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<li class="toctree-l1 has-children"><a class="reference internal" href="../supervised_learning.html">1. Supervised learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
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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 current active"><a class="current reference internal" href="#">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>
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<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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<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>
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<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>
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<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="tuning-the-decision-threshold-for-class-prediction">
<span id="tunedthresholdclassifiercv"></span><h1><span class="section-number">3.3. </span>Tuning the decision threshold for class prediction<a class="headerlink" href="#tuning-the-decision-threshold-for-class-prediction" title="Link to this heading">#</a></h1>
<p>Classification is best divided into two parts:</p>
<ul class="simple">
<li><p>the statistical problem of learning a model to predict, ideally, class probabilities;</p></li>
<li><p>the decision problem to take concrete action based on those probability predictions.</p></li>
</ul>
<p>Let’s take a straightforward example related to weather forecasting: the first point is
related to answering “what is the chance that it will rain tomorrow?” while the second
point is related to answering “should I take an umbrella tomorrow?”.</p>
<p>When it comes to the scikit-learn API, the first point is addressed providing scores
using <a class="reference internal" href="../glossary.html#term-predict_proba"><span class="xref std std-term">predict_proba</span></a> or <a class="reference internal" href="../glossary.html#term-decision_function"><span class="xref std std-term">decision_function</span></a>. The former returns conditional
probability estimates <span class="math notranslate nohighlight">\(P(y|X)\)</span> for each class, while the latter returns a decision
score for each class.</p>
<p>The decision corresponding to the labels are obtained with <a class="reference internal" href="../glossary.html#term-predict"><span class="xref std std-term">predict</span></a>. In binary
classification, a decision rule or action is then defined by thresholding the scores,
leading to the prediction of a single class label for each sample. For binary
classification in scikit-learn, class labels predictions are obtained by hard-coded
cut-off rules: a positive class is predicted when the conditional probability
<span class="math notranslate nohighlight">\(P(y|X)\)</span> is greater than 0.5 (obtained with <a class="reference internal" href="../glossary.html#term-predict_proba"><span class="xref std std-term">predict_proba</span></a>) or if the
decision score is greater than 0 (obtained with <a class="reference internal" href="../glossary.html#term-decision_function"><span class="xref std std-term">decision_function</span></a>).</p>
<p>Here, we show an example that illustrates the relation between conditional
probability estimates <span class="math notranslate nohighlight">\(P(y|X)\)</span> and class labels:</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.datasets</span> <span class="kn">import</span> <span class="n">make_classification</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <span class="n">DecisionTreeClassifier</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_classification</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">classifier</span> <span class="o">=</span> <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">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="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">classifier</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="mi">4</span><span class="p">])</span>
<span class="go">array([[0.94 , 0.06 ],</span>
<span class="go"> [0.94 , 0.06 ],</span>
<span class="go"> [0.0416..., 0.9583...],</span>
<span class="go"> [0.0416..., 0.9583...]])</span>
<span class="gp">>>> </span><span class="n">classifier</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="mi">4</span><span class="p">])</span>
<span class="go">array([0, 0, 1, 1])</span>
</pre></div>
</div>
<p>While these hard-coded rules might at first seem reasonable as default behavior, they
are most certainly not ideal for most use cases. Let’s illustrate with an example.</p>
<p>Consider a scenario where a predictive model is being deployed to assist
physicians in detecting tumors. In this setting, physicians will most likely be
interested in identifying all patients with cancer and not missing anyone with cancer so
that they can provide them with the right treatment. In other words, physicians
prioritize achieving a high recall rate. This emphasis on recall comes, of course, with
the trade-off of potentially more false-positive predictions, reducing the precision of
the model. That is a risk physicians are willing to take because the cost of a missed
cancer is much higher than the cost of further diagnostic tests. Consequently, when it
comes to deciding whether to classify a patient as having cancer or not, it may be more
