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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_sampler_initial-sampling-method.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_sampler_initial-sampling-method.py:


==================================
Comparing initial sampling methods
==================================

Holger Nahrstaedt 2020 Sigurd Carlsen October 2019

.. currentmodule:: skopt


When doing baysian optimization we often want to reserve some of the
early part of the optimization to pure exploration. By default the
optimizer suggests purely random samples for the first n_initial_points
(10 by default). The downside to this is that there is no guarantee that
these samples are spread out evenly across all the dimensions.

Sampling methods as Latin hypercube, Sobol', Halton and Hammersly
take advantage of the fact that we know beforehand how many random
points we want to sample. Then these points can be "spread out" in
such a way that each dimension is explored.

See also the example on an integer space
:ref:`sphx_glr_auto_examples_initial_sampling_method_integer.py`

.. GENERATED FROM PYTHON SOURCE LINES 25-36

.. code-block:: Python


    print(__doc__)
    import numpy as np

    np.random.seed(123)
    import matplotlib.pyplot as plt
    from scipy.spatial.distance import pdist

    from skopt.sampler import Grid, Halton, Hammersly, Lhs, Sobol
    from skopt.space import Space








.. GENERATED FROM PYTHON SOURCE LINES 37-56

.. code-block:: Python



    def plot_searchspace(x, title):
        fig, ax = plt.subplots()
        plt.plot(np.array(x)[:, 0], np.array(x)[:, 1], 'bo', label='samples')
        plt.plot(np.array(x)[:, 0], np.array(x)[:, 1], 'bo', markersize=80, alpha=0.5)
        # ax.legend(loc="best", numpoints=1)
        ax.set_xlabel("X1")
        ax.set_xlim([-5, 10])
        ax.set_ylabel("X2")
        ax.set_ylim([0, 15])
        plt.title(title)


    n_samples = 10

    space = Space([(-5.0, 10.0), (0.0, 15.0)])
    # space.set_transformer("normalize")








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Random sampling
---------------

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.. code-block:: Python

    x = space.rvs(n_samples)
    plot_searchspace(x, "Random samples")
    pdist_data = []
    x_label = []
    pdist_data.append(pdist(x).flatten())
    x_label.append("random")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_001.png
   :alt: Random samples
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_001.png
   :class: sphx-glr-single-img





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Sobol'
------

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.. code-block:: Python


    sobol = Sobol()
    x = sobol.generate(space.dimensions, n_samples)
    plot_searchspace(x, "Sobol'")
    pdist_data.append(pdist(x).flatten())
    x_label.append("sobol'")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_002.png
   :alt: Sobol'
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    D:\git\scikit-optimize\skopt\sampler\sobol.py:521: UserWarning: The balance properties of Sobol' points require n to be a power of 2. 0 points have been previously generated, then: n=0+10=10. 
      warnings.warn(




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Classic Latin hypercube sampling
--------------------------------

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.. code-block:: Python


    lhs = Lhs(lhs_type="classic", criterion=None)
    x = lhs.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'classic LHS')
    pdist_data.append(pdist(x).flatten())
    x_label.append("lhs")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_003.png
   :alt: classic LHS
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_003.png
   :class: sphx-glr-single-img





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Centered Latin hypercube sampling
---------------------------------

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.. code-block:: Python


    lhs = Lhs(lhs_type="centered", criterion=None)
    x = lhs.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'centered LHS')
    pdist_data.append(pdist(x).flatten())
    x_label.append("center")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_004.png
   :alt: centered LHS
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_004.png
   :class: sphx-glr-single-img





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Maximin optimized hypercube sampling
------------------------------------

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.. code-block:: Python


    lhs = Lhs(criterion="maximin", iterations=10000)
    x = lhs.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'maximin LHS')
    pdist_data.append(pdist(x).flatten())
    x_label.append("maximin")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_005.png
   :alt: maximin LHS
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_005.png
   :class: sphx-glr-single-img





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Correlation optimized hypercube sampling
----------------------------------------

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.. code-block:: Python


    lhs = Lhs(criterion="correlation", iterations=10000)
    x = lhs.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'correlation LHS')
    pdist_data.append(pdist(x).flatten())
    x_label.append("corr")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_006.png
   :alt: correlation LHS
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_006.png
   :class: sphx-glr-single-img





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Ratio optimized hypercube sampling
----------------------------------

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.. code-block:: Python


    lhs = Lhs(criterion="ratio", iterations=10000)
    x = lhs.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'ratio LHS')
    pdist_data.append(pdist(x).flatten())
    x_label.append("ratio")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_007.png
   :alt: ratio LHS
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_007.png
   :class: sphx-glr-single-img





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Halton sampling
---------------

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.. code-block:: Python


    halton = Halton()
    x = halton.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'Halton')
    pdist_data.append(pdist(x).flatten())
    x_label.append("halton")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_008.png
   :alt: Halton
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_008.png
   :class: sphx-glr-single-img





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Hammersly sampling
------------------

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.. code-block:: Python


    hammersly = Hammersly()
    x = hammersly.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'Hammersly')
    pdist_data.append(pdist(x).flatten())
    x_label.append("hammersly")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_009.png
   :alt: Hammersly
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_009.png
   :class: sphx-glr-single-img





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Grid sampling
-------------

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.. code-block:: Python


    grid = Grid(border="include", use_full_layout=False)
    x = grid.generate(space.dimensions, n_samples)
    plot_searchspace(x, 'Grid')
    pdist_data.append(pdist(x).flatten())
    x_label.append("grid")




.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_010.png
   :alt: Grid
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_010.png
   :class: sphx-glr-single-img





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Pdist boxplot of all methods
----------------------------

This boxplot shows the distance between all generated points using
Euclidian distance. The higher the value, the better the sampling method.
It can be seen that random has the worst performance

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.. code-block:: Python


    fig, ax = plt.subplots()
    ax.boxplot(pdist_data)
    plt.grid(True)
    plt.ylabel("pdist")
    _ = ax.set_ylim(0, 12)
    _ = ax.set_xticklabels(x_label, rotation=45, fontsize=8)



.. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_011.png
   :alt: initial sampling method
   :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method_011.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 5.517 seconds)


.. _sphx_glr_download_auto_examples_sampler_initial-sampling-method.py:

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        :alt: Launch binder
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