
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/model_selection/plot_tuned_decision_threshold.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_model_selection_plot_tuned_decision_threshold.py>`
        to download the full example code or to run this example in your browser via JupyterLite or Binder.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_model_selection_plot_tuned_decision_threshold.py:


======================================================
Post-hoc tuning the cut-off point of decision function
======================================================

Once a binary classifier is trained, the :term:`predict` method outputs class label
predictions corresponding to a thresholding of either the :term:`decision_function` or
the :term:`predict_proba` output. The default threshold is defined as a posterior
probability estimate of 0.5 or a decision score of 0.0. However, this default strategy
may not be optimal for the task at hand.

This example shows how to use the
:class:`~sklearn.model_selection.TunedThresholdClassifierCV` to tune the decision
threshold, depending on a metric of interest.

.. GENERATED FROM PYTHON SOURCE LINES 16-20

.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause








.. GENERATED FROM PYTHON SOURCE LINES 21-27

The diabetes dataset
--------------------

To illustrate the tuning of the decision threshold, we will use the diabetes dataset.
This dataset is available on OpenML: https://www.openml.org/d/37. We use the
:func:`~sklearn.datasets.fetch_openml` function to fetch this dataset.

.. GENERATED FROM PYTHON SOURCE LINES 27-32

.. code-block:: Python

    from sklearn.datasets import fetch_openml

    diabetes = fetch_openml(data_id=37, as_frame=True, parser="pandas")
    data, target = diabetes.data, diabetes.target








.. GENERATED FROM PYTHON SOURCE LINES 33-34

We look at the target to understand the type of problem we are dealing with.

.. GENERATED FROM PYTHON SOURCE LINES 34-36

.. code-block:: Python

    target.value_counts()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    class
    tested_negative    500
    tested_positive    268
    Name: count, dtype: int64



.. GENERATED FROM PYTHON SOURCE LINES 37-41

We can see that we are dealing with a binary classification problem. Since the
labels are not encoded as 0 and 1, we make it explicit that we consider the class
labeled "tested_negative" as the negative class (which is also the most frequent)
and the class labeled "tested_positive" the positive as the positive class:

.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: Python

    neg_label, pos_label = target.value_counts().index








.. GENERATED FROM PYTHON SOURCE LINES 44-53

We can also observe that this binary problem is slightly imbalanced where we have
around twice more samples from the negative class than from the positive class. When
it comes to evaluation, we should consider this aspect to interpret the results.

Our vanilla classifier
----------------------

We define a basic predictive model composed of a scaler followed by a logistic
regression classifier.

.. GENERATED FROM PYTHON SOURCE LINES 53-60

.. code-block:: Python

    from sklearn.linear_model import LogisticRegression
    from sklearn.pipeline import make_pipeline
    from sklearn.preprocessing import StandardScaler