beneficial to classify them as positive for cancer when the conditional probability
estimate is much lower than 0.5.</p>
<section id="post-tuning-the-decision-threshold">
<h2><span class="section-number">3.3.1. </span>Post-tuning the decision threshold<a class="headerlink" href="#post-tuning-the-decision-threshold" title="Link to this heading">#</a></h2>
<p>One solution to address the problem stated in the introduction is to tune the decision
threshold of the classifier once the model has been trained. The
<a class="reference internal" href="generated/sklearn.model_selection.TunedThresholdClassifierCV.html#sklearn.model_selection.TunedThresholdClassifierCV" title="sklearn.model_selection.TunedThresholdClassifierCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">TunedThresholdClassifierCV</span></code></a> tunes this threshold using
an internal cross-validation. The optimum threshold is chosen to maximize a given
metric.</p>
<p>The following image illustrates the tuning of the decision threshold for a gradient
boosting classifier. While the vanilla and tuned classifiers provide the same
<a class="reference internal" href="../glossary.html#term-predict_proba"><span class="xref std std-term">predict_proba</span></a> outputs and thus the same Receiver Operating Characteristic (ROC)
and Precision-Recall curves, the class label predictions differ because of the tuned
decision threshold. The vanilla classifier predicts the class of interest for a
conditional probability greater than 0.5 while the tuned classifier predicts the class
of interest for a very low probability (around 0.02). This decision threshold optimizes
a utility metric defined by the business (in this case an insurance company).</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/model_selection/plot_cost_sensitive_learning.html"><img alt="../_images/sphx_glr_plot_cost_sensitive_learning_002.png" src="../_images/sphx_glr_plot_cost_sensitive_learning_002.png" />
</a>
</figure>
<section id="options-to-tune-the-decision-threshold">
<h3><span class="section-number">3.3.1.1. </span>Options to tune the decision threshold<a class="headerlink" href="#options-to-tune-the-decision-threshold" title="Link to this heading">#</a></h3>
<p>The decision threshold can be tuned through different strategies controlled by the
parameter <code class="docutils literal notranslate"><span class="pre">scoring</span></code>.</p>
<p>One way to tune the threshold is by maximizing a pre-defined scikit-learn metric. These
metrics can be found by calling the function <a class="reference internal" href="generated/sklearn.metrics.get_scorer_names.html#sklearn.metrics.get_scorer_names" title="sklearn.metrics.get_scorer_names"><code class="xref py py-func docutils literal notranslate"><span class="pre">get_scorer_names</span></code></a>.
By default, the balanced accuracy is the metric used but be aware that one should choose
a meaningful metric for their use case.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>It is important to notice that these metrics come with default parameters, notably
the label of the class of interest (i.e. <code class="docutils literal notranslate"><span class="pre">pos_label</span></code>). Thus, if this label is not
the right one for your application, you need to define a scorer and pass the right
<code class="docutils literal notranslate"><span class="pre">pos_label</span></code> (and additional parameters) using the
<a class="reference internal" href="generated/sklearn.metrics.make_scorer.html#sklearn.metrics.make_scorer" title="sklearn.metrics.make_scorer"><code class="xref py py-func docutils literal notranslate"><span class="pre">make_scorer</span></code></a>. Refer to <a class="reference internal" href="model_evaluation.html#scoring"><span class="std std-ref">Defining your scoring strategy from metric functions</span></a> to get
information to define your own scoring function. For instance, we show how to pass
the information to the scorer that the label of interest is <code class="docutils literal notranslate"><span class="pre">0</span></code> when maximizing the
<a class="reference internal" href="generated/sklearn.metrics.f1_score.html#sklearn.metrics.f1_score" title="sklearn.metrics.f1_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">f1_score</span></code></a>:</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.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">TunedThresholdClassifierCV</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">make_scorer</span><span class="p">,</span> <span class="n">f1_score</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_classification</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">n_samples</span><span class="o">=</span><span class="mi">1_000</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.9</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">pos_label</span> <span class="o">=</span> <span class="mi">0</span>
<span class="gp">>>> </span><span class="n">scorer</span> <span class="o">=</span> <span class="n">make_scorer</span><span class="p">(</span><span class="n">f1_score</span><span class="p">,</span> <span class="n">pos_label</span><span class="o">=</span><span class="n">pos_label</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">base_model</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">model</span> <span class="o">=</span> <span class="n">TunedThresholdClassifierCV</span><span class="p">(</span><span class="n">base_model</span><span class="p">,</span> <span class="n">scoring</span><span class="o">=</span><span class="n">scorer</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">scorer</span><span class="p">(</span><span class="n">model</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">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="go">0.88...</span>
