.. _example_gaussian_process_plot_gpr_noisy_targets.py:


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Gaussian Processes regression: basic introductory example
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A simple one-dimensional regression example computed in two different ways:

1. A noise-free case
2. A noisy case with known noise-level per datapoint

In both cases, the kernel's 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 ``alpha`` is applied as a Tikhonov
regularization of the assumed covariance between the training points.



.. rst-class:: horizontal


    *

      .. image:: images/plot_gpr_noisy_targets_001.png
            :scale: 47

    *

      .. image:: images/plot_gpr_noisy_targets_002.png
            :scale: 47




**Python source code:** :download:`plot_gpr_noisy_targets.py <plot_gpr_noisy_targets.py>`

.. literalinclude:: plot_gpr_noisy_targets.py
    :lines: 21-

**Total running time of the example:**  0.83 seconds
( 0 minutes  0.83 seconds)