known by the name Hyperparam(cid:173) eters) are Maximum Likelihood (ML) and Maximum APosterior (MAP) approaches. In this paper, we propose and investigate pre(cid:173) dictive approaches, namely, maximization of Geisser's Surrogate Predictive Probability (GPP) and minimization of mean square er(cid:173) ror 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.