    model = make_pipeline(StandardScaler(), LogisticRegression())
    model






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    </style><body><div id="sk-container-id-66" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),
                    (&#x27;logisticregression&#x27;, LogisticRegression())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label  sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-285" type="checkbox" ><label for="sk-estimator-id-285" class="sk-toggleable__label  sk-toggleable__label-arrow"><div><div>Pipeline</div></div><div><a class="sk-estimator-doc-link " rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.pipeline.Pipeline.html">?<span>Documentation for Pipeline</span></a><span class="sk-estimator-doc-link ">i<span>Not fitted</span></span></div></label><div class="sk-toggleable__content " data-param-prefix="">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('steps',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=steps,-list%20of%20tuples">
                steps
                <span class="param-doc-description">steps: list of tuples<br><br>List of (name of step, estimator) tuples that are to be chained in<br>sequential order. To be compatible with the scikit-learn API, all steps<br>must define `fit`. All non-last steps must also define `transform`. See<br>:ref:`Combining Estimators <combining_estimators>` for more details.</span>
            </a>
        </td>
                <td class="value">[(&#x27;standardscaler&#x27;, ...), (&#x27;logisticregression&#x27;, ...)]</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('transform_input',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=transform_input,-list%20of%20str%2C%20default%3DNone">
                transform_input
                <span class="param-doc-description">transform_input: list of str, default=None<br><br>The names of the :term:`metadata` parameters that should be transformed by the<br>pipeline before passing it to the step consuming it.<br><br>This enables transforming some input arguments to ``fit`` (other than ``X``)<br>to be transformed by the steps of the pipeline up to the step which requires<br>them. Requirement is defined via :ref:`metadata routing <metadata_routing>`.<br>For instance, this can be used to pass a validation set through the pipeline.<br><br>You can only set this if metadata routing is enabled, which you<br>can enable using ``sklearn.set_config(enable_metadata_routing=True)``.<br><br>.. versionadded:: 1.6</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('memory',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=memory,-str%20or%20object%20with%20the%20joblib.Memory%20interface%2C%20default%3DNone">
                memory
                <span class="param-doc-description">memory: str or object with the joblib.Memory interface, default=None<br><br>Used to cache the fitted transformers of the pipeline. The last step<br>will never be cached, even if it is a transformer. By default, no<br>caching is performed. If a string is given, it is the path to the<br>caching directory. Enabling caching triggers a clone of the transformers<br>before fitting. Therefore, the transformer instance given to the<br>pipeline cannot be inspected directly. Use the attribute ``named_steps``<br>or ``steps`` to inspect estimators within the pipeline. Caching the<br>transformers is advantageous when fitting is time consuming. See<br>:ref:`sphx_glr_auto_examples_neighbors_plot_caching_nearest_neighbors.py`<br>for an example on how to enable caching.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('verbose',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=verbose,-bool%2C%20default%3DFalse">
                verbose
                <span class="param-doc-description">verbose: bool, default=False<br><br>If True, the time elapsed while fitting each step will be printed as it<br>is completed.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-estimator  sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-286" type="checkbox" ><label for="sk-estimator-id-286" class="sk-toggleable__label  sk-toggleable__label-arrow"><div><div>StandardScaler</div></div><div><a class="sk-estimator-doc-link " rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.StandardScaler.html">?<span>Documentation for StandardScaler</span></a></div></label><div class="sk-toggleable__content " data-param-prefix="standardscaler__">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('copy',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=copy,-bool%2C%20default%3DTrue">
                copy
