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<li class="toctree-l1 current active has-children"><a class="reference internal" href="../supervised_learning.html">1. Supervised learning</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="linear_model.html">1.1. Linear Models</a></li>
<li class="toctree-l2"><a class="reference internal" href="lda_qda.html">1.2. Linear and Quadratic Discriminant Analysis</a></li>
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<li class="toctree-l2"><a class="reference internal" href="tree.html">1.10. Decision Trees</a></li>
<li class="toctree-l2 current active"><a class="current reference internal" href="#">1.11. Ensembles: Gradient boosting, random forests, bagging, voting, stacking</a></li>
<li class="toctree-l2"><a class="reference internal" href="multiclass.html">1.12. Multiclass and multioutput algorithms</a></li>
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<li class="toctree-l2"><a class="reference internal" href="isotonic.html">1.15. Isotonic regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="calibration.html">1.16. Probability calibration</a></li>
<li class="toctree-l2"><a class="reference internal" href="neural_networks_supervised.html">1.17. Neural network models (supervised)</a></li>
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<li class="toctree-l2"><a class="reference internal" href="mixture.html">2.1. Gaussian mixture models</a></li>
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<li class="toctree-l2"><a class="reference internal" href="neural_networks_unsupervised.html">2.9. Neural network models (unsupervised)</a></li>
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<li class="toctree-l2"><a class="reference internal" href="cross_validation.html">3.1. Cross-validation: evaluating estimator performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="grid_search.html">3.2. Tuning the hyper-parameters of an estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="classification_threshold.html">3.3. Tuning the decision threshold for class prediction</a></li>
<li class="toctree-l2"><a class="reference internal" href="model_evaluation.html">3.4. Metrics and scoring: quantifying the quality of predictions</a></li>
<li class="toctree-l2"><a class="reference internal" href="learning_curve.html">3.5. Validation curves: plotting scores to evaluate models</a></li>
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<li class="toctree-l2"><a class="reference internal" href="partial_dependence.html">4.1. Partial Dependence and Individual Conditional Expectation plots</a></li>
<li class="toctree-l2"><a class="reference internal" href="permutation_importance.html">4.2. Permutation feature importance</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../visualizations.html">5. Visualizations</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compose.html">6.1. Pipelines and composite estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="feature_extraction.html">6.2. Feature extraction</a></li>
<li class="toctree-l2"><a class="reference internal" href="preprocessing.html">6.3. Preprocessing data</a></li>
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<li class="toctree-l2"><a class="reference internal" href="unsupervised_reduction.html">6.5. Unsupervised dimensionality reduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="random_projection.html">6.6. Random Projection</a></li>
<li class="toctree-l2"><a class="reference internal" href="kernel_approximation.html">6.7. Kernel Approximation</a></li>
<li class="toctree-l2"><a class="reference internal" href="metrics.html">6.8. Pairwise metrics, Affinities and Kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="preprocessing_targets.html">6.9. Transforming the prediction target (<code class="docutils literal notranslate"><span class="pre">y</span></code>)</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../datasets.html">7. Dataset loading utilities</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../datasets/toy_dataset.html">7.1. Toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/real_world.html">7.2. Real world datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/sample_generators.html">7.3. Generated datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/loading_other_datasets.html">7.4. Loading other datasets</a></li>
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</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../computing.html">8. Computing with scikit-learn</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../computing/scaling_strategies.html">8.1. Strategies to scale computationally: bigger data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/computational_performance.html">8.2. Computational Performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/parallelism.html">8.3. Parallelism, resource management, and configuration</a></li>
</ul>
</details></li>
<li class="toctree-l1"><a class="reference internal" href="../model_persistence.html">9. Model persistence</a></li>
