
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/release_highlights/plot_release_highlights_1_8_0.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_release_highlights_plot_release_highlights_1_8_0.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_release_highlights_plot_release_highlights_1_8_0.py:


=======================================
Release Highlights for scikit-learn 1.8
=======================================

.. currentmodule:: sklearn

We are pleased to announce the release of scikit-learn 1.8! Many bug fixes
and improvements were added, as well as some key new features. Below we
detail the highlights of this release. **For an exhaustive list of
all the changes**, please refer to the :ref:`release notes <release_notes_1_8>`.

To install the latest version (with pip)::

    pip install --upgrade scikit-learn

or with conda::

    conda install -c conda-forge scikit-learn

.. GENERATED FROM PYTHON SOURCE LINES 25-78

Array API support (enables GPU computations)
--------------------------------------------
The progressive adoption of the Python array API standard in
scikit-learn means that PyTorch and CuPy input arrays
are used directly. This means that in scikit-learn estimators
and functions non-CPU devices, such as GPUs, can be used
to perform the computation. As a result performance is improved
and integration with these libraries is easier.

In scikit-learn 1.8, several estimators and functions have been updated to
support array API compatible inputs, for example PyTorch tensors and CuPy
arrays.

Array API support was added to the following estimators:
:class:`preprocessing.StandardScaler`,
:class:`preprocessing.PolynomialFeatures`, :class:`linear_model.RidgeCV`,
:class:`linear_model.RidgeClassifierCV`, :class:`mixture.GaussianMixture` and
:class:`calibration.CalibratedClassifierCV`.

Array API support was also added to several metrics in :mod:`sklearn.metrics`
module, see :ref:`array_api_supported` for more details.

Please refer to the :ref:`array API support<array_api>` page for instructions
to use scikit-learn with array API compatible libraries such as PyTorch or CuPy.
Note: Array API support is experimental and must be explicitly enabled both
in SciPy and scikit-learn.

Here is an excerpt of using a feature engineering preprocessor on the CPU,
followed by :class:`calibration.CalibratedClassifierCV`
and :class:`linear_model.RidgeCV` together on a GPU with the help of PyTorch:

.. code-block:: python

    ridge_pipeline_gpu = make_pipeline(
        # Ensure that all features (including categorical features) are preprocessed
        # on the CPU and mapped to a numerical representation.
        feature_preprocessor,
        # Move the results to the GPU and perform computations there
        FunctionTransformer(
            lambda x: torch.tensor(x.to_numpy().astype(np.float32), device="cuda"))
        ,
        CalibratedClassifierCV(
            RidgeClassifierCV(alphas=alphas), method="temperature"
        ),
    )
    with sklearn.config_context(array_api_dispatch=True):
        cv_results = cross_validate(ridge_pipeline_gpu, features, target)


See the `full notebook on Google Colab
<https://colab.research.google.com/drive/1ztH8gUPv31hSjEeR_8pw20qShTwViGRx?usp=sharing>`_
for more details. On this particular example, using the Colab GPU vs using a
single CPU core leads to a 10x speedup which is quite typical for such workloads.

.. GENERATED FROM PYTHON SOURCE LINES 80-125

Free-threaded CPython 3.14 support
----------------------------------

scikit-learn has support for free-threaded CPython, in particular
free-threaded wheels are available for all of our supported platforms on Python
3.14.

We would be very interested by user feedback. Here are a few things you can
try:

- install free-threaded CPython 3.14, run your favourite
  scikit-learn script and check that nothing breaks unexpectedly.
  Note that CPython 3.14 (rather than 3.13) is strongly advised because a
  number of free-threaded bugs have been fixed since CPython 3.13.
- if you use some estimators with a `n_jobs` parameter, try changing the
  default backend to threading with `joblib.parallel_config` as in the
  snippet below. This could potentially speed-up your code because the
  default joblib backend is process-based and incurs more overhead than
  threads.

