Predictive App roaches for Choosing Hyperparameters in Gaussian Processes

Part of Advances in Neural Information Processing Systems 12 (NIPS 1999)

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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.