<li class="toctree-l1"><a class="reference internal" href="../common_pitfalls.html">10. Common pitfalls and recommended practices</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../dispatching.html">11. Dispatching</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="array_api.html">11.1. Array API support (experimental)</a></li>
</ul>
</details></li>
<li class="toctree-l1"><a class="reference internal" href="../machine_learning_map.html">12. Choosing the right estimator</a></li>
<li class="toctree-l1"><a class="reference internal" href="../presentations.html">13. External Resources, Videos and Talks</a></li>
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<section id="ensembles-gradient-boosting-random-forests-bagging-voting-stacking">
<span id="ensemble"></span><h1><span class="section-number">1.11. </span>Ensembles: Gradient boosting, random forests, bagging, voting, stacking<a class="headerlink" href="#ensembles-gradient-boosting-random-forests-bagging-voting-stacking" title="Link to this heading">#</a></h1>
<p><strong>Ensemble methods</strong> combine the predictions of several
base estimators built with a given learning algorithm in order to improve
generalizability / robustness over a single estimator.</p>
<p>Two very famous examples of ensemble methods are <a class="reference internal" href="#gradient-boosting"><span class="std std-ref">gradient-boosted trees</span></a> and <a class="reference internal" href="#forest"><span class="std std-ref">random forests</span></a>.</p>
<p>More generally, ensemble models can be applied to any base learner beyond
trees, in averaging methods such as <a class="reference internal" href="#bagging"><span class="std std-ref">Bagging methods</span></a>,
<a class="reference internal" href="#stacking"><span class="std std-ref">model stacking</span></a>, or <a class="reference internal" href="#voting-classifier"><span class="std std-ref">Voting</span></a>, or in
boosting, as <a class="reference internal" href="#adaboost"><span class="std std-ref">AdaBoost</span></a>.</p>
<section id="gradient-boosted-trees">
<span id="gradient-boosting"></span><h2><span class="section-number">1.11.1. </span>Gradient-boosted trees<a class="headerlink" href="#gradient-boosted-trees" title="Link to this heading">#</a></h2>
<p><a class="reference external" href="https://en.wikipedia.org/wiki/Gradient_boosting">Gradient Tree Boosting</a>
or Gradient Boosted Decision Trees (GBDT) is a generalization
of boosting to arbitrary differentiable loss functions, see the seminal work of
<a class="reference internal" href="#friedman2001" id="id1"><span>[Friedman2001]</span></a>. GBDT is an excellent model for both regression and
classification, in particular for tabular data.</p>
<aside class="topic">
<p class="topic-title"><a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingClassifier</span></code></a> vs <a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingClassifier.html#sklearn.ensemble.HistGradientBoostingClassifier" title="sklearn.ensemble.HistGradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingClassifier</span></code></a></p>
<p>Scikit-learn provides two implementations of gradient-boosted trees:
<a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingClassifier.html#sklearn.ensemble.HistGradientBoostingClassifier" title="sklearn.ensemble.HistGradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingClassifier</span></code></a> vs
<a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingClassifier</span></code></a> for classification, and the
corresponding classes for regression. The former can be <strong>orders of
magnitude faster</strong> than the latter when the number of samples is
larger than tens of thousands of samples.</p>
<p>Missing values and categorical data are natively supported by the
Hist… version, removing the need for additional preprocessing such as
imputation.</p>
<p><a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingClassifier</span></code></a> and
<a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="sklearn.ensemble.GradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingRegressor</span></code></a>, might be preferred for small sample
sizes since binning may lead to split points that are too approximate
in this setting.</p>
</aside>
<section id="histogram-based-gradient-boosting">
<span id="id2"></span><h3><span class="section-number">1.11.1.1. </span>Histogram-Based Gradient Boosting<a class="headerlink" href="#histogram-based-gradient-boosting" title="Link to this heading">#</a></h3>
<p>Scikit-learn 0.21 introduced two new implementations of
gradient boosted trees, namely <a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingClassifier.html#sklearn.ensemble.HistGradientBoostingClassifier" title="sklearn.ensemble.HistGradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingClassifier</span></code></a>
and <a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingRegressor.html#sklearn.ensemble.HistGradientBoostingRegressor" title="sklearn.ensemble.HistGradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingRegressor</span></code></a>, inspired by
