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<li><a class="reference internal" href="#">Gradient Boosting regularization</a></li>
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<section class="sphx-glr-example-title" id="gradient-boosting-regularization">
<span id="sphx-glr-auto-examples-ensemble-plot-gradient-boosting-regularization-py"></span><h1>Gradient Boosting regularization<a class="headerlink" href="#gradient-boosting-regularization" title="Link to this heading">¶</a></h1>
<p>Illustration of the effect of different regularization strategies
for Gradient Boosting. The example is taken from Hastie et al 2009 <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
<p>The loss function used is binomial deviance. Regularization via
shrinkage (<code class="docutils literal notranslate"><span class="pre">learning_rate</span> <span class="pre"><</span> <span class="pre">1.0</span></code>) improves performance considerably.
In combination with shrinkage, stochastic gradient boosting
(<code class="docutils literal notranslate"><span class="pre">subsample</span> <span class="pre"><</span> <span class="pre">1.0</span></code>) can produce more accurate models by reducing the
variance via bagging.
Subsampling without shrinkage usually does poorly.
Another strategy to reduce the variance is by subsampling the features
analogous to the random splits in Random Forests
(via the <code class="docutils literal notranslate"><span class="pre">max_features</span></code> parameter).</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id2" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p>T. Hastie, R. Tibshirani and J. Friedman, “Elements of Statistical
Learning Ed. 2”, Springer, 2009.</p>
</aside>
</aside>
<img src="../../_images/sphx_glr_plot_gradient_boosting_regularization_001.png" srcset="../../_images/sphx_glr_plot_gradient_boosting_regularization_001.png" alt="plot gradient boosting regularization" class = "sphx-glr-single-img"/><div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Peter Prettenhofer <[email protected]></span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 clause</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">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">ensemble</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.log_loss.html#sklearn.metrics.log_loss" title="sklearn.metrics.log_loss" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">log_loss</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.make_hastie_10_2.html#sklearn.datasets.make_hastie_10_2" title="sklearn.datasets.make_hastie_10_2" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">datasets</span><span class="o">.</span><span class="n">make_hastie_10_2</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">4000</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="c1"># map labels from {-1, 1} to {0, 1}</span>
<span class="n">labels</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.unique.html#numpy.unique" title="numpy.unique" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">unique</span></a><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">return_inverse</span><span class="o">=</span><span class="kc">True</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">test_size</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">original_params</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"n_estimators"</span><span class="p">:</span> <span class="mi">400</span><span class="p">,</span>
<span class="s2">"max_leaf_nodes"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
<span class="s2">"max_depth"</span><span class="p">:</span> <span class="kc">None</span><span class="p">,</span>
<span class="s2">"random_state"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
<span class="s2">"min_samples_split"</span><span class="p">:</span> <span class="mi">5</span><span class="p">,</span>
<span class="p">}</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
<span class="k">for</span> <span class="n">label</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="n">setting</span> <span class="ow">in</span> <span class="p">[</span>
<span class="p">(</span><span class="s2">"No shrinkage"</span><span class="p">,</span> <span class="s2">"orange"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"learning_rate"</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span> <span class="s2">"subsample"</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">}),</span>
<span class="p">(</span><span class="s2">"learning_rate=0.2"</span><span class="p">,</span> <span class="s2">"turquoise"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"learning_rate"</span><span class="p">:</span> <span class="mf">0.2</span><span class="p">,</span> <span class="s2">"subsample"</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">}),</span>
<span class="p">(</span><span class="s2">"subsample=0.5"</span><span class="p">,</span> <span class="s2">"blue"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"learning_rate"</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span> <span class="s2">"subsample"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">}),</span>
<span class="p">(</span>
<span class="s2">"learning_rate=0.2, subsample=0.5"</span><span class="p">,</span>
<span class="s2">"gray"</span><span class="p">,</span>
<span class="p">{</span><span class="s2">"learning_rate"</span><span class="p">:</span> <span class="mf">0.2</span><span class="p">,</span> <span class="s2">"subsample"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">},</span>
<span class="p">),</span>
<span class="p">(</span>
<span class="s2">"learning_rate=0.2, max_features=2"</span><span class="p">,</span>
<span class="s2">"magenta"</span><span class="p">,</span>
<span class="p">{</span><span class="s2">"learning_rate"</span><span class="p">:</span> <span class="mf">0.2</span><span class="p">,</span> <span class="s2">"max_features"</span><span class="p">:</span> <span class="mi">2</span><span class="p">},</span>
<span class="p">),</span>
<span class="p">]:</span>
<span class="n">params</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">original_params</span><span class="p">)</span>
<span class="n">params</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">setting</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ensemble</span><span class="o">.</span><span class="n">GradientBoostingClassifier</span></a><span class="p">(</span><span class="o">**</span><span class="n">params</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="c1"># compute test set deviance</span>
<span class="n">test_deviance</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">((</span><span class="n">params</span><span class="p">[</span><span class="s2">"n_estimators"</span><span class="p">],),</span> <span class="n">dtype</span><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">np</span><span class="o">.</span><span class="n">float64</span></a><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">y_proba</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">staged_predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)):</span>
<span class="n">test_deviance</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <a href="../../modules/generated/sklearn.metrics.log_loss.html#sklearn.metrics.log_loss" title="sklearn.metrics.log_loss" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">log_loss</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_proba</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">])</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span>
<span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">test_deviance</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="o">+</span> <span class="mi">1</span><span class="p">)[::</span><span class="mi">5</span><span class="p">],</span>
<span class="n">test_deviance</span><span class="p">[::</span><span class="mi">5</span><span class="p">],</span>
<span class="s2">"-"</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"Boosting Iterations"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"Test Set Deviance"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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