
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/ensemble/plot_voting_decision_regions.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_ensemble_plot_voting_decision_regions.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_ensemble_plot_voting_decision_regions.py:


===============================================================
Visualizing the probabilistic predictions of a VotingClassifier
===============================================================

.. currentmodule:: sklearn

Plot the predicted class probabilities in a toy dataset predicted by three
different classifiers and averaged by the :class:`~ensemble.VotingClassifier`.

First, three linear classifiers are initialized. Two are spline models with
interaction terms, one using constant extrapolation and the other using periodic
extrapolation. The third classifier is a :class:`~kernel_approximation.Nystroem`
with the default "rbf" kernel.

In the first part of this example, these three classifiers are used to
demonstrate soft-voting using :class:`~ensemble.VotingClassifier` with weighted
average. We set `weights=[2, 1, 3]`, meaning the constant extrapolation spline
model's predictions are weighted twice as much as the periodic spline model's,
and the Nystroem model's predictions are weighted three times as much as the
periodic spline.

The second part demonstrates how soft predictions can be converted into hard
predictions.

.. GENERATED FROM PYTHON SOURCE LINES 27-31

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 32-33

We first generate a noisy XOR dataset, which is a binary classification task.

.. GENERATED FROM PYTHON SOURCE LINES 33-65

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    import pandas as pd
    from matplotlib.colors import ListedColormap

    n_samples = 500
    rng = np.random.default_rng(0)
    feature_names = ["Feature #0", "Feature #1"]
    common_scatter_plot_params = dict(
        cmap=ListedColormap(["tab:red", "tab:blue"]),
        edgecolor="white",
        linewidth=1,
    )

    xor = pd.DataFrame(
        np.random.RandomState(0).uniform(low=-1, high=1, size=(n_samples, 2)),
        columns=feature_names,
    )
    noise = rng.normal(loc=0, scale=0.1, size=(n_samples, 2))
    target_xor = np.logical_xor(
        xor["Feature #0"] + noise[:, 0] > 0, xor["Feature #1"] + noise[:, 1] > 0
    )

    X = xor[feature_names]
    y = target_xor.astype(np.int32)

    fig, ax = plt.subplots()
    ax.scatter(X["Feature #0"], X["Feature #1"], c=y, **common_scatter_plot_params)
    ax.set_title("The XOR dataset")
    plt.show()




.. image-sg:: /auto_examples/ensemble/images/sphx_glr_plot_voting_decision_regions_001.png
   :alt: The XOR dataset
   :srcset: /auto_examples/ensemble/images/sphx_glr_plot_voting_decision_regions_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 66-73

Due to the inherent non-linear separability of the XOR dataset, tree-based
models would often be preferred. However, appropriate feature engineering
combined with a linear model can yield effective results, with the added
benefit of producing better-calibrated probabilities for samples located in
the transition regions affected by noise.

We define and fit the models on the whole dataset.

.. GENERATED FROM PYTHON SOURCE LINES 73-116

.. code-block:: Python


    from sklearn.ensemble import VotingClassifier
    from sklearn.kernel_approximation import Nystroem
    from sklearn.linear_model import LogisticRegression
    from sklearn.pipeline import make_pipeline
    from sklearn.preprocessing import PolynomialFeatures, SplineTransformer, StandardScaler

    clf1 = make_pipeline(
        SplineTransformer(degree=2, n_knots=2),
        PolynomialFeatures(interaction_only=True),
        LogisticRegression(C=10),
    )
    clf2 = make_pipeline(
        SplineTransformer(
            degree=2,
            n_knots=4,
            extrapolation="periodic",
            include_bias=True,
        ),
        PolynomialFeatures(interaction_only=True),
        LogisticRegression(C=10),
    )
    clf3 = make_pipeline(
        StandardScaler(),
        Nystroem(gamma=2, random_state=0),
        LogisticRegression(C=10),
    )
    weights = [2, 1, 3]
    eclf = VotingClassifier(
        estimators=[
            ("constant splines model", clf1),
            ("periodic splines model", clf2),
            ("nystroem model", clf3),
        ],
        voting="soft",
        weights=weights,
    )

    clf1.fit(X, y)
    clf2.fit(X, y)
    clf3.fit(X, y)
    eclf.fit(X, y)






