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<li><a class="reference internal" href="#">Permutation Importance vs Random Forest Feature Importance (MDI)</a><ul>
<li><a class="reference internal" href="#data-loading-and-feature-engineering">Data Loading and Feature Engineering</a></li>
<li><a class="reference internal" href="#accuracy-of-the-model">Accuracy of the Model</a></li>
<li><a class="reference internal" href="#tree-s-feature-importance-from-mean-decrease-in-impurity-mdi">Tree’s Feature Importance from Mean Decrease in Impurity (MDI)</a></li>
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<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-inspection-plot-permutation-importance-py"><span class="std std-ref">here</span></a>
to download the full example code or to run this example in your browser via Binder</p>
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<section class="sphx-glr-example-title" id="permutation-importance-vs-random-forest-feature-importance-mdi">
<span id="sphx-glr-auto-examples-inspection-plot-permutation-importance-py"></span><h1>Permutation Importance vs Random Forest Feature Importance (MDI)<a class="headerlink" href="#permutation-importance-vs-random-forest-feature-importance-mdi" title="Permalink to this heading">¶</a></h1>
<p>In this example, we will compare the impurity-based feature importance of
<a class="reference internal" href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="sklearn.ensemble.RandomForestClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomForestClassifier</span></code></a> with the
permutation importance on the titanic dataset using
<a class="reference internal" href="../../modules/generated/sklearn.inspection.permutation_importance.html#sklearn.inspection.permutation_importance" title="sklearn.inspection.permutation_importance"><code class="xref py py-func docutils literal notranslate"><span class="pre">permutation_importance</span></code></a>. We will show that the
impurity-based feature importance can inflate the importance of numerical
features.</p>
<p>Furthermore, the impurity-based feature importance of random forests suffers
from being computed on statistics derived from the training dataset: the
importances can be high even for features that are not predictive of the target
variable, as long as the model has the capacity to use them to overfit.</p>
<p>This example shows how to use Permutation Importances as an alternative that
can mitigate those limitations.</p>
<aside class="topic">
<p class="topic-title">References:</p>
<ul class="simple">
<li><p><a class="reference external" href="https://doi.org/10.1023/A:1010933404324">L. Breiman, “Random Forests”, Machine Learning, 45(1), 5-32,
2001.</a></p></li>
</ul>
</aside>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
</pre></div>
</div>
<section id="data-loading-and-feature-engineering">
<h2>Data Loading and Feature Engineering<a class="headerlink" href="#data-loading-and-feature-engineering" title="Permalink to this heading">¶</a></h2>
<p>Let’s use pandas to load a copy of the titanic dataset. The following shows
how to apply separate preprocessing on numerical and categorical features.</p>
<p>We further include two random variables that are not correlated in any way
with the target variable (<code class="docutils literal notranslate"><span class="pre">survived</span></code>):</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">random_num</span></code> is a high cardinality numerical variable (as many unique
values as records).</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">random_cat</span></code> is a low cardinality categorical variable (3 possible
values).</p></li>
</ul>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_openml.html#sklearn.datasets.fetch_openml" title="sklearn.datasets.fetch_openml" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_openml</span></a>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_openml.html#sklearn.datasets.fetch_openml" title="sklearn.datasets.fetch_openml" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_openml</span></a><span class="p">(</span>
<span class="s2">"titanic"</span><span class="p">,</span> <span class="n">version</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">as_frame</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">parser</span><span class="o">=</span><span class="s2">"pandas"</span>
<span class="p">)</span>
<span class="n">rng</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="n">seed</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="n">X</span><span class="p">[</span><span class="s2">"random_cat"</span><span class="p">]</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">X</span><span class="p">[</span><span class="s2">"random_num"</span><span class="p">]</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">categorical_columns</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"pclass"</span><span class="p">,</span> <span class="s2">"sex"</span><span class="p">,</span> <span class="s2">"embarked"</span><span class="p">,</span> <span class="s2">"random_cat"</span><span class="p">]</span>