                <span class="param-doc-description">copy: bool, default=True<br><br>If False, try to avoid a copy and do inplace scaling instead.<br>This is not guaranteed to always work inplace; e.g. if the data is<br>not a NumPy array or scipy.sparse CSR matrix, a copy may still be<br>returned.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('with_mean',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=with_mean,-bool%2C%20default%3DTrue">
                with_mean
                <span class="param-doc-description">with_mean: bool, default=True<br><br>If True, center the data before scaling.<br>This does not work (and will raise an exception) when attempted on<br>sparse matrices, because centering them entails building a dense<br>matrix which in common use cases is likely to be too large to fit in<br>memory.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('with_std',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=with_std,-bool%2C%20default%3DTrue">
                with_std
                <span class="param-doc-description">with_std: bool, default=True<br><br>If True, scale the data to unit variance (or equivalently,<br>unit standard deviation).</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-item"><div class="sk-estimator  sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-287" type="checkbox" ><label for="sk-estimator-id-287" class="sk-toggleable__label  sk-toggleable__label-arrow"><div><div>LogisticRegression</div></div><div><a class="sk-estimator-doc-link " rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html">?<span>Documentation for LogisticRegression</span></a></div></label><div class="sk-toggleable__content " data-param-prefix="logisticregression__">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('penalty',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=penalty,-%7B%27l1%27%2C%20%27l2%27%2C%20%27elasticnet%27%2C%20None%7D%2C%20default%3D%27l2%27">
                penalty
                <span class="param-doc-description">penalty: {'l1', 'l2', 'elasticnet', None}, default='l2'<br><br>Specify the norm of the penalty:<br><br>- `None`: no penalty is added;<br>- `'l2'`: add a L2 penalty term and it is the default choice;<br>- `'l1'`: add a L1 penalty term;<br>- `'elasticnet'`: both L1 and L2 penalty terms are added.<br><br>.. warning::<br>   Some penalties may not work with some solvers. See the parameter<br>   `solver` below, to know the compatibility between the penalty and<br>   solver.<br><br>.. versionadded:: 0.19<br>   l1 penalty with SAGA solver (allowing 'multinomial' + L1)<br><br>.. deprecated:: 1.8<br>   `penalty` was deprecated in version 1.8 and will be removed in 1.10.<br>   Use `l1_ratio` instead. `l1_ratio=0` for `penalty='l2'`, `l1_ratio=1` for<br>   `penalty='l1'` and `l1_ratio` set to any float between 0 and 1 for<br>   `'penalty='elasticnet'`.</span>
            </a>
        </td>
                <td class="value">&#x27;deprecated&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('C',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=C,-float%2C%20default%3D1.0">
                C
                <span class="param-doc-description">C: float, default=1.0<br><br>Inverse of regularization strength; must be a positive float.<br>Like in support vector machines, smaller values specify stronger<br>regularization. `C=np.inf` results in unpenalized logistic regression.<br>For a visual example on the effect of tuning the `C` parameter<br>with an L1 penalty, see:<br>:ref:`sphx_glr_auto_examples_linear_model_plot_logistic_path.py`.</span>
            </a>
        </td>
                <td class="value">1.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('l1_ratio',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=l1_ratio,-float%2C%20default%3D0.0">
                l1_ratio
                <span class="param-doc-description">l1_ratio: float, default=0.0<br><br>The Elastic-Net mixing parameter, with `0 <= l1_ratio <= 1`. Setting<br>`l1_ratio=1` gives a pure L1-penalty, setting `l1_ratio=0` a pure L2-penalty.<br>Any value between 0 and 1 gives an Elastic-Net penalty of the form<br>`l1_ratio * L1 + (1 - l1_ratio) * L2`.<br><br>.. warning::<br>   Certain values of `l1_ratio`, i.e. some penalties, may not work with some<br>   solvers. See the parameter `solver` below, to know the compatibility between<br>   the penalty and solver.<br><br>.. versionchanged:: 1.8<br>    Default value changed from None to 0.0.<br><br>.. deprecated:: 1.8<br>    `None` is deprecated and will be removed in version 1.10. Always use<br>    `l1_ratio` to specify the penalty type.</span>
            </a>
        </td>
