Probabilistic cross-validation estimators for Gaussian process regression
Luca Martino, Valero Laparra, Gustau Camps‐Valls · 2017
Gaussian Processes (GPs) are state-of-the-art tools for regression. Inference of GP hyperparameters is typically done by maximizing the marginal log-likelihood (ML). If the data truly follows the GP model, using the ML approach is optimal and computationally efficient. Unfortunately very often this is not case and suboptimal results are obtained in terms of prediction error. Alternative procedures such as cross-validation (CV) schemes are often employed instead, but they usually incur in high computational costs. We propose a probabilistic version of CV (PCV) based on two different model pieces in order to reduce the dependence on a specific model choice. PCV presents the benefits from both approaches, and allows us to find the solution for either the maximum a posteriori (MAP) or the Minimum Mean Square Error (MMSE) estimators. Experiments in controlled situations reveal that the PCV solution outperforms ML for both estimators, and that PCV-MMSE results outperforms other traditional approaches.