<span class="gp">>>> </span><span class="c1"># compare it with the internal score found by cross-validation</span>
<span class="gp">>>> </span><span class="n">model</span><span class="o">.</span><span class="n">best_score_</span>
<span class="go">0.86...</span>
</pre></div>
</div>
</div>
</section>
<section id="important-notes-regarding-the-internal-cross-validation">
<h3><span class="section-number">3.3.1.2. </span>Important notes regarding the internal cross-validation<a class="headerlink" href="#important-notes-regarding-the-internal-cross-validation" title="Link to this heading">#</a></h3>
<p>By default <a class="reference internal" href="generated/sklearn.model_selection.TunedThresholdClassifierCV.html#sklearn.model_selection.TunedThresholdClassifierCV" title="sklearn.model_selection.TunedThresholdClassifierCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">TunedThresholdClassifierCV</span></code></a> uses a 5-fold
stratified cross-validation to tune the decision threshold. The parameter <code class="docutils literal notranslate"><span class="pre">cv</span></code> allows to
control the cross-validation strategy. It is possible to bypass cross-validation by
setting <code class="docutils literal notranslate"><span class="pre">cv="prefit"</span></code> and providing a fitted classifier. In this case, the decision
threshold is tuned on the data provided to the <code class="docutils literal notranslate"><span class="pre">fit</span></code> method.</p>
<p>However, you should be extremely careful when using this option. You should never use
the same data for training the classifier and tuning the decision threshold due to the
risk of overfitting. Refer to the following example section for more details (cf.
<a class="reference internal" href="../auto_examples/model_selection/plot_cost_sensitive_learning.html#tunedthresholdclassifiercv-no-cv"><span class="std std-ref">Consideration regarding model refitting and cross-validation</span></a>). If you have limited resources, consider using
a float number for <code class="docutils literal notranslate"><span class="pre">cv</span></code> to limit to an internal single train-test split.</p>
<p>The option <code class="docutils literal notranslate"><span class="pre">cv="prefit"</span></code> should only be used when the provided classifier was already
trained, and you just want to find the best decision threshold using a new validation
set.</p>
</section>
<section id="manually-setting-the-decision-threshold">
<span id="fixedthresholdclassifier"></span><h3><span class="section-number">3.3.1.3. </span>Manually setting the decision threshold<a class="headerlink" href="#manually-setting-the-decision-threshold" title="Link to this heading">#</a></h3>
<p>The previous sections discussed strategies to find an optimal decision threshold. It is
also possible to manually set the decision threshold using the class
<a class="reference internal" href="generated/sklearn.model_selection.FixedThresholdClassifier.html#sklearn.model_selection.FixedThresholdClassifier" title="sklearn.model_selection.FixedThresholdClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">FixedThresholdClassifier</span></code></a>. In case that you don’t want
to refit the model when calling <code class="docutils literal notranslate"><span class="pre">fit</span></code>, wrap your sub-estimator with a
<a class="reference internal" href="generated/sklearn.frozen.FrozenEstimator.html#sklearn.frozen.FrozenEstimator" title="sklearn.frozen.FrozenEstimator"><code class="xref py py-class docutils literal notranslate"><span class="pre">FrozenEstimator</span></code></a> and do
<code class="docutils literal notranslate"><span class="pre">FixedThresholdClassifier(FrozenEstimator(estimator),</span> <span class="pre">...)</span></code>.</p>
</section>
<section id="examples">
<h3><span class="section-number">3.3.1.4. </span>Examples<a class="headerlink" href="#examples" title="Link to this heading">#</a></h3>
<ul class="simple">
<li><p>See the example entitled
<a class="reference internal" href="../auto_examples/model_selection/plot_tuned_decision_threshold.html#sphx-glr-auto-examples-model-selection-plot-tuned-decision-threshold-py"><span class="std std-ref">Post-hoc tuning the cut-off point of decision function</span></a>,
to get insights on the post-tuning of the decision threshold.</p></li>
<li><p>See the example entitled
<a class="reference internal" href="../auto_examples/model_selection/plot_cost_sensitive_learning.html#sphx-glr-auto-examples-model-selection-plot-cost-sensitive-learning-py"><span class="std std-ref">Post-tuning the decision threshold for cost-sensitive learning</span></a>,
to learn about cost-sensitive learning and decision threshold tuning.</p></li>
</ul>
</section>
</section>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#post-tuning-the-decision-threshold">3.3.1. Post-tuning the decision threshold</a><ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#options-to-tune-the-decision-threshold">3.3.1.1. Options to tune the decision threshold</a></li>
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