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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>
<li class="toctree-l2"><a class="reference internal" href="linear_model.html">1.1. Linear Models</a></li>
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<li class="toctree-l2"><a class="reference internal" href="ensemble.html">1.11. Ensembles: Gradient boosting, random forests, bagging, voting, stacking</a></li>
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<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-l1 has-children"><a class="reference internal" href="../unsupervised_learning.html">2. Unsupervised learning</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="mixture.html">2.1. Gaussian mixture models</a></li>
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<li class="toctree-l2"><a class="reference internal" href="clustering.html">2.3. Clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="biclustering.html">2.4. Biclustering</a></li>
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<li class="toctree-l2"><a class="reference internal" href="covariance.html">2.6. Covariance estimation</a></li>
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<li class="toctree-l2"><a class="reference internal" href="density.html">2.8. Density Estimation</a></li>
<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-l1 current active has-children"><a class="reference internal" href="../model_selection.html">3. Model selection and evaluation</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="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 current active"><a class="current reference internal" href="#">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-l1 has-children"><a class="reference internal" href="../inspection.html">4. Inspection</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="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>
<li class="toctree-l1 has-children"><a class="reference internal" href="../data_transforms.html">6. Dataset transformations</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="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>
<li class="toctree-l2"><a class="reference internal" href="impute.html">6.4. Imputation of missing values</a></li>
<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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</details></li>
<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="metrics-and-scoring-quantifying-the-quality-of-predictions">
<span id="model-evaluation"></span><h1><span class="section-number">3.4. </span>Metrics and scoring: quantifying the quality of predictions<a class="headerlink" href="#metrics-and-scoring-quantifying-the-quality-of-predictions" title="Link to this heading">#</a></h1>
<section id="which-scoring-function-should-i-use">
<span id="which-scoring-function"></span><h2><span class="section-number">3.4.1. </span>Which scoring function should I use?<a class="headerlink" href="#which-scoring-function-should-i-use" title="Link to this heading">#</a></h2>
<p>Before we take a closer look into the details of the many scores and
<a class="reference internal" href="../glossary.html#term-evaluation-metrics"><span class="xref std std-term">evaluation metrics</span></a>, we want to give some guidance, inspired by statistical
decision theory, on the choice of <strong>scoring functions</strong> for <strong>supervised learning</strong>,
see <a class="reference internal" href="#gneiting2009" id="id1"><span>[Gneiting2009]</span></a>:</p>
<ul class="simple">
<li><p><em>Which scoring function should I use?</em></p></li>
<li><p><em>Which scoring function is a good one for my task?</em></p></li>
</ul>
<p>In a nutshell, if the scoring function is given, e.g. in a kaggle competition
or in a business context, use that one.
If you are free to choose, it starts by considering the ultimate goal and application
of the prediction. It is useful to distinguish two steps:</p>
<ul class="simple">
<li><p>Predicting</p></li>
<li><p>Decision making</p></li>
</ul>
<p><strong>Predicting:</strong>
Usually, the response variable <span class="math notranslate nohighlight">\(Y\)</span> is a random variable, in the sense that there
is <em>no deterministic</em> function <span class="math notranslate nohighlight">\(Y = g(X)\)</span> of the features <span class="math notranslate nohighlight">\(X\)</span>.
Instead, there is a probability distribution <span class="math notranslate nohighlight">\(F\)</span> of <span class="math notranslate nohighlight">\(Y\)</span>.
One can aim to predict the whole distribution, known as <em>probabilistic prediction</em>,
or—more the focus of scikit-learn—issue a <em>point prediction</em> (or point forecast)
by choosing a property or functional of that distribution <span class="math notranslate nohighlight">\(F\)</span>.
Typical examples are the mean (expected value), the median or a quantile of the
response variable <span class="math notranslate nohighlight">\(Y\)</span> (conditionally on <span class="math notranslate nohighlight">\(X\)</span>).</p>
<p>Once that is settled, use a <strong>strictly consistent</strong> scoring function for that
(target) functional, see <a class="reference internal" href="#gneiting2009" id="id2"><span>[Gneiting2009]</span></a>.
This means using a scoring function that is aligned with <em>measuring the distance
between predictions</em> <code class="docutils literal notranslate"><span class="pre">y_pred</span></code> <em>and the true target functional using observations of</em>
<span class="math notranslate nohighlight">\(Y\)</span>, i.e. <code class="docutils literal notranslate"><span class="pre">y_true</span></code>.