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    </style><body><div id="sk-container-id-35" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>VotingClassifier(estimators=[(&#x27;constant splines model&#x27;,
                                  Pipeline(steps=[(&#x27;splinetransformer&#x27;,
                                                   SplineTransformer(degree=2,
                                                                     n_knots=2)),
                                                  (&#x27;polynomialfeatures&#x27;,
                                                   PolynomialFeatures(interaction_only=True)),
                                                  (&#x27;logisticregression&#x27;,
                                                   LogisticRegression(C=10))])),
                                 (&#x27;periodic splines model&#x27;,
                                  Pipeline(steps=[(&#x27;splinetransformer&#x27;,
                                                   SplineTransformer(degree=2,
                                                                     extrapolation=&#x27;periodic&#x27;,
                                                                     n_knots=4)),
                                                  (&#x27;polynomialfeatures&#x27;,
                                                   PolynomialFeatures(interaction_only=True)),
                                                  (&#x27;logisticregression&#x27;,
                                                   LogisticRegression(C=10))])),
                                 (&#x27;nystroem model&#x27;,
                                  Pipeline(steps=[(&#x27;standardscaler&#x27;,
                                                   StandardScaler()),
                                                  (&#x27;nystroem&#x27;,
                                                   Nystroem(gamma=2,
                                                            random_state=0)),
                                                  (&#x27;logisticregression&#x27;,
                                                   LogisticRegression(C=10))]))],
                     voting=&#x27;soft&#x27;, weights=[2, 1, 3])</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 fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-145" type="checkbox" ><label for="sk-estimator-id-145" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>VotingClassifier</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.ensemble.VotingClassifier.html">?<span>Documentation for VotingClassifier</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted" 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('estimators',
                              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.ensemble.VotingClassifier.html#:~:text=estimators,-list%20of%20%28str%2C%20estimator%29%20tuples">
                estimators
                <span class="param-doc-description">estimators: list of (str, estimator) tuples<br><br>Invoking the ``fit`` method on the ``VotingClassifier`` will fit clones<br>of those original estimators that will be stored in the class attribute<br>``self.estimators_``. An estimator can be set to ``'drop'`` using<br>:meth:`set_params`.<br><br>.. versionchanged:: 0.21<br>    ``'drop'`` is accepted. Using None was deprecated in 0.22 and<br>    support was removed in 0.24.</span>
            </a>
        </td>
                <td class="value">[(&#x27;constant splines model&#x27;, ...), (&#x27;periodic splines model&#x27;, ...), ...]</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('voting',
                              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.ensemble.VotingClassifier.html#:~:text=voting,-%7B%27hard%27%2C%20%27soft%27%7D%2C%20default%3D%27hard%27">
                voting
                <span class="param-doc-description">voting: {'hard', 'soft'}, default='hard'<br><br>If 'hard', uses predicted class labels for majority rule voting.<br>Else if 'soft', predicts the class label based on the argmax of<br>the sums of the predicted probabilities, which is recommended for<br>an ensemble of well-calibrated classifiers.</span>
            </a>
        </td>
                <td class="value">&#x27;soft&#x27;</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('weights',
                              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.ensemble.VotingClassifier.html#:~:text=weights,-array-like%20of%20shape%20%28n_classifiers%2C%29%2C%20default%3DNone">
                weights
                <span class="param-doc-description">weights: array-like of shape (n_classifiers,), default=None<br><br>Sequence of weights (`float` or `int`) to weight the occurrences of<br>predicted class labels (`hard` voting) or class probabilities<br>before averaging (`soft` voting). Uses uniform weights if `None`.</span>
            </a>
        </td>
                <td class="value">[2, 1, ...]</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.ensemble.VotingClassifier.html#:~:text=n_jobs,-int%2C%20default%3DNone">
                n_jobs
                <span class="param-doc-description">n_jobs: int, default=None<br><br>The number of jobs to run in parallel for ``fit``.<br>``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.<br>``-1`` means using all processors. See :term:`Glossary <n_jobs>`<br>for more details.<br><br>.. versionadded:: 0.18</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('flatten_transform',
                              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.ensemble.VotingClassifier.html#:~:text=flatten_transform,-bool%2C%20default%3DTrue">
                flatten_transform
                <span class="param-doc-description">flatten_transform: bool, default=True<br><br>Affects shape of transform output only when voting='soft'<br>If voting='soft' and flatten_transform=True, transform method returns<br>matrix with shape (n_samples, n_classifiers * n_classes). If<br>flatten_transform=False, it returns<br>(n_classifiers, n_samples, n_classes).</span>
            </a>
        </td>
                <td class="value">True</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.ensemble.VotingClassifier.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 will be printed as it<br>is completed.<br><br>.. versionadded:: 0.23</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-parallel"><div class="sk-parallel-item"><div class="sk-item"><div class="sk-label-container"><div class="sk-label fitted sk-toggleable"><label>constant splines model</label></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-serial"><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-146" type="checkbox" ><label for="sk-estimator-id-146" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>SplineTransformer</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.SplineTransformer.html">?<span>Documentation for SplineTransformer</span></a></div></label><div class="sk-toggleable__content fitted" data-param-prefix="constant splines model__splinetransformer__">
            <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('n_knots',
                              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.SplineTransformer.html#:~:text=n_knots,-int%2C%20default%3D5">
                n_knots
                <span class="param-doc-description">n_knots: int, default=5<br><br>Number of knots of the splines if `knots` equals one of<br>{'uniform', 'quantile'}. Must be larger or equal 2. Ignored if `knots`<br>is array-like.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('degree',
                              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.SplineTransformer.html#:~:text=degree,-int%2C%20default%3D3">