<span class="n">numerical_columns</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"age"</span><span class="p">,</span> <span class="s2">"sibsp"</span><span class="p">,</span> <span class="s2">"parch"</span><span class="p">,</span> <span class="s2">"fare"</span><span class="p">,</span> <span class="s2">"random_num"</span><span class="p">]</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">categorical_columns</span> <span class="o">+</span> <span class="n">numerical_columns</span><span class="p">]</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="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">stratify</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
</pre></div>
</div>
<p>We define a predictive model based on a random forest. Therefore, we will make
the following preprocessing steps:</p>
<ul class="simple">
<li><p>use <a class="reference internal" href="../../modules/generated/sklearn.preprocessing.OrdinalEncoder.html#sklearn.preprocessing.OrdinalEncoder" title="sklearn.preprocessing.OrdinalEncoder"><code class="xref py py-class docutils literal notranslate"><span class="pre">OrdinalEncoder</span></code></a> to encode the
categorical features;</p></li>
<li><p>use <a class="reference internal" href="../../modules/generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> to fill missing values for
numerical features using a mean strategy.</p></li>
</ul>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><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="sklearn.ensemble.RandomForestClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RandomForestClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer" class="sphx-glr-backref-module-sklearn-impute sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SimpleImputer</span></a>
<span class="kn">from</span> <span class="nn">sklearn.compose</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.compose.ColumnTransformer.html#sklearn.compose.ColumnTransformer" title="sklearn.compose.ColumnTransformer" class="sphx-glr-backref-module-sklearn-compose sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ColumnTransformer</span></a>
<span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Pipeline</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.OrdinalEncoder.html#sklearn.preprocessing.OrdinalEncoder" title="sklearn.preprocessing.OrdinalEncoder" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">OrdinalEncoder</span></a>
<span class="n">categorical_encoder</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.OrdinalEncoder.html#sklearn.preprocessing.OrdinalEncoder" title="sklearn.preprocessing.OrdinalEncoder" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">OrdinalEncoder</span></a><span class="p">(</span>
<span class="n">handle_unknown</span><span class="o">=</span><span class="s2">"use_encoded_value"</span><span class="p">,</span> <span class="n">unknown_value</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">encoded_missing_value</span><span class="o">=-</span><span class="mi">1</span>
<span class="p">)</span>
<span class="n">numerical_pipe</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer" class="sphx-glr-backref-module-sklearn-impute sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SimpleImputer</span></a><span class="p">(</span><span class="n">strategy</span><span class="o">=</span><span class="s2">"mean"</span><span class="p">)</span>
<span class="n">preprocessing</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.compose.ColumnTransformer.html#sklearn.compose.ColumnTransformer" title="sklearn.compose.ColumnTransformer" class="sphx-glr-backref-module-sklearn-compose sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ColumnTransformer</span></a><span class="p">(</span>
<span class="p">[</span>
<span class="p">(</span><span class="s2">"cat"</span><span class="p">,</span> <span class="n">categorical_encoder</span><span class="p">,</span> <span class="n">categorical_columns</span><span class="p">),</span>
<span class="p">(</span><span class="s2">"num"</span><span class="p">,</span> <span class="n">numerical_pipe</span><span class="p">,</span> <span class="n">numerical_columns</span><span class="p">),</span>
<span class="p">],</span>
<span class="n">verbose_feature_names_out</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">rf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Pipeline</span></a><span class="p">(</span>
<span class="p">[</span>
<span class="p">(</span><span class="s2">"preprocess"</span><span class="p">,</span> <span class="n">preprocessing</span><span class="p">),</span>
<span class="p">(</span><span class="s2">"classifier"</span><span class="p">,</span> <a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="sklearn.ensemble.RandomForestClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RandomForestClassifier</span></a><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)),</span>
<span class="p">]</span>
<span class="p">)</span>
<span class="n">rf</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>
</pre></div>
</div>
<div class="output_subarea output_html rendered_html output_result">