For classification <strong>strictly proper scoring rules</strong>, see
<a class="reference external" href="https://en.wikipedia.org/wiki/Scoring_rule">Wikipedia entry for Scoring rule</a>
and <a class="reference internal" href="#gneiting2007" id="id3"><span>[Gneiting2007]</span></a>, coincide with strictly consistent scoring functions.
The table further below provides examples.
One could say that consistent scoring functions act as <em>truth serum</em> in that
they guarantee <em>“that truth telling […] is an optimal strategy in
expectation”</em> <a class="reference internal" href="#gneiting2014" id="id4"><span>[Gneiting2014]</span></a>.</p>
<p>Once a strictly consistent scoring function is chosen, it is best used for both: as
loss function for model training and as metric/score in model evaluation and model
comparison.</p>
<p>Note that for regressors, the prediction is done with <a class="reference internal" href="../glossary.html#term-predict"><span class="xref std std-term">predict</span></a> while for
classifiers it is usually <a class="reference internal" href="../glossary.html#term-predict_proba"><span class="xref std std-term">predict_proba</span></a>.</p>
<p><strong>Decision Making:</strong>
The most common decisions are done on binary classification tasks, where the result of
<a class="reference internal" href="../glossary.html#term-predict_proba"><span class="xref std std-term">predict_proba</span></a> is turned into a single outcome, e.g., from the predicted
probability of rain a decision is made on how to act (whether to take mitigating
measures like an umbrella or not).
For classifiers, this is what <a class="reference internal" href="../glossary.html#term-predict"><span class="xref std std-term">predict</span></a> returns.
See also <a class="reference internal" href="classification_threshold.html#tunedthresholdclassifiercv"><span class="std std-ref">Tuning the decision threshold for class prediction</span></a>.
There are many scoring functions which measure different aspects of such a
decision, most of them are covered with or derived from the
<a class="reference internal" href="generated/sklearn.metrics.confusion_matrix.html#sklearn.metrics.confusion_matrix" title="sklearn.metrics.confusion_matrix"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.confusion_matrix</span></code></a>.</p>
<p><strong>List of strictly consistent scoring functions:</strong>
Here, we list some of the most relevant statistical functionals and corresponding
strictly consistent scoring functions for tasks in practice. Note that the list is not
complete and that there are more of them.
For further criteria on how to select a specific one, see <a class="reference internal" href="#fissler2022" id="id5"><span>[Fissler2022]</span></a>.</p>
<div class="pst-scrollable-table-container"><table class="table">
<thead>
<tr class="row-odd"><th class="head"><p>functional</p></th>
<th class="head"><p>scoring or loss function</p></th>
<th class="head"><p>response <code class="docutils literal notranslate"><span class="pre">y</span></code></p></th>
<th class="head"><p>prediction</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><strong>Classification</strong></p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>mean</p></td>
<td><p><a class="reference internal" href="#brier-score-loss"><span class="std std-ref">Brier score</span></a> <sup>1</sup></p></td>
<td><p>multi-class</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict_proba</span></code></p></td>
</tr>
<tr class="row-even"><td><p>mean</p></td>
<td><p><a class="reference internal" href="#log-loss"><span class="std std-ref">log loss</span></a></p></td>
<td><p>multi-class</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict_proba</span></code></p></td>
</tr>
<tr class="row-odd"><td><p>mode</p></td>
<td><p><a class="reference internal" href="#zero-one-loss"><span class="std std-ref">zero-one loss</span></a> <sup>2</sup></p></td>
<td><p>multi-class</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code>, categorical</p></td>
</tr>
<tr class="row-even"><td><p><strong>Regression</strong></p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>mean</p></td>
<td><p><a class="reference internal" href="#mean-squared-error"><span class="std std-ref">squared error</span></a> <sup>3</sup></p></td>
<td><p>all reals</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code>, all reals</p></td>
</tr>
<tr class="row-even"><td><p>mean</p></td>
<td><p><a class="reference internal" href="#mean-tweedie-deviance"><span class="std std-ref">Poisson deviance</span></a></p></td>
<td><p>non-negative</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code>, strictly positive</p></td>
</tr>
<tr class="row-odd"><td><p>mean</p></td>
<td><p><a class="reference internal" href="#mean-tweedie-deviance"><span class="std std-ref">Gamma deviance</span></a></p></td>
<td><p>strictly positive</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code>, strictly positive</p></td>
</tr>
<tr class="row-even"><td><p>mean</p></td>
<td><p><a class="reference internal" href="#mean-tweedie-deviance"><span class="std std-ref">Tweedie deviance</span></a></p></td>
<td><p>depends on <code class="docutils literal notranslate"><span class="pre">power</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code>, depends on <code class="docutils literal notranslate"><span class="pre">power</span></code></p></td>
</tr>
<tr class="row-odd"><td><p>median</p></td>
<td><p><a class="reference internal" href="#mean-absolute-error"><span class="std std-ref">absolute error</span></a></p></td>
<td><p>all reals</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code>, all reals</p></td>
</tr>
<tr class="row-even"><td><p>quantile</p></td>
<td><p><a class="reference internal" href="#pinball-loss"><span class="std std-ref">pinball loss</span></a></p></td>
<td><p>all reals</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code>, all reals</p></td>
</tr>
<tr class="row-odd"><td><p>mode</p></td>
<td><p>no consistent one exists</p></td>
<td><p>reals</p></td>
<td></td>
</tr>
</tbody>
</table>
</div>
<p><sup>1</sup> The Brier score is just a different name for the squared error in case of
classification.</p>
<p><sup>2</sup> The zero-one loss is only consistent but not strictly consistent for the mode.