                degree
                <span class="param-doc-description">degree: int, default=3<br><br>The polynomial degree of the spline basis. Must be a non-negative<br>integer.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('knots',
                              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.SplineTransformer.html#:~:text=knots,-int%2C%20default%3D5">
                knots
                <span class="param-doc-description">knots: {'uniform', 'quantile'} or array-like of shape         (n_knots, n_features), default='uniform'<br><br>Set knot positions such that first knot <= features <= last knot.<br><br>- If 'uniform', `n_knots` number of knots are distributed uniformly<br>  from min to max values of the features.<br>- If 'quantile', they are distributed uniformly along the quantiles of<br>  the features.<br>- If an array-like is given, it directly specifies the sorted knot<br>  positions including the boundary knots. Note that, internally,<br>  `degree` number of knots are added before the first knot, the same<br>  after the last knot.</span>
            </a>
        </td>
                <td class="value">&#x27;uniform&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('extrapolation',
                              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.SplineTransformer.html#:~:text=extrapolation,-%7B%27error%27%2C%20%27constant%27%2C%20%27linear%27%2C%20%27continue%27%2C%20%27periodic%27%7D%2C%20%20%20%20%20%20%20%20%20default%3D%27constant%27">
                extrapolation
                <span class="param-doc-description">extrapolation: {'error', 'constant', 'linear', 'continue', 'periodic'},         default='constant'<br><br>If 'error', values outside the min and max values of the training<br>features raises a `ValueError`. If 'constant', the value of the<br>splines at minimum and maximum value of the features is used as<br>constant extrapolation. If 'linear', a linear extrapolation is used.<br>If 'continue', the splines are extrapolated as is, i.e. option<br>`extrapolate=True` in :class:`scipy.interpolate.BSpline`. If<br>'periodic', periodic splines with a periodicity equal to the distance<br>between the first and last knot are used. Periodic splines enforce<br>equal function values and derivatives at the first and last knot.<br>For example, this makes it possible to avoid introducing an arbitrary<br>jump between Dec 31st and Jan 1st in spline features derived from a<br>naturally periodic "day-of-year" input feature. In this case it is<br>recommended to manually set the knot values to control the period.</span>
            </a>
        </td>
                <td class="value">&#x27;constant&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('include_bias',
                              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.SplineTransformer.html#:~:text=include_bias,-bool%2C%20default%3DTrue">
                include_bias
                <span class="param-doc-description">include_bias: bool, default=True<br><br>If False, then the last spline element inside the data range<br>of a feature is dropped. As B-splines sum to one over the spline basis<br>functions for each data point, they implicitly include a bias term,<br>i.e. a column of ones. It acts as an intercept term in a linear models.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('order',
                              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.SplineTransformer.html#:~:text=order,-%7B%27C%27%2C%20%27F%27%7D%2C%20default%3D%27C%27">
                order
                <span class="param-doc-description">order: {'C', 'F'}, default='C'<br><br>Order of output array in the dense case. `'F'` order is faster to compute, but<br>may slow down subsequent estimators.</span>
            </a>
        </td>
                <td class="value">&#x27;C&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('handle_missing',
                              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.SplineTransformer.html#:~:text=handle_missing,-%7B%27error%27%2C%20%27zeros%27%7D%2C%20default%3D%27error%27">
                handle_missing
                <span class="param-doc-description">handle_missing: {'error', 'zeros'}, default='error'<br><br>Specifies the way missing values are handled.<br><br>- 'error' : Raise an error if `np.nan` values are present during :meth:`fit`.<br>- 'zeros' : Encode splines of missing values with values `0`.<br><br>Note that `handle_missing='zeros'` differs from first imputing missing values<br>with zeros and then creating the spline basis. The latter creates spline basis<br>functions which have non-zero values at the missing values<br>whereas this option simply sets all spline basis function values to zero at the<br>missing values.<br><br>.. versionadded:: 1.8</span>
            </a>
        </td>
                <td class="value">&#x27;error&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('sparse_output',
                              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.SplineTransformer.html#:~:text=sparse_output,-bool%2C%20default%3DFalse">
                sparse_output
                <span class="param-doc-description">sparse_output: bool, default=False<br><br>Will return sparse CSR matrix if set True else will return an array.<br><br>.. versionadded:: 1.2</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-147" type="checkbox" ><label for="sk-estimator-id-147" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>PolynomialFeatures</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.PolynomialFeatures.html">?<span>Documentation for PolynomialFeatures</span></a></div></label><div class="sk-toggleable__content fitted" data-param-prefix="constant splines model__polynomialfeatures__">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('degree',
                              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.PolynomialFeatures.html#:~:text=degree,-int%20or%20tuple%20%28min_degree%2C%20max_degree%29%2C%20default%3D2">
                degree
                <span class="param-doc-description">degree: int or tuple (min_degree, max_degree), default=2<br><br>If a single int is given, it specifies the maximal degree of the<br>polynomial features. If a tuple `(min_degree, max_degree)` is passed,<br>then `min_degree` is the minimum and `max_degree` is the maximum<br>polynomial degree of the generated features. Note that `min_degree=0`<br>and `min_degree=1` are equivalent as outputting the degree zero term is<br>determined by `include_bias`.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('interaction_only',
                              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.PolynomialFeatures.html#:~:text=interaction_only,-bool%2C%20default%3DFalse">
                interaction_only
                <span class="param-doc-description">interaction_only: bool, default=False<br><br>If `True`, only interaction features are produced: features that are<br>products of at most `degree` *distinct* input features, i.e. terms with<br>power of 2 or higher of the same input feature are excluded:<br><br>- included: `x[0]`, `x[1]`, `x[0] * x[1]`, etc.<br>- excluded: `x[0] ** 2`, `x[0] ** 2 * x[1]`, etc.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('include_bias',
                              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.PolynomialFeatures.html#:~:text=include_bias,-bool%2C%20default%3DTrue">
                include_bias
                <span class="param-doc-description">include_bias: bool, default=True<br><br>If `True` (default), then include a bias column, the feature in which<br>all polynomial powers are zero (i.e. a column of ones - acts as an<br>intercept term in a linear model).</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('order',