                <td class="value">0.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('dual',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=dual,-bool%2C%20default%3DFalse">
                dual
                <span class="param-doc-description">dual: bool, default=False<br><br>Dual (constrained) or primal (regularized, see also<br>:ref:`this equation <regularized-logistic-loss>`) formulation. Dual formulation<br>is only implemented for l2 penalty with liblinear solver. Prefer `dual=False`<br>when n_samples > n_features.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('tol',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=tol,-float%2C%20default%3D1e-4">
                tol
                <span class="param-doc-description">tol: float, default=1e-4<br><br>Tolerance for stopping criteria.</span>
            </a>
        </td>
                <td class="value">0.0001</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('fit_intercept',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=fit_intercept,-bool%2C%20default%3DTrue">
                fit_intercept
                <span class="param-doc-description">fit_intercept: bool, default=True<br><br>Specifies if a constant (a.k.a. bias or intercept) should be<br>added to the decision function.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('intercept_scaling',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=intercept_scaling,-float%2C%20default%3D1">
                intercept_scaling
                <span class="param-doc-description">intercept_scaling: float, default=1<br><br>Useful only when the solver `liblinear` is used<br>and `self.fit_intercept` is set to `True`. In this case, `x` becomes<br>`[x, self.intercept_scaling]`,<br>i.e. a "synthetic" feature with constant value equal to<br>`intercept_scaling` is appended to the instance vector.<br>The intercept becomes<br>``intercept_scaling * synthetic_feature_weight``.<br><br>.. note::<br>    The synthetic feature weight is subject to L1 or L2<br>    regularization as all other features.<br>    To lessen the effect of regularization on synthetic feature weight<br>    (and therefore on the intercept) `intercept_scaling` has to be increased.</span>
            </a>
        </td>
                <td class="value">1</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('class_weight',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=class_weight,-dict%20or%20%27balanced%27%2C%20default%3DNone">
                class_weight
                <span class="param-doc-description">class_weight: dict or 'balanced', default=None<br><br>Weights associated with classes in the form ``{class_label: weight}``.<br>If not given, all classes are supposed to have weight one.<br><br>The "balanced" mode uses the values of y to automatically adjust<br>weights inversely proportional to class frequencies in the input data<br>as ``n_samples / (n_classes * np.bincount(y))``.<br><br>Note that these weights will be multiplied with sample_weight (passed<br>through the fit method) if sample_weight is specified.<br><br>.. versionadded:: 0.17<br>   *class_weight='balanced'*</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('random_state',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=random_state,-int%2C%20RandomState%20instance%2C%20default%3DNone">
                random_state
                <span class="param-doc-description">random_state: int, RandomState instance, default=None<br><br>Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the<br>data. See :term:`Glossary <random_state>` for details.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('solver',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=solver,-%7B%27lbfgs%27%2C%20%27liblinear%27%2C%20%27newton-cg%27%2C%20%27newton-cholesky%27%2C%20%27sag%27%2C%20%27saga%27%7D%2C%20%20%20%20%20%20%20%20%20%20%20%20%20default%3D%27lbfgs%27">
                solver
                <span class="param-doc-description">solver: {'lbfgs', 'liblinear', 'newton-cg', 'newton-cholesky', 'sag', 'saga'},             default='lbfgs'<br><br>Algorithm to use in the optimization problem. Default is 'lbfgs'.<br>To choose a solver, you might want to consider the following aspects:<br><br>- 'lbfgs' is a good default solver because it works reasonably well for a wide<br>  class of problems.<br>- For :term:`multiclass` problems (`n_classes >= 3`), all solvers except<br>  'liblinear' minimize the full multinomial loss, 'liblinear' will raise an<br>  error.