<a class="reference external" href="https://github.com/Microsoft/LightGBM">LightGBM</a> (See <a class="reference internal" href="#lightgbm" id="id3"><span>[LightGBM]</span></a>).</p>
<p>These histogram-based estimators can be <strong>orders of magnitude faster</strong>
than <a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingClassifier</span></code></a> and
<a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="sklearn.ensemble.GradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingRegressor</span></code></a> when the number of samples is larger
than tens of thousands of samples.</p>
<p>They also have built-in support for missing values, which avoids the need
for an imputer.</p>
<p>These fast estimators first bin the input samples <code class="docutils literal notranslate"><span class="pre">X</span></code> into
integer-valued bins (typically 256 bins) which tremendously reduces the
number of splitting points to consider, and allows the algorithm to
leverage integer-based data structures (histograms) instead of relying on
sorted continuous values when building the trees. The API of these
estimators is slightly different, and some of the features from
<a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingClassifier</span></code></a> and <a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="sklearn.ensemble.GradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingRegressor</span></code></a>
are not yet supported, for instance some loss functions.</p>
<p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/inspection/plot_partial_dependence.html#sphx-glr-auto-examples-inspection-plot-partial-dependence-py"><span class="std std-ref">Partial Dependence and Individual Conditional Expectation Plots</span></a></p></li>
<li><p><a class="reference internal" href="../auto_examples/ensemble/plot_forest_hist_grad_boosting_comparison.html#sphx-glr-auto-examples-ensemble-plot-forest-hist-grad-boosting-comparison-py"><span class="std std-ref">Comparing Random Forests and Histogram Gradient Boosting models</span></a></p></li>
</ul>
<section id="usage">
<h4><span class="section-number">1.11.1.1.1. </span>Usage<a class="headerlink" href="#usage" title="Link to this heading">#</a></h4>
<p>Most of the parameters are unchanged from
<a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingClassifier</span></code></a> and <a class="reference internal" href="generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor" title="sklearn.ensemble.GradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">GradientBoostingRegressor</span></code></a>.
One exception is the <code class="docutils literal notranslate"><span class="pre">max_iter</span></code> parameter that replaces <code class="docutils literal notranslate"><span class="pre">n_estimators</span></code>, and
controls the number of iterations of the boosting process:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">HistGradientBoostingClassifier</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_hastie_10_2</span>
<span class="gp">>>> </span><span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_hastie_10_2</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="gp">>>> </span><span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="mi">2000</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="mi">2000</span><span class="p">:]</span>
<span class="gp">>>> </span><span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">y</span><span class="p">[:</span><span class="mi">2000</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="mi">2000</span><span class="p">:]</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">HistGradientBoostingClassifier</span><span class="p">(</span><span class="n">max_iter</span><span class="o">=</span><span class="mi">100</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>
<span class="gp">>>> </span><span class="n">clf</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="n">y_test</span><span class="p">)</span>
<span class="go">0.8965</span>
</pre></div>
</div>
<p>Available losses for <strong>regression</strong> are:</p>
<ul class="simple">
<li><p>‘squared_error’, which is the default loss;</p></li>
<li><p>‘absolute_error’, which is less sensitive to outliers than the squared error;</p></li>
<li><p>‘gamma’, which is well suited to model strictly positive outcomes;</p></li>
<li><p>‘poisson’, which is well suited to model counts and frequencies;</p></li>
<li><p>‘quantile’, which allows for estimating a conditional quantile that can later
be used to obtain prediction intervals.</p></li>
</ul>
<p>For <strong>classification</strong>, ‘log_loss’ is the only option. For binary classification
it uses the binary log loss, also known as binomial deviance or binary
cross-entropy. For <code class="docutils literal notranslate"><span class="pre">n_classes</span> <span class="pre">>=</span> <span class="pre">3</span></code>, it uses the multi-class log loss function,
with multinomial deviance and categorical cross-entropy as alternative names.
