Robust prediction interval estimation for Gaussian processes by cross-validation method

Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage solutions that observations on average, but they do not pay attention coverage and width of Prediction Intervals. A robust two-step approach is used address problem adjusting calibrating Intervals for Gaussian Processes Regression. First, covariance hyperparameters are determined by a standard method. Leave-One-Out Coverage Probability introduced as metric adjust assess optimal type II nominal level. Then relaxation method applied choose minimize Wasserstein distance between distribution with initial (obtained Estimation) proposed achieve desired Probability. The gives appropriate probabilities small widths.