                              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.PolynomialFeatures.html#:~:text=order,-%7B%27C%27%2C%20%27F%27%7D%2C%20default%3D%27C%27">
                order
                <span class="param-doc-description">order: {'C', 'F'}, default='C'<br><br>Order of output array in the dense case. `'F'` order is faster to<br>compute, but may slow down subsequent estimators.<br><br>.. versionadded:: 0.21</span>
            </a>
        </td>
                <td class="value">&#x27;C&#x27;</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-148" type="checkbox" ><label for="sk-estimator-id-148" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>LogisticRegression</div></div><div><a class="sk-estimator-doc-link fitted" 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 fitted" data-param-prefix="constant splines model__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="user-set">
                <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">10</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></div><div class="sk-parallel-item"><div class="sk-item"><div class="sk-label-container"><div class="sk-label fitted sk-toggleable"><label>periodic splines model</label></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-serial"><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-149" type="checkbox" ><label for="sk-estimator-id-149" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>SplineTransformer</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.SplineTransformer.html">?<span>Documentation for SplineTransformer</span></a></div></label><div class="sk-toggleable__content fitted" data-param-prefix="periodic splines model__splinetransformer__">
            <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('n_knots',
                              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.SplineTransformer.html#:~:text=n_knots,-int%2C%20default%3D5">
                n_knots
                <span class="param-doc-description">n_knots: int, default=5<br><br>Number of knots of the splines if `knots` equals one of<br>{'uniform', 'quantile'}. Must be larger or equal 2. Ignored if `knots`<br>is array-like.</span>
            </a>
        </td>
                <td class="value">4</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('degree',
                              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.SplineTransformer.html#:~:text=degree,-int%2C%20default%3D3">
                degree
                <span class="param-doc-description">degree: int, default=3<br><br>The polynomial degree of the spline basis. Must be a non-negative<br>integer.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('knots',
                              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.SplineTransformer.html#:~:text=knots,-int%2C%20default%3D5">
                knots
                <span class="param-doc-description">knots: {'uniform', 'quantile'} or array-like of shape         (n_knots, n_features), default='uniform'<br><br>Set knot positions such that first knot <= features <= last knot.<br><br>- If 'uniform', `n_knots` number of knots are distributed uniformly<br>  from min to max values of the features.<br>- If 'quantile', they are distributed uniformly along the quantiles of<br>  the features.<br>- If an array-like is given, it directly specifies the sorted knot<br>  positions including the boundary knots. Note that, internally,<br>  `degree` number of knots are added before the first knot, the same<br>  after the last knot.</span>
            </a>
        </td>
                <td class="value">&#x27;uniform&#x27;</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('extrapolation',
                              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.SplineTransformer.html#:~:text=extrapolation,-%7B%27error%27%2C%20%27constant%27%2C%20%27linear%27%2C%20%27continue%27%2C%20%27periodic%27%7D%2C%20%20%20%20%20%20%20%20%20default%3D%27constant%27">
                extrapolation
                <span class="param-doc-description">extrapolation: {'error', 'constant', 'linear', 'continue', 'periodic'},         default='constant'<br><br>If 'error', values outside the min and max values of the training<br>features raises a `ValueError`. If 'constant', the value of the<br>splines at minimum and maximum value of the features is used as<br>constant extrapolation. If 'linear', a linear extrapolation is used.<br>If 'continue', the splines are extrapolated as is, i.e. option<br>`extrapolate=True` in :class:`scipy.interpolate.BSpline`. If<br>'periodic', periodic splines with a periodicity equal to the distance<br>between the first and last knot are used. Periodic splines enforce<br>equal function values and derivatives at the first and last knot.<br>For example, this makes it possible to avoid introducing an arbitrary<br>jump between Dec 31st and Jan 1st in spline features derived from a<br>naturally periodic "day-of-year" input feature. In this case it is<br>recommended to manually set the knot values to control the period.</span>
            </a>
        </td>
                <td class="value">&#x27;periodic&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('include_bias',
                              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.SplineTransformer.html#:~:text=include_bias,-bool%2C%20default%3DTrue">
                include_bias
                <span class="param-doc-description">include_bias: bool, default=True<br><br>If False, then the last spline element inside the data range<br>of a feature is dropped. As B-splines sum to one over the spline basis<br>functions for each data point, they implicitly include a bias term,<br>i.e. a column of ones. It acts as an intercept term in a linear models.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('order',
                              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.SplineTransformer.html#:~:text=order,-%7B%27C%27%2C%20%27F%27%7D%2C%20default%3D%27C%27">
                order
                <span class="param-doc-description">order: {'C', 'F'}, default='C'<br><br>Order of output array in the dense case. `'F'` order is faster to compute, but<br>may slow down subsequent estimators.</span>
            </a>
        </td>
                <td class="value">&#x27;C&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('handle_missing',
                              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.SplineTransformer.html#:~:text=handle_missing,-%7B%27error%27%2C%20%27zeros%27%7D%2C%20default%3D%27error%27">
                handle_missing
                <span class="param-doc-description">handle_missing: {'error', 'zeros'}, default='error'<br><br>Specifies the way missing values are handled.<br><br>- 'error' : Raise an error if `np.nan` values are present during :meth:`fit`.<br>- 'zeros' : Encode splines of missing values with values `0`.<br><br>Note that `handle_missing='zeros'` differs from first imputing missing values<br>with zeros and then creating the spline basis. The latter creates spline basis<br>functions which have non-zero values at the missing values<br>whereas this option simply sets all spline basis function values to zero at the<br>missing values.<br><br>.. versionadded:: 1.8</span>
            </a>
        </td>
                <td class="value">&#x27;error&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('sparse_output',
                              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.SplineTransformer.html#:~:text=sparse_output,-bool%2C%20default%3DFalse">
                sparse_output