<br>- 'newton-cholesky' is a good choice for<br>  `n_samples` >> `n_features * n_classes`, especially with one-hot encoded<br>  categorical features with rare categories. Be aware that the memory usage<br>  of this solver has a quadratic dependency on `n_features * n_classes`<br>  because it explicitly computes the full Hessian matrix.<br>- For small datasets, 'liblinear' is a good choice, whereas 'sag'<br>  and 'saga' are faster for large ones;<br>- 'liblinear' can only handle binary classification by default. To apply a<br>  one-versus-rest scheme for the multiclass setting one can wrap it with the<br>  :class:`~sklearn.multiclass.OneVsRestClassifier`.<br><br>.. warning::<br>   The choice of the algorithm depends on the penalty chosen (`l1_ratio=0`<br>   for L2-penalty, `l1_ratio=1` for L1-penalty and `0 < l1_ratio < 1` for<br>   Elastic-Net) and on (multinomial) multiclass support:<br><br>   ================= ======================== ======================<br>   solver            l1_ratio                 multinomial multiclass<br>   ================= ======================== ======================<br>   'lbfgs'           l1_ratio=0               yes<br>   'liblinear'       l1_ratio=1 or l1_ratio=0 no<br>   'newton-cg'       l1_ratio=0               yes<br>   'newton-cholesky' l1_ratio=0               yes<br>   'sag'             l1_ratio=0               yes<br>   'saga'            0<=l1_ratio<=1           yes<br>   ================= ======================== ======================<br><br>.. note::<br>   'sag' and 'saga' fast convergence is only guaranteed on features<br>   with approximately the same scale. You can preprocess the data with<br>   a scaler from :mod:`sklearn.preprocessing`.<br><br>.. seealso::<br>   Refer to the :ref:`User Guide <Logistic_regression>` for more<br>   information regarding :class:`LogisticRegression` and more specifically the<br>   :ref:`Table <logistic_regression_solvers>`<br>   summarizing solver/penalty supports.<br><br>.. versionadded:: 0.17<br>   Stochastic Average Gradient (SAG) descent solver. Multinomial support in<br>   version 0.18.<br>.. versionadded:: 0.19<br>   SAGA solver.<br>.. versionchanged:: 0.22<br>   The default solver changed from 'liblinear' to 'lbfgs' in 0.22.<br>.. versionadded:: 1.2<br>   newton-cholesky solver. Multinomial support in version 1.6.</span>
            </a>
        </td>
                <td class="value">&#x27;lbfgs&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_iter',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=max_iter,-int%2C%20default%3D100">
                max_iter
                <span class="param-doc-description">max_iter: int, default=100<br><br>Maximum number of iterations taken for the solvers to converge.</span>
            </a>
        </td>
                <td class="value">100</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('verbose',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=verbose,-int%2C%20default%3D0">
                verbose
                <span class="param-doc-description">verbose: int, default=0<br><br>For the liblinear and lbfgs solvers set verbose to any positive<br>number for verbosity.</span>
            </a>
        </td>
                <td class="value">0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('warm_start',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=warm_start,-bool%2C%20default%3DFalse">
                warm_start
                <span class="param-doc-description">warm_start: bool, default=False<br><br>When set to True, reuse the solution of the previous call to fit as<br>initialization, otherwise, just erase the previous solution.<br>Useless for liblinear solver. See :term:`the Glossary <warm_start>`.<br><br>.. versionadded:: 0.17<br>   *warm_start* to support *lbfgs*, *newton-cg*, *sag*, *saga* solvers.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('n_jobs',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html#:~:text=n_jobs,-int%2C%20default%3DNone">
                n_jobs
                <span class="param-doc-description">n_jobs: int, default=None<br><br>Does not have any effect.<br><br>.. deprecated:: 1.8<br>   `n_jobs` is deprecated in version 1.8 and will be removed in 1.10.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div></div></div></div></div><script>function copyToClipboard(text, element) {
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    document.querySelectorAll('.copy-paste-icon').forEach(function(element) {
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        const paramName = element.parentElement.nextElementSibling
            .textContent.trim().split(' ')[0];
        const fullParamName = paramPrefix ? `${paramPrefix}${paramName}` : paramName;

