.. _example_gaussian_process_plot_gp_regression.py: ========================================================= Gaussian Processes regression: basic introductory example ========================================================= A simple one-dimensional regression exercise computed in two different ways: 1. A noise-free case with a cubic correlation model 2. A noisy case with a squared Euclidean correlation model In both cases, the model parameters are estimated using the maximum likelihood principle. The figures illustrate the interpolating property of the Gaussian Process model as well as its probabilistic nature in the form of a pointwise 95% confidence interval. Note that the parameter nugget is applied as a Tikhonov regularization of the assumed covariance between the training points. In the special case of the squared euclidean correlation model, nugget is mathematically equivalent to a normalized variance: That is .. math:: \mathrm{nugget}_i = \left[\frac{\sigma_i}{y_i}\right]^2 .. rst-class:: horizontal * .. image:: images/plot_gp_regression_001.png :scale: 47 * .. image:: images/plot_gp_regression_002.png :scale: 47 **Python source code:** :download:plot_gp_regression.py  .. literalinclude:: plot_gp_regression.py :lines: 30- **Total running time of the example:** 1.03 seconds ( 0 minutes 1.03 seconds)