                <span class="param-doc-description">sparse_output: bool, default=False<br><br>Will return sparse CSR matrix if set True else will return an array.<br><br>.. versionadded:: 1.2</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-150" type="checkbox" ><label for="sk-estimator-id-150" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>PolynomialFeatures</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.preprocessing.PolynomialFeatures.html">?<span>Documentation for PolynomialFeatures</span></a></div></label><div class="sk-toggleable__content fitted" data-param-prefix="periodic splines model__polynomialfeatures__">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('degree',
                              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.PolynomialFeatures.html#:~:text=degree,-int%20or%20tuple%20%28min_degree%2C%20max_degree%29%2C%20default%3D2">
                degree
                <span class="param-doc-description">degree: int or tuple (min_degree, max_degree), default=2<br><br>If a single int is given, it specifies the maximal degree of the<br>polynomial features. If a tuple `(min_degree, max_degree)` is passed,<br>then `min_degree` is the minimum and `max_degree` is the maximum<br>polynomial degree of the generated features. Note that `min_degree=0`<br>and `min_degree=1` are equivalent as outputting the degree zero term is<br>determined by `include_bias`.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('interaction_only',
                              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.PolynomialFeatures.html#:~:text=interaction_only,-bool%2C%20default%3DFalse">
                interaction_only
                <span class="param-doc-description">interaction_only: bool, default=False<br><br>If `True`, only interaction features are produced: features that are<br>products of at most `degree` *distinct* input features, i.e. terms with<br>power of 2 or higher of the same input feature are excluded:<br><br>- included: `x[0]`, `x[1]`, `x[0] * x[1]`, etc.<br>- excluded: `x[0] ** 2`, `x[0] ** 2 * x[1]`, etc.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('include_bias',
                              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.PolynomialFeatures.html#:~:text=include_bias,-bool%2C%20default%3DTrue">
                include_bias
                <span class="param-doc-description">include_bias: bool, default=True<br><br>If `True` (default), then include a bias column, the feature in which<br>all polynomial powers are zero (i.e. a column of ones - acts as an<br>intercept term in a linear model).</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('order',
                              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.PolynomialFeatures.html#:~:text=order,-%7B%27C%27%2C%20%27F%27%7D%2C%20default%3D%27C%27">
                order
                <span class="param-doc-description">order: {'C', 'F'}, default='C'<br><br>Order of output array in the dense case. `'F'` order is faster to<br>compute, but may slow down subsequent estimators.<br><br>.. versionadded:: 0.21</span>
            </a>
        </td>
                <td class="value">&#x27;C&#x27;</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-151" type="checkbox" ><label for="sk-estimator-id-151" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>LogisticRegression</div></div><div><a class="sk-estimator-doc-link fitted" 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 fitted" data-param-prefix="periodic splines model__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="user-set">
                <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">10</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></div><div class="sk-parallel-item"><div class="sk-item"><div class="sk-label-container"><div class="sk-label fitted sk-toggleable"><label>nystroem model</label></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-serial"><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-152" type="checkbox" ><label for="sk-estimator-id-152" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>StandardScaler</div></div><div><a class="sk-estimator-doc-link fitted" 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 fitted" data-param-prefix="nystroem model__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 fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-153" type="checkbox" ><label for="sk-estimator-id-153" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>Nystroem</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.kernel_approximation.Nystroem.html">?<span>Documentation for Nystroem</span></a></div></label><div class="sk-toggleable__content fitted" data-param-prefix="nystroem model__nystroem__">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('kernel',
                              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.kernel_approximation.Nystroem.html#:~:text=kernel,-str%20or%20callable%2C%20default%3D%27rbf%27">
                kernel
                <span class="param-doc-description">kernel: str or callable, default='rbf'<br><br>Kernel map to be approximated. A callable should accept two arguments<br>and the keyword arguments passed to this object as `kernel_params`, and<br>should return a floating point number.</span>
            </a>
        </td>
                <td class="value">&#x27;rbf&#x27;</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('gamma',
                              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.kernel_approximation.Nystroem.html#:~:text=gamma,-float%2C%20default%3DNone">
                gamma
                <span class="param-doc-description">gamma: float, default=None<br><br>Gamma parameter for the RBF, laplacian, polynomial, exponential chi2<br>and sigmoid kernels. Interpretation of the default value is left to<br>the kernel; see the documentation for sklearn.metrics.pairwise.<br>Ignored by other kernels.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('coef0',
                              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.kernel_approximation.Nystroem.html#:~:text=coef0,-float%2C%20default%3DNone">
                coef0
                <span class="param-doc-description">coef0: float, default=None<br><br>Zero coefficient for polynomial and sigmoid kernels.<br>Ignored by other kernels.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('degree',
                              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.kernel_approximation.Nystroem.html#:~:text=degree,-float%2C%20default%3DNone">
                degree
                <span class="param-doc-description">degree: float, default=None<br><br>Degree of the polynomial kernel. Ignored by other kernels.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('kernel_params',
                              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.kernel_approximation.Nystroem.html#:~:text=kernel_params,-dict%2C%20default%3DNone">
                kernel_params
                <span class="param-doc-description">kernel_params: dict, default=None<br><br>Additional parameters (keyword arguments) for kernel function passed<br>as callable object.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('n_components',
                              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.kernel_approximation.Nystroem.html#:~:text=n_components,-int%2C%20default%3D100">
                n_components
                <span class="param-doc-description">n_components: int, default=100<br><br>Number of features to construct.<br>How many data points will be used to construct the mapping.</span>
            </a>
        </td>
                <td class="value">100</td>
            </tr>
    