  .. code-block:: python

      grid_search = GridSearchCV(clf, param_grid=param_grid, n_jobs=4)
      with joblib.parallel_config(backend="threading"):
          grid_search.fit(X, y)

- don't hesitate to report any issue or unexpected performance behaviour by
  opening a `GitHub issue <https://github.com/scikit-learn/scikit-learn/issues/new/choose>`_!

Free-threaded (also known as nogil) CPython is a version of CPython that aims
to enable efficient multi-threaded use cases by removing the Global
Interpreter Lock (GIL).

For more details about free-threaded CPython see `py-free-threading doc
<https://py-free-threading.github.io>`_, in particular `how to install a
free-threaded CPython <https://py-free-threading.github.io/installing-cpython/>`_
and `Ecosystem compatibility tracking <https://py-free-threading.github.io/tracking/>`_.

In scikit-learn, one hope with free-threaded Python is to more efficiently
leverage multi-core CPUs by using thread workers instead of subprocess
workers for parallel computation when passing `n_jobs>1` in functions or
estimators. Efficiency gains are expected by removing the need for
inter-process communication. Be aware that switching the default joblib
backend and testing that everything works well with free-threaded Python is an
ongoing long-term effort.

.. GENERATED FROM PYTHON SOURCE LINES 127-135

Temperature scaling in `CalibratedClassifierCV`
-----------------------------------------------
Probability calibration of classifiers with temperature scaling is available in
:class:`calibration.CalibratedClassifierCV` by setting `method="temperature"`.
This method is particularly well suited for multiclass problems because it provides
(better) calibrated probabilities with a single free parameter. This is in
contrast to all the other available calibrations methods
which use a "One-vs-Rest" scheme that adds more parameters for each class.

.. GENERATED FROM PYTHON SOURCE LINES 135-145

.. code-block:: Python


    from sklearn.calibration import CalibratedClassifierCV
    from sklearn.datasets import make_classification
    from sklearn.naive_bayes import GaussianNB

    X, y = make_classification(n_classes=3, n_informative=8, random_state=42)
    clf = GaussianNB().fit(X, y)
    sig = CalibratedClassifierCV(clf, method="sigmoid", ensemble=False).fit(X, y)
    ts = CalibratedClassifierCV(clf, method="temperature", ensemble=False).fit(X, y)








.. GENERATED FROM PYTHON SOURCE LINES 146-149

The following example shows that temperature scaling can produce better calibrated
probabilities than sigmoid calibration in multi-class classification problem
with 3 classes.

.. GENERATED FROM PYTHON SOURCE LINES 149-184

.. code-block:: Python


    import matplotlib.pyplot as plt

    from sklearn.calibration import CalibrationDisplay

    fig, axes = plt.subplots(
        figsize=(8, 4.5),
        ncols=3,
        sharey=True,
    )
    for i, c in enumerate(ts.classes_):
        CalibrationDisplay.from_predictions(
            y == c, clf.predict_proba(X)[:, i], name="Uncalibrated", ax=axes[i], marker="s"
        )
        CalibrationDisplay.from_predictions(
            y == c,
            ts.predict_proba(X)[:, i],
            name="Temperature scaling",
            ax=axes[i],
            marker="o",
        )
        CalibrationDisplay.from_predictions(
            y == c, sig.predict_proba(X)[:, i], name="Sigmoid", ax=axes[i], marker="v"
        )
        axes[i].set_title(f"Class {c}")
        axes[i].set_xlabel(None)
        axes[i].set_ylabel(None)
        axes[i].get_legend().remove()
    fig.suptitle("Reliability Diagrams per Class")
    fig.supxlabel("Mean Predicted Probability")
    fig.supylabel("Fraction of Class")
    fig.legend(*axes[0].get_legend_handles_labels(), loc=(0.72, 0.5))
    plt.subplots_adjust(right=0.7)
    _ = fig.show()