The zero-one loss is equivalent to one minus the accuracy score, meaning it gives
different score values but the same ranking.</p>
<p><sup>3</sup> R² gives the same ranking as squared error.</p>
<p><strong>Fictitious Example:</strong>
Let’s make the above arguments more tangible. Consider a setting in network reliability
engineering, such as maintaining stable internet or Wi-Fi connections.
As provider of the network, you have access to the dataset of log entries of network
connections containing network load over time and many interesting features.
Your goal is to improve the reliability of the connections.
In fact, you promise your customers that on at least 99% of all days there are no
connection discontinuities larger than 1 minute.
Therefore, you are interested in a prediction of the 99% quantile (of longest
connection interruption duration per day) in order to know in advance when to add
more bandwidth and thereby satisfy your customers. So the <em>target functional</em> is the
99% quantile. From the table above, you choose the pinball loss as scoring function
(fair enough, not much choice given), for model training (e.g.
<code class="docutils literal notranslate"><span class="pre">HistGradientBoostingRegressor(loss="quantile",</span> <span class="pre">quantile=0.99)</span></code>) as well as model
evaluation (<code class="docutils literal notranslate"><span class="pre">mean_pinball_loss(...,</span> <span class="pre">alpha=0.99)</span></code> - we apologize for the different
argument names, <code class="docutils literal notranslate"><span class="pre">quantile</span></code> and <code class="docutils literal notranslate"><span class="pre">alpha</span></code>) be it in grid search for finding
hyperparameters or in comparing to other models like
<code class="docutils literal notranslate"><span class="pre">QuantileRegressor(quantile=0.99)</span></code>.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="gneiting2007" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">Gneiting2007</a><span class="fn-bracket">]</span></span>
<p>T. Gneiting and A. E. Raftery. <a class="reference external" href="https://doi.org/10.1198/016214506000001437">Strictly Proper
Scoring Rules, Prediction, and Estimation</a>
In: Journal of the American Statistical Association 102 (2007),
pp. 359– 378.
<a class="reference external" href="www.stat.washington.edu/people/raftery/Research/PDF/Gneiting2007jasa.pdf">link to pdf</a></p>
</div>
<div class="citation" id="gneiting2009" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>Gneiting2009<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id2">2</a>)</span>
<p>T. Gneiting. <a class="reference external" href="https://arxiv.org/abs/0912.0902">Making and Evaluating Point Forecasts</a>
Journal of the American Statistical Association 106 (2009): 746 - 762.</p>
</div>
<div class="citation" id="gneiting2014" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">Gneiting2014</a><span class="fn-bracket">]</span></span>
<p>T. Gneiting and M. Katzfuss. <a class="reference external" href="https://doi.org/10.1146/annurev-st atistics-062713-085831">Probabilistic Forecasting</a>. In: Annual Review of Statistics and Its Application 1.1 (2014), pp. 125–151.</p>
</div>
<div class="citation" id="fissler2022" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id5">Fissler2022</a><span class="fn-bracket">]</span></span>
<p>T. Fissler, C. Lorentzen and M. Mayer. <a class="reference external" href="https://arxiv.org/abs/2202.12780">Model
Comparison and Calibration Assessment: User Guide for Consistent Scoring
Functions in Machine Learning and Actuarial Practice.</a></p>
</div>
</div>
</section>
<section id="scoring-api-overview">
<span id="id6"></span><h2><span class="section-number">3.4.2. </span>Scoring API overview<a class="headerlink" href="#scoring-api-overview" title="Link to this heading">#</a></h2>
<p>There are 3 different APIs for evaluating the quality of a model’s
predictions:</p>
<ul class="simple">
<li><p><strong>Estimator score method</strong>: Estimators have a <code class="docutils literal notranslate"><span class="pre">score</span></code> method providing a
default evaluation criterion for the problem they are designed to solve.
