.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/sampler/initial-sampling-method.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` 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 25-38 .. code-block:: default print(__doc__) import numpy as np np.random.seed(123) import matplotlib.pyplot as plt from skopt.space import Space from skopt.sampler import Sobol from skopt.sampler import Lhs from skopt.sampler import Halton from skopt.sampler import Hammersly from skopt.sampler import Grid from scipy.spatial.distance import pdist .. GENERATED FROM PYTHON SOURCE LINES 39-56 .. code-block:: default 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., 10.), (0., 15.)]) # space.set_transformer("normalize") .. GENERATED FROM PYTHON SOURCE LINES 57-59 Random sampling --------------- .. GENERATED FROM PYTHON SOURCE LINES 59-66 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 67-69 Sobol' ------ .. GENERATED FROM PYTHON SOURCE LINES 69-76 .. code-block:: default 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 Out: .. code-block:: none /home/circleci/project/skopt/sampler/sobol.py:246: 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("The balance properties of Sobol' points require " .. GENERATED FROM PYTHON SOURCE LINES 77-79 Classic Latin hypercube sampling -------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 79-86 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 87-89 Centered Latin hypercube sampling --------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 89-96 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 97-99 Maximin optimized hypercube sampling ------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 99-106 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 107-109 Correlation optimized hypercube sampling ---------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 109-116 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 117-119 Ratio optimized hypercube sampling ---------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 119-126 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 127-129 Halton sampling --------------- .. GENERATED FROM PYTHON SOURCE LINES 129-136 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 137-139 Hammersly sampling ------------------ .. GENERATED FROM PYTHON SOURCE LINES 139-146 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 147-149 Grid sampling ------------- .. GENERATED FROM PYTHON SOURCE LINES 149-156 .. code-block:: default 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 .. GENERATED FROM PYTHON SOURCE LINES 157-163 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 .. GENERATED FROM PYTHON SOURCE LINES 163-170 .. code-block:: default 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 7.448 seconds) **Estimated memory usage:** 9 MB .. _sphx_glr_download_auto_examples_sampler_initial-sampling-method.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-optimize/scikit-optimize/master?urlpath=lab/tree/notebooks/auto_examples/sampler/initial-sampling-method.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: initial-sampling-method.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: initial-sampling-method.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_