.. 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-integer.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-integer.py: =================================================== Comparing initial sampling methods on integer space =================================================== 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 a real space :ref:`sphx_glr_auto_examples_initial_sampling_method.py` .. GENERATED FROM PYTHON SOURCE LINES 24-37 .. code-block:: default print(__doc__) import numpy as np np.random.seed(1234) 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 38-55 .. 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], 'bs', markersize=40, alpha=0.5) # ax.legend(loc="best", numpoints=1) ax.set_xlabel("X1") ax.set_xlim([0, 5]) ax.set_ylabel("X2") ax.set_ylim([0, 5]) plt.title(title) ax.grid(True) n_samples = 10 space = Space([(0, 5), (0, 5)]) .. GENERATED FROM PYTHON SOURCE LINES 56-58 Random sampling --------------- .. GENERATED FROM PYTHON SOURCE LINES 58-66 .. code-block:: default x = space.rvs(n_samples) plot_searchspace(x, "Random samples") pdist_data = [] x_label = [] print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("random") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_001.png :alt: Random samples :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 27 .. GENERATED FROM PYTHON SOURCE LINES 67-69 Sobol' ------ .. GENERATED FROM PYTHON SOURCE LINES 69-77 .. code-block:: default sobol = Sobol() x = sobol.generate(space.dimensions, n_samples) plot_searchspace(x, "Sobol'") print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("sobol'") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_002.png :alt: Sobol' :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_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 " empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 78-80 Classic latin hypercube sampling -------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 80-88 .. code-block:: default lhs = Lhs(lhs_type="classic", criterion=None) x = lhs.generate(space.dimensions, n_samples) plot_searchspace(x, 'classic LHS') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("lhs") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_003.png :alt: classic LHS :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 89-91 Centered latin hypercube sampling --------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 91-99 .. code-block:: default lhs = Lhs(lhs_type="centered", criterion=None) x = lhs.generate(space.dimensions, n_samples) plot_searchspace(x, 'centered LHS') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("center") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_004.png :alt: centered LHS :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 100-102 Maximin optimized hypercube sampling ------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 102-110 .. code-block:: default lhs = Lhs(criterion="maximin", iterations=10000) x = lhs.generate(space.dimensions, n_samples) plot_searchspace(x, 'maximin LHS') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("maximin") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_005.png :alt: maximin LHS :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 111-113 Correlation optimized hypercube sampling ---------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 113-121 .. code-block:: default lhs = Lhs(criterion="correlation", iterations=10000) x = lhs.generate(space.dimensions, n_samples) plot_searchspace(x, 'correlation LHS') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("corr") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_006.png :alt: correlation LHS :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_006.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 122-124 Ratio optimized hypercube sampling ---------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 124-132 .. code-block:: default lhs = Lhs(criterion="ratio", iterations=10000) x = lhs.generate(space.dimensions, n_samples) plot_searchspace(x, 'ratio LHS') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("ratio") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_007.png :alt: ratio LHS :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_007.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 133-135 Halton sampling --------------- .. GENERATED FROM PYTHON SOURCE LINES 135-143 .. code-block:: default halton = Halton() x = halton.generate(space.dimensions, n_samples) plot_searchspace(x, 'Halton') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("halton") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_008.png :alt: Halton :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_008.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 144-146 Hammersly sampling ------------------ .. GENERATED FROM PYTHON SOURCE LINES 146-154 .. code-block:: default hammersly = Hammersly() x = hammersly.generate(space.dimensions, n_samples) plot_searchspace(x, 'Hammersly') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("hammersly") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_009.png :alt: Hammersly :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_009.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 155-157 Grid sampling ------------- .. GENERATED FROM PYTHON SOURCE LINES 157-165 .. code-block:: default grid = Grid(border="include", use_full_layout=False) x = grid.generate(space.dimensions, n_samples) plot_searchspace(x, 'Grid') print("empty fields: %d" % (36 - np.size(np.unique(x, axis=0), 0))) pdist_data.append(pdist(x).flatten()) x_label.append("grid") .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_010.png :alt: Grid :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_010.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none empty fields: 26 .. GENERATED FROM PYTHON SOURCE LINES 166-172 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 172-179 .. code-block:: default fig, ax = plt.subplots() ax.boxplot(pdist_data) plt.grid(True) plt.ylabel("pdist") _ = ax.set_ylim(0, 6) _ = ax.set_xticklabels(x_label, rotation=45, fontsize=8) .. image-sg:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_011.png :alt: initial sampling method integer :srcset: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_011.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 7.380 seconds) **Estimated memory usage:** 9 MB .. _sphx_glr_download_auto_examples_sampler_initial-sampling-method-integer.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-integer.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: initial-sampling-method-integer.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: initial-sampling-method-integer.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_