.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/mlearning/transformer/plot_scaling_data.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_mlearning_transformer_plot_scaling_data.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_mlearning_transformer_plot_scaling_data.py:


Scaling
=======

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.. code-block:: Python


    from __future__ import annotations

    from gemseo.algos.design_space import DesignSpace
    from gemseo.algos.doe.openturns.openturns import OpenTURNS
    from gemseo.algos.optimization_problem import OptimizationProblem
    from gemseo.core.mdo_functions.mdo_function import MDOFunction
    from gemseo.mlearning.regression.algos.gpr import GaussianProcessRegressor
    from gemseo.mlearning.regression.quality.r2_measure import R2Measure
    from gemseo.problems.optimization.rosenbrock import Rosenbrock








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Scaling data around zero is important to avoid numerical issues
when fitting a machine learning model.
This is all the more true as
the variables have different ranges
or the fitting relies on numerical optimization techniques.
This example illustrates the latter point.

First,
we consider the Rosenbrock function :math:`f(x)=(1-x_1)^2+100(x_2-x_1^2)^2`
over the domain :math:`[-2,2]^2`:

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.. code-block:: Python

    problem = Rosenbrock()








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In order to approximate this function with a regression model,
we sample it 30 times with an optimized Latin hypercube sampling (LHS) technique

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.. code-block:: Python

    opt_lhs = OpenTURNS("OT_OPT_LHS")
    opt_lhs.execute(problem, n_samples=30)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='margin: 1em;'>Optimization result:<br/><ul><li>Design variables: [0.86803148 0.78478463]</li><li>Objective function: 0.11542217328145475</li><li>Feasible solution: True</li></ul></div>
    </div>
    <br />
    <br />

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and save the samples in an :class:`.IODataset`:

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.. code-block:: Python

    dataset_train = problem.to_dataset(opt_naming=False)








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We do the same with a full-factorial design of experiments (DOE) of size 900:

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.. code-block:: Python

    full_fact = OpenTURNS("OT_FULLFACT")
    full_fact.execute(problem, n_samples=30 * 30)
    dataset_test = problem.to_dataset(opt_naming=False)








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Then,
we create a first Gaussian process regressor from the training dataset:

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.. code-block:: Python

    gpr = GaussianProcessRegressor(dataset_train)
    gpr.learn()








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and compute its R2 quality from the test dataset:

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.. code-block:: Python

    r2 = R2Measure(gpr)
    r2.compute_test_measure(dataset_test)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([0.97049746])



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Then,
we create a second Gaussian process regressor from the training dataset
with the default input and output transformers that are :class:`.MinMaxScaler`:

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.. code-block:: Python

    gpr = GaussianProcessRegressor(
        dataset_train, transformer=GaussianProcessRegressor.DEFAULT_TRANSFORMER
    )
    gpr.learn()








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We can see that the scaling improves the R2 quality (recall: the higher, the better):

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.. code-block:: Python

    r2 = R2Measure(gpr)
    r2.compute_test_measure(dataset_test)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([0.97049746])



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We note that in this case, the input scaling does not contribute to this improvement:

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.. code-block:: Python

    gpr = GaussianProcessRegressor(dataset_train, transformer={"outputs": "MinMaxScaler"})
    gpr.learn()
    r2 = R2Measure(gpr)
    r2.compute_test_measure(dataset_test)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([0.97049746])



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We can also see that using a :class:`.StandardScaler` is less relevant in this case:

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.. code-block:: Python

    gpr = GaussianProcessRegressor(dataset_train, transformer={"outputs": "StandardScaler"})
    gpr.learn()
    r2 = R2Measure(gpr)
    r2.compute_test_measure(dataset_test)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([0.97049746])



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Finally,
we rewrite the Rosenbrock function as :math:`f(x)=(1-x_1)^2+100(0.01x_2-x_1^2)^2`
and its domain as :math:`[-2,2]\times[-200,200]`:

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.. code-block:: Python

    design_space = DesignSpace()
    design_space.add_variable("x1", lower_bound=-2, upper_bound=2)
    design_space.add_variable("x2", lower_bound=-200, upper_bound=200)








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in order to have inputs with different orders of magnitude.
We create the learning and test datasets in the same way:

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.. code-block:: Python

    problem = OptimizationProblem(design_space)
    problem.objective = MDOFunction(
        lambda x: (1 - x[0]) ** 2 + 100 * (0.01 * x[1] - x[0] ** 2) ** 2, "f"
    )
    opt_lhs.execute(problem, n_samples=30)
    dataset_train = problem.to_dataset(opt_naming=False)
    full_fact.execute(problem, n_samples=30 * 30)
    dataset_test = problem.to_dataset(opt_naming=False)








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and build a first Gaussian process regressor with a min-max scaler for the outputs:

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.. code-block:: Python

    gpr = GaussianProcessRegressor(dataset_train, transformer={"outputs": "MinMaxScaler"})
    gpr.learn()
    r2 = R2Measure(gpr)
    r2.compute_test_measure(dataset_test)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([0.90669624])



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The R2 quality is degraded
because estimating the model's correlation lengths is complicated.
This can be facilitated by setting a :class:`.MinMaxScaler` for the inputs:

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.. code-block:: Python

    gpr = GaussianProcessRegressor(
        dataset_train, transformer={"inputs": "MinMaxScaler", "outputs": "MinMaxScaler"}
    )
    gpr.learn()
    r2 = R2Measure(gpr)
    r2.compute_test_measure(dataset_test)




.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([0.97432803])




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.914 seconds)


.. _sphx_glr_download_examples_mlearning_transformer_plot_scaling_data.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_scaling_data.ipynb <plot_scaling_data.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_scaling_data.py <plot_scaling_data.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_scaling_data.zip <plot_scaling_data.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_