.. 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`
.. 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
.. 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)])
Random sampling
---------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_001.png
:alt: Random samples
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 27
Sobol
-----
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_002.png
:alt: Sobol
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
Classic latin hypercube sampling
--------------------------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_003.png
:alt: classic LHS
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 27
Centered latin hypercube sampling
---------------------------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_004.png
:alt: centered LHS
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
Maximin optimized hypercube sampling
------------------------------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_005.png
:alt: maximin LHS
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
Correlation optimized hypercube sampling
----------------------------------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_006.png
:alt: correlation LHS
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
Ratio optimized hypercube sampling
----------------------------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_007.png
:alt: ratio LHS
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
Halton sampling
---------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_008.png
:alt: Halton
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
Hammersly sampling
------------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_009.png
:alt: Hammersly
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
Grid sampling
-------------
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_010.png
:alt: Grid
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
empty fields: 26
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
.. 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:: /auto_examples/sampler/images/sphx_glr_initial-sampling-method-integer_011.png
:alt: initial sampling method integer
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 10.339 seconds)
**Estimated memory usage:** 8 MB
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