Prediction performance after learning in Gaussian process regression
This work improves uncertainty quantification for practitioners using Gaussian process regression, though it is incremental as it builds on existing theoretical bounds.
The paper addresses the underestimation of prediction errors in Gaussian process regression by deriving a more accurate mean square-error bound that accounts for model learning from data, demonstrating its effectiveness with synthetic and real data examples.
This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean square-error (MSE). This approach, however, does not take into account that the statistical model is learned from the data. We show that this omission leads to a systematic underestimation of the prediction errors. Starting from a generalization of the Cramér-Rao bound, we derive a more accurate MSE bound which provides a measure of uncertainty for prediction of Gaussian processes. The improved bound is easily computed and we illustrate it using synthetic and real data examples. of uncertainty for prediction of Gaussian processes and illustrate it using synthetic and real data examples.