            <tr class="user-set">
                <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.kernel_approximation.Nystroem.html#:~:text=random_state,-int%2C%20RandomState%20instance%20or%20None%2C%20default%3DNone">
                random_state
                <span class="param-doc-description">random_state: int, RandomState instance or None, default=None<br><br>Pseudo-random number generator to control the uniform sampling without<br>replacement of `n_components` of the training data to construct the<br>basis kernel.<br>Pass an int for reproducible output across multiple function calls.<br>See :term:`Glossary <random_state>`.</span>
            </a>
        </td>
                <td class="value">0</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.kernel_approximation.Nystroem.html#:~:text=n_jobs,-int%2C%20default%3DNone">
                n_jobs
                <span class="param-doc-description">n_jobs: int, default=None<br><br>The number of jobs to use for the computation. This works by breaking<br>down the kernel matrix into `n_jobs` even slices and computing them in<br>parallel.<br><br>``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.<br>``-1`` means using all processors. See :term:`Glossary <n_jobs>`<br>for more details.<br><br>.. versionadded:: 0.24</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-154" type="checkbox" ><label for="sk-estimator-id-154" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>LogisticRegression</div></div><div><a class="sk-estimator-doc-link fitted" 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 fitted" data-param-prefix="nystroem model__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="user-set">
                <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">10</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></div></div></div></div></div><script>function copyToClipboard(text, element) {
        // Get the parameter prefix from the closest toggleable content
        const toggleableContent = element.closest('.sk-toggleable__content');
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        const fullParamName = paramPrefix ? `${paramPrefix}${text}` : text;