The appropriate loss version is selected based on <a class="reference internal" href="../glossary.html#term-y"><span class="xref std std-term">y</span></a> passed to
<a class="reference internal" href="../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>.</p>
<p>The size of the trees can be controlled through the <code class="docutils literal notranslate"><span class="pre">max_leaf_nodes</span></code>,
<code class="docutils literal notranslate"><span class="pre">max_depth</span></code>, and <code class="docutils literal notranslate"><span class="pre">min_samples_leaf</span></code> parameters.</p>
<p>The number of bins used to bin the data is controlled with the <code class="docutils literal notranslate"><span class="pre">max_bins</span></code>
parameter. Using less bins acts as a form of regularization. It is generally
recommended to use as many bins as possible (255), which is the default.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">l2_regularization</span></code> parameter acts as a regularizer for the loss function,
and corresponds to <span class="math notranslate nohighlight">\(\lambda\)</span> in the following expression (see equation (2)
in <a class="reference internal" href="#xgboost" id="id4"><span>[XGBoost]</span></a>):</p>
<div class="math notranslate nohighlight">
\[\mathcal{L}(\phi) = \sum_i l(\hat{y}_i, y_i) + \frac12 \sum_k \lambda ||w_k||^2\]</div>
<details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3" id="details-on-l2-regularization">
<summary class="sd-summary-title sd-card-header">
<span class="sd-summary-text">Details on l2 regularization<a class="headerlink" href="#details-on-l2-regularization" title="Link to this dropdown">#</a></span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
<p class="sd-card-text">It is important to notice that the loss term <span class="math notranslate nohighlight">\(l(\hat{y}_i, y_i)\)</span> describes
only half of the actual loss function except for the pinball loss and absolute
error.</p>
<p class="sd-card-text">The index <span class="math notranslate nohighlight">\(k\)</span> refers to the k-th tree in the ensemble of trees. In the
case of regression and binary classification, gradient boosting models grow one
tree per iteration, then <span class="math notranslate nohighlight">\(k\)</span> runs up to <code class="docutils literal notranslate"><span class="pre">max_iter</span></code>. In the case of
multiclass classification problems, the maximal value of the index <span class="math notranslate nohighlight">\(k\)</span> is
<code class="docutils literal notranslate"><span class="pre">n_classes</span></code> <span class="math notranslate nohighlight">\(\times\)</span> <code class="docutils literal notranslate"><span class="pre">max_iter</span></code>.</p>
<p class="sd-card-text">If <span class="math notranslate nohighlight">\(T_k\)</span> denotes the number of leaves in the k-th tree, then <span class="math notranslate nohighlight">\(w_k\)</span>
is a vector of length <span class="math notranslate nohighlight">\(T_k\)</span>, which contains the leaf values of the form <code class="docutils literal notranslate"><span class="pre">w</span>
<span class="pre">=</span> <span class="pre">-sum_gradient</span> <span class="pre">/</span> <span class="pre">(sum_hessian</span> <span class="pre">+</span> <span class="pre">l2_regularization)</span></code> (see equation (5) in
<a class="reference internal" href="#xgboost" id="id5"><span>[XGBoost]</span></a>).</p>
<p class="sd-card-text">The leaf values <span class="math notranslate nohighlight">\(w_k\)</span> are derived by dividing the sum of the gradients of
the loss function by the combined sum of hessians. Adding the regularization to
the denominator penalizes the leaves with small hessians (flat regions),
resulting in smaller updates. Those <span class="math notranslate nohighlight">\(w_k\)</span> values contribute then to the
model’s prediction for a given input that ends up in the corresponding leaf. The
final prediction is the sum of the base prediction and the contributions from
each tree. The result of that sum is then transformed by the inverse link
function depending on the choice of the loss function (see
<a class="reference internal" href="#gradient-boosting-formulation"><span class="std std-ref">Mathematical formulation</span></a>).</p>
<p class="sd-card-text">Notice that the original paper <a class="reference internal" href="#xgboost" id="id6"><span>[XGBoost]</span></a> introduces a term <span class="math notranslate nohighlight">\(\gamma\sum_k
T_k\)</span> that penalizes the number of leaves (making it a smooth version of
<code class="docutils literal notranslate"><span class="pre">max_leaf_nodes</span></code>) not presented here as it is not implemented in scikit-learn;
whereas <span class="math notranslate nohighlight">\(\lambda\)</span> penalizes the magnitude of the individual tree
predictions before being rescaled by the learning rate, see
<a class="reference internal" href="#gradient-boosting-shrinkage"><span class="std std-ref">Shrinkage via learning rate</span></a>.</p>
</div>
</details><p>Note that <strong>early-stopping is enabled by default if the number of samples is
larger than 10,000</strong>. The early-stopping behaviour is controlled via the
<code class="docutils literal notranslate"><span class="pre">early_stopping</span></code>, <code class="docutils literal notranslate"><span class="pre">scoring</span></code>, <code class="docutils literal notranslate"><span class="pre">validation_fraction</span></code>,
<code class="docutils literal notranslate"><span class="pre">n_iter_no_change</span></code>, and <code class="docutils literal notranslate"><span class="pre">tol</span></code> parameters. It is possible to early-stop
using an arbitrary <a class="reference internal" href="../glossary.html#term-scorer"><span class="xref std std-term">scorer</span></a>, or just the training or validation loss.