        element.setAttribute('title', fullParamName);
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    /**
     * Adapted from Skrub
     * https://github.com/skrub-data/skrub/blob/403466d1d5d4dc76a7ef569b3f8228db59a31dc3/skrub/_reporting/_data/templates/report.js#L789
     * @returns "light" or "dark"
     */
    function detectTheme(element) {
        const body = document.querySelector('body');

        // Check VSCode theme
        const themeKindAttr = body.getAttribute('data-vscode-theme-kind');
        const themeNameAttr = body.getAttribute('data-vscode-theme-name');

        if (themeKindAttr && themeNameAttr) {
            const themeKind = themeKindAttr.toLowerCase();
            const themeName = themeNameAttr.toLowerCase();

            if (themeKind.includes("dark") || themeName.includes("dark")) {
                return "dark";
            }
            if (themeKind.includes("light") || themeName.includes("light")) {
                return "light";
            }
        }

        // Check Jupyter theme
        if (body.getAttribute('data-jp-theme-light') === 'false') {
            return 'dark';
        } else if (body.getAttribute('data-jp-theme-light') === 'true') {
            return 'light';
        }

        // Guess based on a parent element's color
        const color = window.getComputedStyle(element.parentNode, null).getPropertyValue('color');
        const match = color.match(/^rgb\s*\(\s*(\d+)\s*,\s*(\d+)\s*,\s*(\d+)\s*\)\s*$/i);
        if (match) {
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            // https://en.wikipedia.org/wiki/HSL_and_HSV#Lightness
            const luma = 0.299 * r + 0.587 * g + 0.114 * b;

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                // If the text is very bright we have a dark theme
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    function forceTheme(elementId) {
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        } else {
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            estimatorElement.classList.add(theme);
        }
    }

    forceTheme('sk-container-id-66');</script></body>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 61-71

We evaluate our model using cross-validation. We use the accuracy and the balanced
accuracy to report the performance of our model. The balanced accuracy is a metric
that is less sensitive to class imbalance and will allow us to put the accuracy
score in perspective.

Cross-validation allows us to study the variance of the decision threshold across
different splits of the data. However, the dataset is rather small and it would be
detrimental to use more than 5 folds to evaluate the dispersion. Therefore, we use
a :class:`~sklearn.model_selection.RepeatedStratifiedKFold` where we apply several
repetitions of 5-fold cross-validation.

.. GENERATED FROM PYTHON SOURCE LINES 71-96

.. code-block:: Python

    import pandas as pd

    from sklearn.model_selection import RepeatedStratifiedKFold, cross_validate

    scoring = ["accuracy", "balanced_accuracy"]
    cv_scores = [
        "train_accuracy",
        "test_accuracy",
        "train_balanced_accuracy",
        "test_balanced_accuracy",
    ]
    cv = RepeatedStratifiedKFold(n_splits=5, n_repeats=10, random_state=42)
    cv_results_vanilla_model = pd.DataFrame(
        cross_validate(
            model,
            data,
            target,
            scoring=scoring,
            cv=cv,
            return_train_score=True,
            return_estimator=True,
        )
    )
    cv_results_vanilla_model[cv_scores].aggregate(["mean", "std"]).T






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>mean</th>
          <th>std</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>train_accuracy</th>
          <td>0.779751</td>
          <td>0.007822</td>
        </tr>
        <tr>
          <th>test_accuracy</th>
          <td>0.770926</td>
          <td>0.030585</td>
        </tr>
        <tr>
          <th>train_balanced_accuracy</th>
          <td>0.732913</td>
          <td>0.009788</td>
        </tr>
        <tr>
          <th>test_balanced_accuracy</th>
          <td>0.723665</td>
          <td>0.035914</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 97-116

Our predictive model succeeds to grasp the relationship between the data and the
target. The training and testing scores are close to each other, meaning that our
predictive model is not overfitting. We can also observe that the balanced accuracy is
lower than the accuracy, due to the class imbalance previously mentioned.

For this classifier, we let the decision threshold, used convert the probability of
the positive class into a class prediction, to its default value: 0.5. However, this
threshold might not be optimal. If our interest is to maximize the balanced accuracy,
we should select another threshold that would maximize this metric.

The :class:`~sklearn.model_selection.TunedThresholdClassifierCV` meta-estimator allows
to tune the decision threshold of a classifier given a metric of interest.

Tuning the decision threshold
-----------------------------

We create a :class:`~sklearn.model_selection.TunedThresholdClassifierCV` and
configure it to maximize the balanced accuracy. We evaluate the model using the same
cross-validation strategy as previously.

.. GENERATED FROM PYTHON SOURCE LINES 116-132

.. code-block:: Python

    from sklearn.model_selection import TunedThresholdClassifierCV

    tuned_model = TunedThresholdClassifierCV(estimator=model, scoring="balanced_accuracy")
    cv_results_tuned_model = pd.DataFrame(
        cross_validate(
            tuned_model,
            data,
            target,
            scoring=scoring,
            cv=cv,
            return_train_score=True,
            return_estimator=True,
        )
    )
    cv_results_tuned_model[cv_scores].aggregate(["mean", "std"]).T