        const originalStyle = element.style;
        const computedStyle = window.getComputedStyle(element);
        const originalWidth = computedStyle.width;
        const originalHTML = element.innerHTML.replace('Copied!', '');

        navigator.clipboard.writeText(fullParamName)
            .then(() => {
                element.style.width = originalWidth;
                element.style.color = 'green';
                element.innerHTML = "Copied!";

                setTimeout(() => {
                    element.innerHTML = originalHTML;
                    element.style = originalStyle;
                }, 2000);
            })
            .catch(err => {
                console.error('Failed to copy:', err);
                element.style.color = 'red';
                element.innerHTML = "Failed!";
                setTimeout(() => {
                    element.innerHTML = originalHTML;
                    element.style = originalStyle;
                }, 2000);
            });
        return false;
    }

    document.querySelectorAll('.copy-paste-icon').forEach(function(element) {
        const toggleableContent = element.closest('.sk-toggleable__content');
        const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : '';
        const paramName = element.parentElement.nextElementSibling
            .textContent.trim().split(' ')[0];
        const fullParamName = paramPrefix ? `${paramPrefix}${paramName}` : paramName;

        element.setAttribute('title', fullParamName);
    });


    /**
     * 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) {
            const [r, g, b] = [
                parseFloat(match[1]),
                parseFloat(match[2]),
                parseFloat(match[3])
            ];

            // https://en.wikipedia.org/wiki/HSL_and_HSV#Lightness
            const luma = 0.299 * r + 0.587 * g + 0.114 * b;

            if (luma > 180) {
                // If the text is very bright we have a dark theme
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            }
            if (luma < 75) {
                // If the text is very dark we have a light theme
                return 'light';
            }
            // Otherwise fall back to the next heuristic.
        }

        // Fallback to system preference
        return window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light';
    }


    function forceTheme(elementId) {
        const estimatorElement = document.querySelector(`#${elementId}`);
        if (estimatorElement === null) {
            console.error(`Element with id ${elementId} not found.`);
        } else {
            const theme = detectTheme(estimatorElement);
            estimatorElement.classList.add(theme);
        }
    }

    forceTheme('sk-container-id-35');</script></body>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 117-121

Finally we use :class:`~inspection.DecisionBoundaryDisplay` to plot the
predicted probabilities. By using a diverging colormap (such as `"RdBu"`), we
can ensure that darker colors correspond to `predict_proba` close to either 0
or 1, and white corresponds to `predict_proba` of 0.5.

.. GENERATED FROM PYTHON SOURCE LINES 121-157

.. code-block:: Python


    from itertools import product

    from sklearn.inspection import DecisionBoundaryDisplay

    fig, axarr = plt.subplots(2, 2, sharex="col", sharey="row", figsize=(10, 8))
    for idx, clf, title in zip(
        product([0, 1], [0, 1]),
        [clf1, clf2, clf3, eclf],
        [
            "Splines with\nconstant extrapolation",
            "Splines with\nperiodic extrapolation",
            "RBF Nystroem",
            "Soft Voting",
        ],
    ):
        disp = DecisionBoundaryDisplay.from_estimator(
            clf,
            X,
            response_method="predict_proba",
            plot_method="pcolormesh",
            cmap="RdBu",
            alpha=0.8,
            ax=axarr[idx[0], idx[1]],
        )
        axarr[idx[0], idx[1]].scatter(
            X["Feature #0"],
            X["Feature #1"],
            c=y,
            **common_scatter_plot_params,
        )
        axarr[idx[0], idx[1]].set_title(title)
        fig.colorbar(disp.surface_, ax=axarr[idx[0], idx[1]], label="Probability estimate")

    plt.show()