<style>#sk-container-id-36 {color: black;background-color: white;}#sk-container-id-36 pre{padding: 0;}#sk-container-id-36 div.sk-toggleable {background-color: white;}#sk-container-id-36 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-36 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-36 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-36 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-36 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-36 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-36 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-36 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-36 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-36 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-36 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-36 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-36 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-36 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-36 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-36 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-36 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-36 div.sk-item {position: relative;z-index: 1;}#sk-container-id-36 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-36 div.sk-item::before, #sk-container-id-36 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-36 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-36 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-36 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-36 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-36 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-36 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-36 div.sk-label-container {text-align: center;}#sk-container-id-36 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-36 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-36" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>Pipeline(steps=[('preprocess',
ColumnTransformer(transformers=[('cat',
OrdinalEncoder(encoded_missing_value=-1,
handle_unknown='use_encoded_value',
unknown_value=-1),
['pclass', 'sex', 'embarked',
'random_cat']),
('num', SimpleImputer(),
['age', 'sibsp', 'parch',
'fare', 'random_num'])],
verbose_feature_names_out=False)),
('classifier', RandomForestClassifier(random_state=42))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-155" type="checkbox" ><label for="sk-estimator-id-155" class="sk-toggleable__label sk-toggleable__label-arrow">Pipeline</label><div class="sk-toggleable__content"><pre>Pipeline(steps=[('preprocess',
ColumnTransformer(transformers=[('cat',
OrdinalEncoder(encoded_missing_value=-1,
handle_unknown='use_encoded_value',
unknown_value=-1),
['pclass', 'sex', 'embarked',
'random_cat']),
('num', SimpleImputer(),
['age', 'sibsp', 'parch',
'fare', 'random_num'])],
verbose_feature_names_out=False)),
('classifier', RandomForestClassifier(random_state=42))])</pre></div></div></div><div class="sk-serial"><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-156" type="checkbox" ><label for="sk-estimator-id-156" class="sk-toggleable__label sk-toggleable__label-arrow">preprocess: ColumnTransformer</label><div class="sk-toggleable__content"><pre>ColumnTransformer(transformers=[('cat',
OrdinalEncoder(encoded_missing_value=-1,
handle_unknown='use_encoded_value',
unknown_value=-1),
['pclass', 'sex', 'embarked', 'random_cat']),
('num', SimpleImputer(),
['age', 'sibsp', 'parch', 'fare',
'random_num'])],
verbose_feature_names_out=False)</pre></div></div></div><div class="sk-parallel"><div class="sk-parallel-item"><div class="sk-item"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-157" type="checkbox" ><label for="sk-estimator-id-157" class="sk-toggleable__label sk-toggleable__label-arrow">cat</label><div class="sk-toggleable__content"><pre>['pclass', 'sex', 'embarked', 'random_cat']</pre></div></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-158" type="checkbox" ><label for="sk-estimator-id-158" class="sk-toggleable__label sk-toggleable__label-arrow">OrdinalEncoder</label><div class="sk-toggleable__content"><pre>OrdinalEncoder(encoded_missing_value=-1, handle_unknown='use_encoded_value',
unknown_value=-1)</pre></div></div></div></div></div></div><div class="sk-parallel-item"><div class="sk-item"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-159" type="checkbox" ><label for="sk-estimator-id-159" class="sk-toggleable__label sk-toggleable__label-arrow">num</label><div class="sk-toggleable__content"><pre>['age', 'sibsp', 'parch', 'fare', 'random_num']</pre></div></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-160" type="checkbox" ><label for="sk-estimator-id-160" class="sk-toggleable__label sk-toggleable__label-arrow">SimpleImputer</label><div class="sk-toggleable__content"><pre>SimpleImputer()</pre></div></div></div></div></div></div></div></div><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-161" type="checkbox" ><label for="sk-estimator-id-161" class="sk-toggleable__label sk-toggleable__label-arrow">RandomForestClassifier</label><div class="sk-toggleable__content"><pre>RandomForestClassifier(random_state=42)</pre></div></div></div></div></div></div></div>
</div>
<br />
<br /></section>
<section id="accuracy-of-the-model">
<h2>Accuracy of the Model<a class="headerlink" href="#accuracy-of-the-model" title="Permalink to this heading">¶</a></h2>
<p>Prior to inspecting the feature importances, it is important to check that
the model predictive performance is high enough. Indeed there would be little
interest of inspecting the important features of a non-predictive model.</p>