Note that for technical reasons, using a callable as a scorer is significantly slower
than using the loss. By default, early-stopping is performed if there are at least
10,000 samples in the training set, using the validation loss.</p>
</section>
<section id="missing-values-support">
<span id="nan-support-hgbt"></span><h4><span class="section-number">1.11.1.1.2. </span>Missing values support<a class="headerlink" href="#missing-values-support" title="Link to this heading">#</a></h4>
<p><a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingClassifier.html#sklearn.ensemble.HistGradientBoostingClassifier" title="sklearn.ensemble.HistGradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingClassifier</span></code></a> and
<a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingRegressor.html#sklearn.ensemble.HistGradientBoostingRegressor" title="sklearn.ensemble.HistGradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingRegressor</span></code></a> have built-in support for missing
values (NaNs).</p>
<p>During training, the tree grower learns at each split point whether samples
with missing values should go to the left or right child, based on the
potential gain. When predicting, samples with missing values are assigned to
the left or right child consequently:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">HistGradientBoostingClassifier</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</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="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">gbdt</span> <span class="o">=</span> <span class="n">HistGradientBoostingClassifier</span><span class="p">(</span><span class="n">min_samples_leaf</span><span class="o">=</span><span class="mi">1</span><span class="p">)</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="gp">>>> </span><span class="n">gbdt</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([0, 0, 1, 1])</span>
</pre></div>
</div>
<p>When the missingness pattern is predictive, the splits can be performed on
whether the feature value is missing or not:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</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="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">gbdt</span> <span class="o">=</span> <span class="n">HistGradientBoostingClassifier</span><span class="p">(</span><span class="n">min_samples_leaf</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">max_depth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">learning_rate</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">1</span><span class="p">)</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="gp">>>> </span><span class="n">gbdt</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([0, 1, 0, 0, 1])</span>
</pre></div>
</div>
<p>If no missing values were encountered for a given feature during training,
then samples with missing values are mapped to whichever child has the most
samples.</p>
<p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/ensemble/plot_hgbt_regression.html#sphx-glr-auto-examples-ensemble-plot-hgbt-regression-py"><span class="std std-ref">Features in Histogram Gradient Boosting Trees</span></a></p></li>
</ul>
</section>
<section id="sample-weight-support">
<span id="sw-hgbdt"></span><h4><span class="section-number">1.11.1.1.3. </span>Sample weight support<a class="headerlink" href="#sample-weight-support" title="Link to this heading">#</a></h4>
<p><a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingClassifier.html#sklearn.ensemble.HistGradientBoostingClassifier" title="sklearn.ensemble.HistGradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingClassifier</span></code></a> and
<a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingRegressor.html#sklearn.ensemble.HistGradientBoostingRegressor" title="sklearn.ensemble.HistGradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingRegressor</span></code></a> support sample weights during
<a class="reference internal" href="../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>.</p>
<p>The following toy example demonstrates that samples with a sample weight of zero are ignored:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="gp">>>> </span><span class="c1"># ignore the first 2 training samples by setting their weight to 0</span>
<span class="gp">>>> </span><span class="n">sample_weight</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">gb</span> <span class="o">=</span> <span class="n">HistGradientBoostingClassifier</span><span class="p">(</span><span class="n">min_samples_leaf</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">gb</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="n">sample_weight</span><span class="o">=</span><span class="n">sample_weight</span><span class="p">)</span>
<span class="go">HistGradientBoostingClassifier(...)</span>
<span class="gp">>>> </span><span class="n">gb</span><span class="o">.</span><span class="n">predict</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
<span class="go">array([1])</span>
<span class="gp">>>> </span><span class="n">gb</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="go">0.99...</span>
</pre></div>
</div>
<p>As you can see, the <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">0]</span></code> is comfortably classified as <code class="docutils literal notranslate"><span class="pre">1</span></code> since the first
two samples are ignored due to their sample weights.</p>