.. image-sg:: /auto_examples/ensemble/images/sphx_glr_plot_voting_decision_regions_002.png
   :alt: Splines with constant extrapolation, Splines with periodic extrapolation, RBF Nystroem, Soft Voting
   :srcset: /auto_examples/ensemble/images/sphx_glr_plot_voting_decision_regions_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 158-166

As a sanity check, we can verify for a given sample that the probability
predicted by the :class:`~ensemble.VotingClassifier` is indeed the weighted
average of the individual classifiers' soft-predictions.

In the case of binary classification such as in the present example, the
:term:`predict_proba` arrays contain the probability of belonging to class 0
(here in red) as the first entry, and the probability of belonging to class 1
(here in blue) as the second entry.

.. GENERATED FROM PYTHON SOURCE LINES 166-172

.. code-block:: Python


    test_sample = pd.DataFrame({"Feature #0": [-0.5], "Feature #1": [1.5]})
    predict_probas = [est.predict_proba(test_sample).ravel() for est in eclf.estimators_]
    for (est_name, _), est_probas in zip(eclf.estimators, predict_probas):
        print(f"{est_name}'s predicted probabilities: {est_probas}")





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

 .. code-block:: none

    constant splines model's predicted probabilities: [0.11272662 0.88727338]
    periodic splines model's predicted probabilities: [0.99726573 0.00273427]
    nystroem model's predicted probabilities: [0.3185838 0.6814162]




.. GENERATED FROM PYTHON SOURCE LINES 173-178

.. code-block:: Python

    print(
        "Weighted average of soft-predictions: "
        f"{np.dot(weights, predict_probas) / np.sum(weights)}"
    )





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

 .. code-block:: none

    Weighted average of soft-predictions: [0.3630784 0.6369216]




.. GENERATED FROM PYTHON SOURCE LINES 179-181

We can see that manual calculation of predicted probabilities above is
equivalent to that produced by the `VotingClassifier`:

.. GENERATED FROM PYTHON SOURCE LINES 181-187

.. code-block:: Python


    print(
        "Predicted probability of VotingClassifier: "
        f"{eclf.predict_proba(test_sample).ravel()}"
    )





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

 .. code-block:: none

    Predicted probability of VotingClassifier: [0.3630784 0.6369216]




.. GENERATED FROM PYTHON SOURCE LINES 188-193

To convert soft predictions into hard predictions when weights are provided,
the weighted average predicted probabilities are computed for each class.
Then, the final class label is then derived from the class label with the
highest average probability, which corresponds to the default threshold at
`predict_proba=0.5` in the case of binary classification.

.. GENERATED FROM PYTHON SOURCE LINES 193-199

.. code-block:: Python


    print(
        "Class with the highest weighted average of soft-predictions: "
        f"{np.argmax(np.dot(weights, predict_probas) / np.sum(weights))}"
    )





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

 .. code-block:: none

    Class with the highest weighted average of soft-predictions: 1




.. GENERATED FROM PYTHON SOURCE LINES 200-201

This is equivalent to the output of `VotingClassifier`'s `predict` method:

.. GENERATED FROM PYTHON SOURCE LINES 201-204

.. code-block:: Python


    print(f"Predicted class of VotingClassifier: {eclf.predict(test_sample).ravel()}")





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

 .. code-block:: none

    Predicted class of VotingClassifier: [1]




.. GENERATED FROM PYTHON SOURCE LINES 205-209

Soft votes can be thresholded as for any other probabilistic classifier. This
allows you to set a threshold probability at which the positive class will be
predicted, instead of simply selecting the class with the highest predicted
probability.

.. GENERATED FROM PYTHON SOURCE LINES 209-219

.. code-block:: Python


    from sklearn.model_selection import FixedThresholdClassifier

    eclf_other_threshold = FixedThresholdClassifier(
        eclf, threshold=0.7, response_method="predict_proba"
    ).fit(X, y)
    print(
        "Predicted class of thresholded VotingClassifier: "
        f"{eclf_other_threshold.predict(test_sample)}"
    )




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

 .. code-block:: none

    Predicted class of thresholded VotingClassifier: [0]





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

   **Total running time of the script:** (0 minutes 0.727 seconds)


.. _sphx_glr_download_auto_examples_ensemble_plot_voting_decision_regions.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/ensemble/plot_voting_decision_regions.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/index.html?path=auto_examples/ensemble/plot_voting_decision_regions.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_voting_decision_regions.recommendations


.. only:: html

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

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