<p>Here one can observe that the train accuracy is very high (the forest model
has enough capacity to completely memorize the training set) but it can still
generalize well enough to the test set thanks to the built-in bagging of
random forests.</p>
<p>It might be possible to trade some accuracy on the training set for a
slightly better accuracy on the test set by limiting the capacity of the
trees (for instance by setting <code class="docutils literal notranslate"><span class="pre">min_samples_leaf=5</span></code> or
<code class="docutils literal notranslate"><span class="pre">min_samples_leaf=10</span></code>) so as to limit overfitting while not introducing too
much underfitting.</p>
<p>However let’s keep our high capacity random forest model for now so as to
illustrate some pitfalls with feature importance on variables with many
unique values.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"RF train accuracy: </span><span class="si">{</span><span class="n">rf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span><span class="w"> </span><span class="n">y_train</span><span class="p">)</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"RF test accuracy: </span><span class="si">{</span><span class="n">rf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="w"> </span><span class="n">y_test</span><span class="p">)</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>RF train accuracy: 1.000
RF test accuracy: 0.814
</pre></div>
</div>
</section>
<section id="tree-s-feature-importance-from-mean-decrease-in-impurity-mdi">
<h2>Tree’s Feature Importance from Mean Decrease in Impurity (MDI)<a class="headerlink" href="#tree-s-feature-importance-from-mean-decrease-in-impurity-mdi" title="Permalink to this heading">¶</a></h2>
<p>The impurity-based feature importance ranks the numerical features to be the
most important features. As a result, the non-predictive <code class="docutils literal notranslate"><span class="pre">random_num</span></code>
variable is ranked as one of the most important features!</p>
<p>This problem stems from two limitations of impurity-based feature
importances:</p>
<ul class="simple">
<li><p>impurity-based importances are biased towards high cardinality features;</p></li>
<li><p>impurity-based importances are computed on training set statistics and
therefore do not reflect the ability of feature to be useful to make
predictions that generalize to the test set (when the model has enough
capacity).</p></li>
</ul>
<p>The bias towards high cardinality features explains why the <code class="docutils literal notranslate"><span class="pre">random_num</span></code> has
a really large importance in comparison with <code class="docutils literal notranslate"><span class="pre">random_cat</span></code> while we would
expect both random features to have a null importance.</p>
<p>The fact that we use training set statistics explains why both the
<code class="docutils literal notranslate"><span class="pre">random_num</span></code> and <code class="docutils literal notranslate"><span class="pre">random_cat</span></code> features have a non-null importance.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="n">feature_names</span> <span class="o">=</span> <span class="n">rf</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">get_feature_names_out</span><span class="p">()</span>
<span class="n">mdi_importances</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.html#pandas.Series" title="pandas.Series" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">Series</span></a><span class="p">(</span>
<span class="n">rf</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">feature_importances_</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="n">feature_names</span>
<span class="p">)</span><span class="o">.</span><span class="n">sort_values</span><span class="p">(</span><span class="n">ascending</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ax</span> <span class="o">=</span> <span class="n">mdi_importances</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">barh</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Random Forest Feature Importances (MDI)"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">figure</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_permutation_importance_001.png" srcset="../../_images/sphx_glr_plot_permutation_importance_001.png" alt="Random Forest Feature Importances (MDI)" class = "sphx-glr-single-img"/><p>As an alternative, the permutation importances of <code class="docutils literal notranslate"><span class="pre">rf</span></code> are computed on a
held out test set. This shows that the low cardinality categorical feature,
<code class="docutils literal notranslate"><span class="pre">sex</span></code> and <code class="docutils literal notranslate"><span class="pre">pclass</span></code> are the most important feature. Indeed, permuting the
values of these features will lead to most decrease in accuracy score of the
model on the test set.</p>
<p>Also note that both random features have very low importances (close to 0) as
expected.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.inspection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.inspection.permutation_importance.html#sklearn.inspection.permutation_importance" title="sklearn.inspection.permutation_importance" class="sphx-glr-backref-module-sklearn-inspection sphx-glr-backref-type-py-function"><span class="n">permutation_importance</span></a>