Most commonly this is <a class="reference internal" href="#accuracy-score"><span class="std std-ref">accuracy</span></a> for classifiers and the
<a class="reference internal" href="#r2-score"><span class="std std-ref">coefficient of determination</span></a> (<span class="math notranslate nohighlight">\(R^2\)</span>) for regressors.
Details for each estimator can be found in its documentation.</p></li>
<li><p><strong>Scoring parameter</strong>: Model-evaluation tools that use
<a class="reference internal" href="cross_validation.html#cross-validation"><span class="std std-ref">cross-validation</span></a> (such as
<a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">model_selection.GridSearchCV</span></code></a>, <a class="reference internal" href="generated/sklearn.model_selection.validation_curve.html#sklearn.model_selection.validation_curve" title="sklearn.model_selection.validation_curve"><code class="xref py py-func docutils literal notranslate"><span class="pre">model_selection.validation_curve</span></code></a> and
<a class="reference internal" href="generated/sklearn.linear_model.LogisticRegressionCV.html#sklearn.linear_model.LogisticRegressionCV" title="sklearn.linear_model.LogisticRegressionCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">linear_model.LogisticRegressionCV</span></code></a>) rely on an internal <em>scoring</em> strategy.
This can be specified using the <code class="docutils literal notranslate"><span class="pre">scoring</span></code> parameter of that tool and is discussed
in the section <a class="reference internal" href="#scoring-parameter"><span class="std std-ref">The scoring parameter: defining model evaluation rules</span></a>.</p></li>
<li><p><strong>Metric functions</strong>: The <a class="reference internal" href="../api/sklearn.metrics.html#module-sklearn.metrics" title="sklearn.metrics"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.metrics</span></code></a> module implements functions
assessing prediction error for specific purposes. These metrics are detailed
in sections on <a class="reference internal" href="#classification-metrics"><span class="std std-ref">Classification metrics</span></a>,
<a class="reference internal" href="#multilabel-ranking-metrics"><span class="std std-ref">Multilabel ranking metrics</span></a>, <a class="reference internal" href="#regression-metrics"><span class="std std-ref">Regression metrics</span></a> and
<a class="reference internal" href="#clustering-metrics"><span class="std std-ref">Clustering metrics</span></a>.</p></li>
</ul>
<p>Finally, <a class="reference internal" href="#dummy-estimators"><span class="std std-ref">Dummy estimators</span></a> are useful to get a baseline
value of those metrics for random predictions.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p>For “pairwise” metrics, between <em>samples</em> and not estimators or
predictions, see the <a class="reference internal" href="metrics.html#metrics"><span class="std std-ref">Pairwise metrics, Affinities and Kernels</span></a> section.</p>
</div>
</section>
<section id="the-scoring-parameter-defining-model-evaluation-rules">
<span id="scoring-parameter"></span><h2><span class="section-number">3.4.3. </span>The <code class="docutils literal notranslate"><span class="pre">scoring</span></code> parameter: defining model evaluation rules<a class="headerlink" href="#the-scoring-parameter-defining-model-evaluation-rules" title="Link to this heading">#</a></h2>
<p>Model selection and evaluation tools that internally use
<a class="reference internal" href="cross_validation.html#cross-validation"><span class="std std-ref">cross-validation</span></a> (such as
<a class="reference internal" href="generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">model_selection.GridSearchCV</span></code></a>, <a class="reference internal" href="generated/sklearn.model_selection.validation_curve.html#sklearn.model_selection.validation_curve" title="sklearn.model_selection.validation_curve"><code class="xref py py-func docutils literal notranslate"><span class="pre">model_selection.validation_curve</span></code></a> and
<a class="reference internal" href="generated/sklearn.linear_model.LogisticRegressionCV.html#sklearn.linear_model.LogisticRegressionCV" title="sklearn.linear_model.LogisticRegressionCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">linear_model.LogisticRegressionCV</span></code></a>) take a <code class="docutils literal notranslate"><span class="pre">scoring</span></code> parameter that
controls what metric they apply to the estimators evaluated.</p>
<p>They can be specified in several ways:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">None</span></code>: the estimator’s default evaluation criterion (i.e., the metric used in the
estimator’s <code class="docutils literal notranslate"><span class="pre">score</span></code> method) is used.</p></li>
<li><p><a class="reference internal" href="#scoring-string-names"><span class="std std-ref">String name</span></a>: common metrics can be passed via a string
name.</p></li>
<li><p><a class="reference internal" href="#scoring-callable"><span class="std std-ref">Callable</span></a>: more complex metrics can be passed via a custom
metric callable (e.g., function).</p></li>
</ul>
<p>Some tools do also accept multiple metric evaluation. See <a class="reference internal" href="#multimetric-scoring"><span class="std std-ref">Using multiple metric evaluation</span></a>
for details.</p>
<section id="string-name-scorers">
<span id="scoring-string-names"></span><h3><span class="section-number">3.4.3.1. </span>String name scorers<a class="headerlink" href="#string-name-scorers" title="Link to this heading">#</a></h3>
<p>For the most common use cases, you can designate a scorer object with the
<code class="docutils literal notranslate"><span class="pre">scoring</span></code> parameter via a string name; the table below shows all possible values.
