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<li><a class="reference internal" href="#">Partial Dependence Plots</a></li>
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<div class="sphx-glr-download-link-note admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Click <a class="reference internal" href="#sphx-glr-download-auto-examples-ensemble-plot-partial-dependence-py"><span class="std std-ref">here</span></a> to download the full example code</p>
</div>
<div class="sphx-glr-example-title section" id="partial-dependence-plots">
<span id="sphx-glr-auto-examples-ensemble-plot-partial-dependence-py"></span><h1>Partial Dependence Plots<a class="headerlink" href="#partial-dependence-plots" title="Permalink to this headline">¶</a></h1>
<p>Partial dependence plots show the dependence between the target function <a class="footnote-reference" href="#id4" id="id1">[2]</a>
and a set of ‘target’ features, marginalizing over the
values of all other features (the complement features). Due to the limits
of human perception the size of the target feature set must be small (usually,
one or two) thus the target features are usually chosen among the most
important features
(see <a class="reference internal" href="../../modules/generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor.feature_importances_" title="sklearn.ensemble.GradientBoostingRegressor.feature_importances_"><code class="xref py py-attr docutils literal"><span class="pre">feature_importances_</span></code></a>).</p>
<p>This example shows how to obtain partial dependence plots from a
<a class="reference internal" href="../../modules/generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="sklearn.ensemble.GradientBoostingRegressor"><code class="xref py py-class docutils literal"><span class="pre">GradientBoostingRegressor</span></code></a> trained on the California
housing dataset. The example is taken from <a class="footnote-reference" href="#id3" id="id2">[1]</a>.</p>
<p>The plot shows four one-way and one two-way partial dependence plots.
The target variables for the one-way PDP are:
median income (<cite>MedInc</cite>), avg. occupants per household (<cite>AvgOccup</cite>),
median house age (<cite>HouseAge</cite>), and avg. rooms per household (<cite>AveRooms</cite>).</p>
<p>We can clearly see that the median house price shows a linear relationship
with the median income (top left) and that the house price drops when the
avg. occupants per household increases (top middle).
The top right plot shows that the house age in a district does not have
a strong influence on the (median) house price; so does the average rooms
per household.
The tick marks on the x-axis represent the deciles of the feature values
in the training data.</p>
<p>Partial dependence plots with two target features enable us to visualize
interactions among them. The two-way partial dependence plot shows the
dependence of median house price on joint values of house age and avg.
occupants per household. We can clearly see an interaction between the
two features:
For an avg. occupancy greater than two, the house price is nearly independent
of the house age, whereas for values less than two there is a strong dependence
on age.</p>
<table class="docutils footnote" frame="void" id="id3" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[1]</a></td><td>T. Hastie, R. Tibshirani and J. Friedman,
“Elements of Statistical Learning Ed. 2”, Springer, 2009.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id4" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[2]</a></td><td>For classification you can think of it as the regression score before
the link function.</td></tr>
</tbody>
</table>
<ul class="sphx-glr-horizontal">
<li><img alt="../../_images/sphx_glr_plot_partial_dependence_001.png" class="sphx-glr-multi-img first" src="../../_images/sphx_glr_plot_partial_dependence_001.png" />
</li>
<li><img alt="../../_images/sphx_glr_plot_partial_dependence_002.png" class="sphx-glr-multi-img first" src="../../_images/sphx_glr_plot_partial_dependence_002.png" />
</li>
</ul>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none"><div class="highlight"><pre><span></span>Training GBRT...
done.