<span class="n">result</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.inspection.permutation_importance.html#sklearn.inspection.permutation_importance" title="sklearn.inspection.permutation_importance" class="sphx-glr-backref-module-sklearn-inspection sphx-glr-backref-type-py-function"><span class="n">permutation_importance</span></a><span class="p">(</span>
<span class="n">rf</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">,</span> <span class="n">n_repeats</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">2</span>
<span class="p">)</span>
<span class="n">sorted_importances_idx</span> <span class="o">=</span> <span class="n">result</span><span class="o">.</span><span class="n">importances_mean</span><span class="o">.</span><span class="n">argsort</span><span class="p">()</span>
<span class="n">importances</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="pandas.DataFrame" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span></a><span class="p">(</span>
<span class="n">result</span><span class="o">.</span><span class="n">importances</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
<span class="n">columns</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">columns</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">],</span>
<span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">importances</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">box</span><span class="p">(</span><span class="n">vert</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">whis</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Permutation Importances (test set)"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"k"</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</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="s2">"Decrease in accuracy score"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">figure</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_permutation_importance_002.png" srcset="../../_images/sphx_glr_plot_permutation_importance_002.png" alt="Permutation Importances (test set)" class = "sphx-glr-single-img"/><p>It is also possible to compute the permutation importances on the training
set. This reveals that <code class="docutils literal notranslate"><span class="pre">random_num</span></code> and <code class="docutils literal notranslate"><span class="pre">random_cat</span></code> get a significantly
higher importance ranking than when computed on the test set. The difference
between those two plots is a confirmation that the RF model has enough
capacity to use that random numerical and categorical features to overfit.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">result</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.inspection.permutation_importance.html#sklearn.inspection.permutation_importance" title="sklearn.inspection.permutation_importance" class="sphx-glr-backref-module-sklearn-inspection sphx-glr-backref-type-py-function"><span class="n">permutation_importance</span></a><span class="p">(</span>
<span class="n">rf</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="n">n_repeats</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">2</span>
<span class="p">)</span>
<span class="n">sorted_importances_idx</span> <span class="o">=</span> <span class="n">result</span><span class="o">.</span><span class="n">importances_mean</span><span class="o">.</span><span class="n">argsort</span><span class="p">()</span>
<span class="n">importances</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="pandas.DataFrame" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span></a><span class="p">(</span>
<span class="n">result</span><span class="o">.</span><span class="n">importances</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
<span class="n">columns</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">columns</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">],</span>
<span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">importances</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">box</span><span class="p">(</span><span class="n">vert</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">whis</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Permutation Importances (train set)"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"k"</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</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="s2">"Decrease in accuracy score"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">figure</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_permutation_importance_003.png" srcset="../../_images/sphx_glr_plot_permutation_importance_003.png" alt="Permutation Importances (train set)" class = "sphx-glr-single-img"/><p>We can further retry the experiment by limiting the capacity of the trees
to overfit by setting <code class="docutils literal notranslate"><span class="pre">min_samples_leaf</span></code> at 20 data points.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">rf</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">classifier__min_samples_leaf</span><span class="o">=</span><span class="mi">20</span><span class="p">)</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>