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>mean</th>
          <th>std</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>train_accuracy</th>
          <td>0.752470</td>
          <td>0.015579</td>
        </tr>
        <tr>
          <th>test_accuracy</th>
          <td>0.739950</td>
          <td>0.036592</td>
        </tr>
        <tr>
          <th>train_balanced_accuracy</th>
          <td>0.757915</td>
          <td>0.009747</td>
        </tr>
        <tr>
          <th>test_balanced_accuracy</th>
          <td>0.744029</td>
          <td>0.035445</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 133-140

In comparison with the vanilla model, we observe that the balanced accuracy score
increased. Of course, it comes at the cost of a lower accuracy score. It means that
our model is now more sensitive to the positive class but makes more mistakes on the
negative class.

However, it is important to note that this tuned predictive model is internally the
same model as the vanilla model: they have the same fitted coefficients.

.. GENERATED FROM PYTHON SOURCE LINES 140-159

.. code-block:: Python

    import matplotlib.pyplot as plt

    vanilla_model_coef = pd.DataFrame(
        [est[-1].coef_.ravel() for est in cv_results_vanilla_model["estimator"]],
        columns=diabetes.feature_names,
    )
    tuned_model_coef = pd.DataFrame(
        [est.estimator_[-1].coef_.ravel() for est in cv_results_tuned_model["estimator"]],
        columns=diabetes.feature_names,
    )

    fig, ax = plt.subplots(ncols=2, figsize=(12, 4), sharex=True, sharey=True)
    vanilla_model_coef.boxplot(ax=ax[0])
    ax[0].set_ylabel("Coefficient value")
    ax[0].set_title("Vanilla model")
    tuned_model_coef.boxplot(ax=ax[1])
    ax[1].set_title("Tuned model")
    _ = fig.suptitle("Coefficients of the predictive models")




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_tuned_decision_threshold_001.png
   :alt: Coefficients of the predictive models, Vanilla model, Tuned model
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_tuned_decision_threshold_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 160-161

Only the decision threshold of each model was changed during the cross-validation.

.. GENERATED FROM PYTHON SOURCE LINES 161-177

.. code-block:: Python

    decision_threshold = pd.Series(
        [est.best_threshold_ for est in cv_results_tuned_model["estimator"]],
    )
    ax = decision_threshold.plot.kde()
    ax.axvline(
        decision_threshold.mean(),
        color="k",
        linestyle="--",
        label=f"Mean decision threshold: {decision_threshold.mean():.2f}",
    )
    ax.set_xlabel("Decision threshold")
    ax.legend(loc="upper right")
    _ = ax.set_title(
        "Distribution of the decision threshold \nacross different cross-validation folds"
    )




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_tuned_decision_threshold_002.png
   :alt: Distribution of the decision threshold  across different cross-validation folds
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_tuned_decision_threshold_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 178-188

In average, a decision threshold around 0.32 maximizes the balanced accuracy, which is
different from the default decision threshold of 0.5. Thus tuning the decision
threshold is particularly important when the output of the predictive model
is used to make decisions. Besides, the metric used to tune the decision threshold
should be chosen carefully. Here, we used the balanced accuracy but it might not be
the most appropriate metric for the problem at hand. The choice of the "right" metric
is usually problem-dependent and might require some domain knowledge. Refer to the
example entitled,
:ref:`sphx_glr_auto_examples_model_selection_plot_cost_sensitive_learning.py`,
for more details.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 35.350 seconds)


.. _sphx_glr_download_auto_examples_model_selection_plot_tuned_decision_threshold.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.8.X?urlpath=lab/tree/notebooks/auto_examples/model_selection/plot_tuned_decision_threshold.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

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        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_tuned_decision_threshold.ipynb <plot_tuned_decision_threshold.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_tuned_decision_threshold.py <plot_tuned_decision_threshold.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_tuned_decision_threshold.zip <plot_tuned_decision_threshold.zip>`


.. include:: plot_tuned_decision_threshold.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