All scorer objects follow the convention that <strong>higher return values are better
than lower return values</strong>. Thus metrics which measure the distance between
the model and the data, like <a class="reference internal" href="generated/sklearn.metrics.mean_squared_error.html#sklearn.metrics.mean_squared_error" title="sklearn.metrics.mean_squared_error"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.mean_squared_error</span></code></a>, are
available as ‘neg_mean_squared_error’ which return the negated value
of the metric.</p>
<div class="pst-scrollable-table-container"><table class="table">
<thead>
<tr class="row-odd"><th class="head"><p>Scoring string name</p></th>
<th class="head"><p>Function</p></th>
<th class="head"><p>Comment</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><strong>Classification</strong></p></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>‘accuracy’</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.accuracy_score.html#sklearn.metrics.accuracy_score" title="sklearn.metrics.accuracy_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.accuracy_score</span></code></a></p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>‘balanced_accuracy’</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.balanced_accuracy_score.html#sklearn.metrics.balanced_accuracy_score" title="sklearn.metrics.balanced_accuracy_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.balanced_accuracy_score</span></code></a></p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>‘top_k_accuracy’</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.top_k_accuracy_score.html#sklearn.metrics.top_k_accuracy_score" title="sklearn.metrics.top_k_accuracy_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.top_k_accuracy_score</span></code></a></p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>‘average_precision’</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.average_precision_score.html#sklearn.metrics.average_precision_score" title="sklearn.metrics.average_precision_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.average_precision_score</span></code></a></p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>‘neg_brier_score’</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.brier_score_loss.html#sklearn.metrics.brier_score_loss" title="sklearn.metrics.brier_score_loss"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.brier_score_loss</span></code></a></p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>‘f1’</p></td>
<td><p><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">metrics.f1_score</span></code></a></p></td>
<td><p>for binary targets</p></td>
</tr>
<tr class="row-odd"><td><p>‘f1_micro’</p></td>
<td><p><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">metrics.f1_score</span></code></a></p></td>
<td><p>micro-averaged</p></td>
</tr>
<tr class="row-even"><td><p>‘f1_macro’</p></td>
<td><p><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">metrics.f1_score</span></code></a></p></td>
<td><p>macro-averaged</p></td>
</tr>
<tr class="row-odd"><td><p>‘f1_weighted’</p></td>
<td><p><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">metrics.f1_score</span></code></a></p></td>
<td><p>weighted average</p></td>
</tr>
<tr class="row-even"><td><p>‘f1_samples’</p></td>
<td><p><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">metrics.f1_score</span></code></a></p></td>
<td><p>by multilabel sample</p></td>
</tr>
<tr class="row-odd"><td><p>‘neg_log_loss’</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.log_loss.html#sklearn.metrics.log_loss" title="sklearn.metrics.log_loss"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.log_loss</span></code></a></p></td>
<td><p>requires <code class="docutils literal notranslate"><span class="pre">predict_proba</span></code> support</p></td>
</tr>
<tr class="row-even"><td><p>‘precision’ etc.</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.precision_score.html#sklearn.metrics.precision_score" title="sklearn.metrics.precision_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.precision_score</span></code></a></p></td>
<td><p>suffixes apply as with ‘f1’</p></td>
</tr>
<tr class="row-odd"><td><p>‘recall’ etc.</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.recall_score.html#sklearn.metrics.recall_score" title="sklearn.metrics.recall_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.recall_score</span></code></a></p></td>
<td><p>suffixes apply as with ‘f1’</p></td>
</tr>
<tr class="row-even"><td><p>‘jaccard’ etc.</p></td>
<td><p><a class="reference internal" href="generated/sklearn.metrics.jaccard_score.html#sklearn.metrics.jaccard_score" title="sklearn.metrics.jaccard_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">metrics.jaccard_score</span></code></a></p></td>
<td><p>suffixes apply as with ‘f1’</p></td>