</pre></div>
</div>
<div class="output_subarea output_html rendered_html output_result">
<style>#sk-container-id-37 {color: black;background-color: white;}#sk-container-id-37 pre{padding: 0;}#sk-container-id-37 div.sk-toggleable {background-color: white;}#sk-container-id-37 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-37 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-37 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-37 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-37 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-37 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-37 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-37 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-37 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-37 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-37 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-37 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-37 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-37 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-37 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-37 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-37 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-37 div.sk-item {position: relative;z-index: 1;}#sk-container-id-37 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-37 div.sk-item::before, #sk-container-id-37 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-37 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-37 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-37 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-37 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-37 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-37 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-37 div.sk-label-container {text-align: center;}#sk-container-id-37 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-37 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-37" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>Pipeline(steps=[('preprocess',
ColumnTransformer(transformers=[('cat',
OrdinalEncoder(encoded_missing_value=-1,
handle_unknown='use_encoded_value',
unknown_value=-1),
['pclass', 'sex', 'embarked',
'random_cat']),
('num', SimpleImputer(),
['age', 'sibsp', 'parch',
'fare', 'random_num'])],
verbose_feature_names_out=False)),
('classifier',
RandomForestClassifier(min_samples_leaf=20, random_state=42))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-162" type="checkbox" ><label for="sk-estimator-id-162" class="sk-toggleable__label sk-toggleable__label-arrow">Pipeline</label><div class="sk-toggleable__content"><pre>Pipeline(steps=[('preprocess',
ColumnTransformer(transformers=[('cat',
OrdinalEncoder(encoded_missing_value=-1,
handle_unknown='use_encoded_value',
unknown_value=-1),
['pclass', 'sex', 'embarked',
'random_cat']),
('num', SimpleImputer(),
['age', 'sibsp', 'parch',
'fare', 'random_num'])],
verbose_feature_names_out=False)),
('classifier',
RandomForestClassifier(min_samples_leaf=20, random_state=42))])</pre></div></div></div><div class="sk-serial"><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-163" type="checkbox" ><label for="sk-estimator-id-163" class="sk-toggleable__label sk-toggleable__label-arrow">preprocess: ColumnTransformer</label><div class="sk-toggleable__content"><pre>ColumnTransformer(transformers=[('cat',
OrdinalEncoder(encoded_missing_value=-1,
handle_unknown='use_encoded_value',
unknown_value=-1),
['pclass', 'sex', 'embarked', 'random_cat']),
('num', SimpleImputer(),
['age', 'sibsp', 'parch', 'fare',
'random_num'])],
verbose_feature_names_out=False)</pre></div></div></div><div class="sk-parallel"><div class="sk-parallel-item"><div class="sk-item"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-164" type="checkbox" ><label for="sk-estimator-id-164" class="sk-toggleable__label sk-toggleable__label-arrow">cat</label><div class="sk-toggleable__content"><pre>['pclass', 'sex', 'embarked', 'random_cat']</pre></div></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-165" type="checkbox" ><label for="sk-estimator-id-165" class="sk-toggleable__label sk-toggleable__label-arrow">OrdinalEncoder</label><div class="sk-toggleable__content"><pre>OrdinalEncoder(encoded_missing_value=-1, handle_unknown='use_encoded_value',
unknown_value=-1)</pre></div></div></div></div></div></div><div class="sk-parallel-item"><div class="sk-item"><div class="sk-label-container"><div class="sk-label sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-166" type="checkbox" ><label for="sk-estimator-id-166" class="sk-toggleable__label sk-toggleable__label-arrow">num</label><div class="sk-toggleable__content"><pre>['age', 'sibsp', 'parch', 'fare', 'random_num']</pre></div></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-167" type="checkbox" ><label for="sk-estimator-id-167" class="sk-toggleable__label sk-toggleable__label-arrow">SimpleImputer</label><div class="sk-toggleable__content"><pre>SimpleImputer()</pre></div></div></div></div></div></div></div></div><div class="sk-item"><div class="sk-estimator sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-168" type="checkbox" ><label for="sk-estimator-id-168" class="sk-toggleable__label sk-toggleable__label-arrow">RandomForestClassifier</label><div class="sk-toggleable__content"><pre>RandomForestClassifier(min_samples_leaf=20, random_state=42)</pre></div></div></div></div></div></div></div>