<p>Implementation detail: taking sample weights into account amounts to
multiplying the gradients (and the hessians) by the sample weights. Note that
the binning stage (specifically the quantiles computation) does not take the
weights into account.</p>
</section>
<section id="categorical-features-support">
<span id="categorical-support-gbdt"></span><h4><span class="section-number">1.11.1.1.4. </span>Categorical Features Support<a class="headerlink" href="#categorical-features-support" title="Link to this heading">#</a></h4>
<p><a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingClassifier.html#sklearn.ensemble.HistGradientBoostingClassifier" title="sklearn.ensemble.HistGradientBoostingClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingClassifier</span></code></a> and
<a class="reference internal" href="generated/sklearn.ensemble.HistGradientBoostingRegressor.html#sklearn.ensemble.HistGradientBoostingRegressor" title="sklearn.ensemble.HistGradientBoostingRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistGradientBoostingRegressor</span></code></a> have native support for categorical
features: they can consider splits on non-ordered, categorical data.</p>
<p>For datasets with categorical features, using the native categorical support
is often better than relying on one-hot encoding
(<a class="reference internal" href="generated/sklearn.preprocessing.OneHotEncoder.html#sklearn.preprocessing.OneHotEncoder" title="sklearn.preprocessing.OneHotEncoder"><code class="xref py py-class docutils literal notranslate"><span class="pre">OneHotEncoder</span></code></a>), because one-hot encoding
requires more tree depth to achieve equivalent splits. It is also usually
better to rely on the native categorical support rather than to treat
categorical features as continuous (ordinal), which happens for ordinal-encoded
categorical data, since categories are nominal quantities where order does not
matter.</p>
<p>To enable categorical support, a boolean mask can be passed to the
<code class="docutils literal notranslate"><span class="pre">categorical_features</span></code> parameter, indicating which feature is categorical. In
the following, the first feature will be treated as categorical and the
second feature as numerical:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">gbdt</span> <span class="o">=</span> <span class="n">HistGradientBoostingClassifier</span><span class="p">(</span><span class="n">categorical_features</span><span class="o">=</span><span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">])</span>
</pre></div>
</div>
<p>Equivalently, one can pass a list of integers indicating the indices of the
categorical features:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">gbdt</span> <span class="o">=</span> <span class="n">HistGradientBoostingClassifier</span><span class="p">(</span><span class="n">categorical_features</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
</pre></div>
</div>
<p>When the input is a DataFrame, it is also possible to pass a list of column
names:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">gbdt</span> <span class="o">=</span> <span class="n">HistGradientBoostingClassifier</span><span class="p">(</span><span class="n">categorical_features</span><span class="o">=</span><span class="p">[</span><span class="s2">"site"</span><span class="p">,</span> <span class="s2">"manufacturer"</span><span class="p">])</span>
</pre></div>
</div>
<p>Finally, when the input is a DataFrame we can use
<code class="docutils literal notranslate"><span class="pre">categorical_features="from_dtype"</span></code> in which case all columns with a categorical
<code class="docutils literal notranslate"><span class="pre">dtype</span></code> will be treated as categorical features.</p>
<p>The cardinality of each categorical feature must be less than the <code class="docutils literal notranslate"><span class="pre">max_bins</span></code>
parameter. For an example using histogram-based gradient boosting on categorical
features, see
<a class="reference internal" href="../auto_examples/ensemble/plot_gradient_boosting_categorical.html#sphx-glr-auto-examples-ensemble-plot-gradient-boosting-categorical-py"><span class="std std-ref">Categorical Feature Support in Gradient Boosting</span></a>.</p>
<p>If there are missing values during training, the missing values will be
treated as a proper category. If there are no missing values during training,
then at prediction time, missing values are mapped to the child node that has
the most samples (just like for continuous features). When predicting,
categories that were not seen during fit time will be treated as missing
values.</p>
<details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3" id="split-finding-with-categorical-features">
<summary class="sd-summary-title sd-card-header">
<span class="sd-summary-text">Split finding with categorical features<a class="headerlink" href="#split-finding-with-categorical-features" title="Link to this dropdown">#</a></span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
<p class="sd-card-text">The canonical way of considering categorical splits in a tree is to consider
all of the <span class="math notranslate nohighlight">\(2^{K - 1} - 1\)</span> partitions, where <span class="math notranslate nohighlight">\(K\)</span> is the number of
categories. This can quickly become prohibitive when <span class="math notranslate nohighlight">\(K\)</span> is large.