Convenience plot with ``partial_dependence_plots``
Custom 3d plot via ``partial_dependence``
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span>
<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="k">import</span> <span class="n">Axes3D</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="View documentation for sklearn.ensemble.GradientBoostingRegressor"><span class="n">GradientBoostingRegressor</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble.partial_dependence</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.ensemble.partial_dependence.plot_partial_dependence.html#sklearn.ensemble.partial_dependence.plot_partial_dependence" title="View documentation for sklearn.ensemble.partial_dependence.plot_partial_dependence"><span class="n">plot_partial_dependence</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble.partial_dependence</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.ensemble.partial_dependence.partial_dependence.html#sklearn.ensemble.partial_dependence.partial_dependence" title="View documentation for sklearn.ensemble.partial_dependence.partial_dependence"><span class="n">partial_dependence</span></a>
<span class="kn">from</span> <span class="nn">sklearn.datasets.california_housing</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_california_housing.html#sklearn.datasets.fetch_california_housing" title="View documentation for sklearn.datasets.california_housing.fetch_california_housing"><span class="n">fetch_california_housing</span></a>
<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
<span class="n">cal_housing</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_california_housing.html#sklearn.datasets.fetch_california_housing" title="View documentation for sklearn.datasets.california_housing.fetch_california_housing"><span class="n">fetch_california_housing</span></a><span class="p">()</span>
<span class="c1"># split 80/20 train-test</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">cal_housing</span><span class="o">.</span><span class="n">data</span><span class="p">,</span>
<span class="n">cal_housing</span><span class="o">.</span><span class="n">target</span><span class="p">,</span>
<span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">names</span> <span class="o">=</span> <span class="n">cal_housing</span><span class="o">.</span><span class="n">feature_names</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Training GBRT..."</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="View documentation for sklearn.ensemble.GradientBoostingRegressor"><span class="n">GradientBoostingRegressor</span></a><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_depth</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span>
<span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">loss</span><span class="o">=</span><span class="s1">'huber'</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">" done."</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Convenience plot with ``partial_dependence_plots``'</span><span class="p">)</span>
<span class="n">features</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.partial_dependence.plot_partial_dependence.html#sklearn.ensemble.partial_dependence.plot_partial_dependence" title="View documentation for sklearn.ensemble.partial_dependence.plot_partial_dependence"><span class="n">plot_partial_dependence</span></a><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">X_train</span><span class="p">,</span> <span class="n">features</span><span class="p">,</span>
<span class="n">feature_names</span><span class="o">=</span><span class="n">names</span><span class="p">,</span>
<span class="n">n_jobs</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">grid_resolution</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Partial dependence of house value on nonlocation features</span><span class="se">\n</span><span class="s1">'</span>
<span class="s1">'for the California housing dataset'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="View documentation for matplotlib.pyplot.subplots_adjust"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="n">top</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span> <span class="c1"># tight_layout causes overlap with suptitle</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Custom 3d plot via ``partial_dependence``'</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
<span class="n">target_feature</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">pdp</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.partial_dependence.partial_dependence.html#sklearn.ensemble.partial_dependence.partial_dependence" title="View documentation for sklearn.ensemble.partial_dependence.partial_dependence"><span class="n">partial_dependence</span></a><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">target_feature</span><span class="p">,</span>
<span class="n">X</span><span class="o">=</span><span class="n">X_train</span><span class="p">,</span> <span class="n">grid_resolution</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="n">XX</span><span class="p">,</span> <span class="n">YY</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="View documentation for numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">pdp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">axes</span><span class="p">)))</span><span class="o">.</span><span class="n">T</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">Axes3D</span><span class="p">(</span><span class="n">fig</span><span class="p">)</span>
<span class="n">surf</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">XX</span><span class="p">,</span> <span class="n">YY</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">rstride</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">cstride</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">BuPu</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">names</span><span class="p">[</span><span class="n">target_feature</span><span class="p">[</span><span class="mi">0</span><span class="p">]])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">names</span><span class="p">[</span><span class="n">target_feature</span><span class="p">[</span><span class="mi">1</span><span class="p">]])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_zlabel</span><span class="p">(</span><span class="s1">'Partial dependence'</span><span class="p">)</span>
<span class="c1"># pretty init view</span>
<span class="n">ax</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="n">elev</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">azim</span><span class="o">=</span><span class="mi">122</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="View documentation for matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">surf</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="View documentation for matplotlib.pyplot.suptitle"><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span></a><span class="p">(</span><span class="s1">'Partial dependence of house value on median</span><span class="se">\n</span><span class="s1">'</span>
<span class="s1">'age and average occupancy'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="View documentation for matplotlib.pyplot.subplots_adjust"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="n">top</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
<span class="c1"># Needed on Windows because plot_partial_dependence uses multiprocessing</span>
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
<span class="n">main</span><span class="p">()</span>
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