</div>
<br />
<br /><p>Observing the accuracy score on the training and testing set, we observe that
the two metrics are very similar now. Therefore, our model is not overfitting
anymore. We can then check the permutation importances with this new model.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"RF train accuracy: </span><span class="si">{</span><span class="n">rf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span><span class="w"> </span><span class="n">y_train</span><span class="p">)</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"RF test accuracy: </span><span class="si">{</span><span class="n">rf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="w"> </span><span class="n">y_test</span><span class="p">)</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>RF train accuracy: 0.810
RF test accuracy: 0.832
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">train_result</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.inspection.permutation_importance.html#sklearn.inspection.permutation_importance" title="sklearn.inspection.permutation_importance" class="sphx-glr-backref-module-sklearn-inspection sphx-glr-backref-type-py-function"><span class="n">permutation_importance</span></a><span class="p">(</span>
<span class="n">rf</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="n">n_repeats</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">2</span>
<span class="p">)</span>
<span class="n">test_results</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.inspection.permutation_importance.html#sklearn.inspection.permutation_importance" title="sklearn.inspection.permutation_importance" class="sphx-glr-backref-module-sklearn-inspection sphx-glr-backref-type-py-function"><span class="n">permutation_importance</span></a><span class="p">(</span>
<span class="n">rf</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">,</span> <span class="n">n_repeats</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">2</span>
<span class="p">)</span>
<span class="n">sorted_importances_idx</span> <span class="o">=</span> <span class="n">train_result</span><span class="o">.</span><span class="n">importances_mean</span><span class="o">.</span><span class="n">argsort</span><span class="p">()</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">train_importances</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="pandas.DataFrame" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span></a><span class="p">(</span>
<span class="n">train_result</span><span class="o">.</span><span class="n">importances</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
<span class="n">columns</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">columns</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">],</span>
<span class="p">)</span>
<span class="n">test_importances</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="pandas.DataFrame" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span></a><span class="p">(</span>
<span class="n">test_results</span><span class="o">.</span><span class="n">importances</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
<span class="n">columns</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">columns</span><span class="p">[</span><span class="n">sorted_importances_idx</span><span class="p">],</span>
<span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">importances</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">([</span><span class="s2">"train"</span><span class="p">,</span> <span class="s2">"test"</span><span class="p">],</span> <span class="p">[</span><span class="n">train_importances</span><span class="p">,</span> <span class="n">test_importances</span><span class="p">]):</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">importances</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">box</span><span class="p">(</span><span class="n">vert</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">whis</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Permutation Importances (</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s2"> set)"</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="s2">"Decrease in accuracy score"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"k"</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">figure</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
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<li><img src="../../_images/sphx_glr_plot_permutation_importance_005.png" srcset="../../_images/sphx_glr_plot_permutation_importance_005.png" alt="Permutation Importances (test set)" class = "sphx-glr-multi-img"/></li>
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<p>Now, we can observe that on both sets, the <code class="docutils literal notranslate"><span class="pre">random_num</span></code> and <code class="docutils literal notranslate"><span class="pre">random_cat</span></code>
features have a lower importance compared to the overfitting random forest.
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