Fortunately, since gradient boosting trees are always regression trees (even
for classification problems), there exist a faster strategy that can yield
equivalent splits. First, the categories of a feature are sorted according to
the variance of the target, for each category <code class="docutils literal notranslate"><span class="pre">k</span></code>. Once the categories are
sorted, one can consider <em>continuous partitions</em>, i.e. treat the categories
as if they were ordered continuous values (see Fisher <a class="reference internal" href="#fisher1958" id="id7"><span>[Fisher1958]</span></a> for a
formal proof). As a result, only <span class="math notranslate nohighlight">\(K - 1\)</span> splits need to be considered
instead of <span class="math notranslate nohighlight">\(2^{K - 1} - 1\)</span>. The initial sorting is a
<span class="math notranslate nohighlight">\(\mathcal{O}(K \log(K))\)</span> operation, leading to a total complexity of
<span class="math notranslate nohighlight">\(\mathcal{O}(K \log(K) + K)\)</span>, instead of <span class="math notranslate nohighlight">\(\mathcal{O}(2^K)\)</span>.</p>
</div>
</details><p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/ensemble/plot_gradient_boosting_categorical.html#sphx-glr-auto-examples-ensemble-plot-gradient-boosting-categorical-py"><span class="std std-ref">Categorical Feature Support in Gradient Boosting</span></a></p></li>
</ul>
</section>
<section id="monotonic-constraints">
<span id="monotonic-cst-gbdt"></span><h4><span class="section-number">1.11.1.1.5. </span>Monotonic Constraints<a class="headerlink" href="#monotonic-constraints" title="Link to this heading">#</a></h4>
<p>Depending on the problem at hand, you may have prior knowledge indicating
that a given feature should in general have a positive (or negative) effect
on the target value. For example, all else being equal, a higher credit
score should increase the probability of getting approved for a loan.
Monotonic constraints allow you to incorporate such prior knowledge into the
model.</p>
<p>For a predictor <span class="math notranslate nohighlight">\(F\)</span> with two features:</p>
<ul>
<li><p>a <strong>monotonic increase constraint</strong> is a constraint of the form:</p>
<div class="math notranslate nohighlight">
\[x_1 \leq x_1' \implies F(x_1, x_2) \leq F(x_1', x_2)\]</div>
</li>
<li><p>a <strong>monotonic decrease constraint</strong> is a constraint of the form:</p>
<div class="math notranslate nohighlight">
\[x_1 \leq x_1' \implies F(x_1, x_2) \geq F(x_1', x_2)\]</div>
</li>
</ul>
<p>You can specify a monotonic constraint on each feature using the
<code class="docutils literal notranslate"><span class="pre">monotonic_cst</span></code> parameter. For each feature, a value of 0 indicates no
constraint, while 1 and -1 indicate a monotonic increase and
monotonic decrease constraint, respectively:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">HistGradientBoostingRegressor</span>
<span class="go">... # monotonic increase, monotonic decrease, and no constraint on the 3 features</span>
<span class="gp">>>> </span><span class="n">gbdt</span> <span class="o">=</span> <span class="n">HistGradientBoostingRegressor</span><span class="p">(</span><span class="n">monotonic_cst</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
</pre></div>
</div>
<p>In a binary classification context, imposing a monotonic increase (decrease) constraint means that higher values of the feature are supposed
to have a positive (negative) effect on the probability of samples
to belong to the positive class.</p>
<p>Nevertheless, monotonic constraints only marginally constrain feature effects on the output.
For instance, monotonic increase and decrease constraints cannot be used to enforce the