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<div class="section" id="oob-errors-for-random-forests">
<span id="sphx-glr-auto-examples-ensemble-plot-ensemble-oob-py"></span><h1>OOB Errors for Random Forests<a class="headerlink" href="#oob-errors-for-random-forests" title="Permalink to this headline">¶</a></h1>
<p>The <code class="docutils literal"><span class="pre">RandomForestClassifier</span></code> is trained using <em>bootstrap aggregation</em>, where
each new tree is fit from a bootstrap sample of the training observations
<img class="math" src="../../_images/math/18d5dc891ec8ac122999974c913987b3563fd7fd.png" alt="z_i = (x_i, y_i)"/>. The <em>out-of-bag</em> (OOB) error is the average error for
each <img class="math" src="../../_images/math/6de62736d8aa90101801d7a1416e97e921d1620f.png" alt="z_i"/> calculated using predictions from the trees that do not
contain <img class="math" src="../../_images/math/6de62736d8aa90101801d7a1416e97e921d1620f.png" alt="z_i"/> in their respective bootstrap sample. This allows the
<code class="docutils literal"><span class="pre">RandomForestClassifier</span></code> to be fit and validated whilst being trained <a class="footnote-reference" href="#id2" id="id1">[1]</a>.</p>
<p>The example below demonstrates how the OOB error can be measured at the
addition of each new tree during training. The resulting plot allows a
practitioner to approximate a suitable value of <code class="docutils literal"><span class="pre">n_estimators</span></code> at which the
error stabilizes.</p>
<table class="docutils footnote" frame="void" id="id2" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[1]</a></td><td>T. Hastie, R. Tibshirani and J. Friedman, “Elements of Statistical
Learning Ed. 2”, p592-593, Springer, 2009.</td></tr>
</tbody>
</table>
<img alt="../../_images/sphx_glr_plot_ensemble_oob_001.png" class="align-center" src="../../_images/sphx_glr_plot_ensemble_oob_001.png" />
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">OrderedDict</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.make_classification.html#sklearn.datasets.make_classification" title="View documentation for sklearn.datasets.make_classification"><span class="n">make_classification</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="View documentation for sklearn.ensemble.RandomForestClassifier"><span class="n">RandomForestClassifier</span></a><span class="p">,</span> <span class="n">ExtraTreesClassifier</span>
<span class="c1"># Author: Kian Ho <[email protected]></span>
<span class="c1"># Gilles Louppe <[email protected]></span>
<span class="c1"># Andreas Mueller <[email protected]></span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 Clause</span>
<span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="n">RANDOM_STATE</span> <span class="o">=</span> <span class="mi">123</span>
<span class="c1"># Generate a binary classification dataset.</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_classification.html#sklearn.datasets.make_classification" title="View documentation for sklearn.datasets.make_classification"><span class="n">make_classification</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span>
<span class="n">n_clusters_per_class</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_informative</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">RANDOM_STATE</span><span class="p">)</span>
<span class="c1"># NOTE: Setting the `warm_start` construction parameter to `True` disables</span>
<span class="c1"># support for parallelized ensembles but is necessary for tracking the OOB</span>
<span class="c1"># error trajectory during training.</span>
<span class="n">ensemble_clfs</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">(</span><span class="s2">"RandomForestClassifier, max_features='sqrt'"</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="View documentation for sklearn.ensemble.RandomForestClassifier"><span class="n">RandomForestClassifier</span></a><span class="p">(</span><span class="n">warm_start</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">oob_score</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="n">max_features</span><span class="o">=</span><span class="s2">"sqrt"</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">RANDOM_STATE</span><span class="p">)),</span>
<span class="p">(</span><span class="s2">"RandomForestClassifier, max_features='log2'"</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="View documentation for sklearn.ensemble.RandomForestClassifier"><span class="n">RandomForestClassifier</span></a><span class="p">(</span><span class="n">warm_start</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">max_features</span><span class="o">=</span><span class="s1">'log2'</span><span class="p">,</span>
<span class="n">oob_score</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">RANDOM_STATE</span><span class="p">)),</span>
<span class="p">(</span><span class="s2">"RandomForestClassifier, max_features=None"</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="View documentation for sklearn.ensemble.RandomForestClassifier"><span class="n">RandomForestClassifier</span></a><span class="p">(</span><span class="n">warm_start</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">max_features</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span>
<span class="n">oob_score</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">RANDOM_STATE</span><span class="p">))</span>
<span class="p">]</span>
<span class="c1"># Map a classifier name to a list of (<n_estimators>, <error rate>) pairs.</span>
<span class="n">error_rate</span> <span class="o">=</span> <span class="n">OrderedDict</span><span class="p">((</span><span class="n">label</span><span class="p">,</span> <span class="p">[])</span> <span class="k">for</span> <span class="n">label</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">ensemble_clfs</span><span class="p">)</span>
<span class="c1"># Range of `n_estimators` values to explore.</span>
<span class="n">min_estimators</span> <span class="o">=</span> <span class="mi">15</span>
<span class="n">max_estimators</span> <span class="o">=</span> <span class="mi">175</span>
<span class="k">for</span> <span class="n">label</span><span class="p">,</span> <span class="n">clf</span> <span class="ow">in</span> <span class="n">ensemble_clfs</span><span class="p">:</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">min_estimators</span><span class="p">,</span> <span class="n">max_estimators</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">set_params</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="n">i</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</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="c1"># Record the OOB error for each `n_estimators=i` setting.</span>
<span class="n">oob_error</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">clf</span><span class="o">.</span><span class="n">oob_score_</span>
<span class="n">error_rate</span><span class="p">[</span><span class="n">label</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">i</span><span class="p">,</span> <span class="n">oob_error</span><span class="p">))</span>
<span class="c1"># Generate the "OOB error rate" vs. "n_estimators" plot.</span>
<span class="k">for</span> <span class="n">label</span><span class="p">,</span> <span class="n">clf_err</span> <span class="ow">in</span> <span class="n">error_rate</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">xs</span><span class="p">,</span> <span class="n">ys</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">clf_err</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlim.html#matplotlib.pyplot.xlim" title="View documentation for matplotlib.pyplot.xlim"><span class="n">plt</span><span class="o">.</span><span class="n">xlim</span></a><span class="p">(</span><span class="n">min_estimators</span><span class="p">,</span> <span class="n">max_estimators</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"n_estimators"</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"OOB error rate"</span><span class="p">)</span>
<a href="http://matplotlib.org/api/legend_api.html#matplotlib.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"upper right"</span><span class="p">)</span>
<a href="http://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>
</pre></div>
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