Gaussian Process Regression: Standard Deviation Meaning

In the following code about the Gaussian Process Regression (GPR): from sklearn.datasets import make_friedman2 from sklearn.gaussian_process import GaussianProcessRegressor from sk

Solution 1:

Gaussian Processes are Bayesian and therefore a fitted regression results in a distribution over the possible parameters. This then allows one to compute a predictive distribution rather than simply point estimates. Setting the argument return_std=True, results in the method returning the standard deviations associated with each query point. These provide theoretical bounds on the predictions, informed by the strength of the evidence (training data) provided.

Cross-validation is typically used when one cannot perform such analytical calculations exactly. The key advantage to Gaussian Process methods are their tractability.