.. image-sg:: /auto_examples/release_highlights/images/sphx_glr_plot_release_highlights_1_8_0_001.png
   :alt: Reliability Diagrams per Class, Class 0, Class 1, Class 2
   :srcset: /auto_examples/release_highlights/images/sphx_glr_plot_release_highlights_1_8_0_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 185-194

Efficiency improvements in linear models
----------------------------------------
The fit time has been massively reduced for squared error based estimators
with L1 penalty: `ElasticNet`, `Lasso`, `MultiTaskElasticNet`,
`MultiTaskLasso` and their CV variants. The fit time improvement is mainly
achieved by **gap safe screening rules**. They enable the coordinate descent
solver to set feature coefficients to zero early on and not look at them
again. The stronger the L1 penalty the earlier features can be excluded from
further updates.

.. GENERATED FROM PYTHON SOURCE LINES 194-207

.. code-block:: Python


    from time import time

    from sklearn.datasets import make_regression
    from sklearn.linear_model import ElasticNetCV

    X, y = make_regression(n_features=10_000, random_state=0)
    model = ElasticNetCV()
    tic = time()
    model.fit(X, y)
    toc = time()
    print(f"Fitting ElasticNetCV took {toc - tic:.3} seconds.")





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

 .. code-block:: none

    Fitting ElasticNetCV took 16.8 seconds.




.. GENERATED FROM PYTHON SOURCE LINES 208-213

HTML representation of estimators
---------------------------------
Hyperparameters in the dropdown table of the HTML representation now include
links to the online documentation. Docstring descriptions are also shown as
tooltips on hover.

.. GENERATED FROM PYTHON SOURCE LINES 213-220

.. code-block:: Python


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

    clf = make_pipeline(StandardScaler(), LogisticRegression(random_state=0, C=10))








.. GENERATED FROM PYTHON SOURCE LINES 221-223

Expand the estimator diagram below by clicking on "LogisticRegression" and then on
"Parameters".

.. GENERATED FROM PYTHON SOURCE LINES 223-227

.. code-block:: Python


    clf







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <style>#sk-container-id-1 {
      /* Definition of color scheme common for light and dark mode */
      --sklearn-color-text: #000;
      --sklearn-color-text-muted: #666;
      --sklearn-color-line: gray;
      /* Definition of color scheme for unfitted estimators */
      --sklearn-color-unfitted-level-0: #fff5e6;
      --sklearn-color-unfitted-level-1: #f6e4d2;
      --sklearn-color-unfitted-level-2: #ffe0b3;
      --sklearn-color-unfitted-level-3: chocolate;
      /* Definition of color scheme for fitted estimators */
      --sklearn-color-fitted-level-0: #f0f8ff;
      --sklearn-color-fitted-level-1: #d4ebff;
      --sklearn-color-fitted-level-2: #b3dbfd;
      --sklearn-color-fitted-level-3: cornflowerblue;
    }

    #sk-container-id-1.light {
      /* Specific color for light theme */
      --sklearn-color-text-on-default-background: black;
      --sklearn-color-background: white;
      --sklearn-color-border-box: black;
      --sklearn-color-icon: #696969;
    }

    #sk-container-id-1.dark {
      --sklearn-color-text-on-default-background: white;
      --sklearn-color-background: #111;
      --sklearn-color-border-box: white;
      --sklearn-color-icon: #878787;
    }

    #sk-container-id-1 {
      color: var(--sklearn-color-text);
    }

    #sk-container-id-1 pre {
      padding: 0;
    }

    #sk-container-id-1 input.sk-hidden--visually {
      border: 0;
      clip: rect(1px 1px 1px 1px);
      clip: rect(1px, 1px, 1px, 1px);
      height: 1px;
      margin: -1px;
      overflow: hidden;
      padding: 0;
      position: absolute;
      width: 1px;
    }

    #sk-container-id-1 div.sk-dashed-wrapped {
      border: 1px dashed var(--sklearn-color-line);
      margin: 0 0.4em 0.5em 0.4em;
      box-sizing: border-box;
      padding-bottom: 0.4em;
      background-color: var(--sklearn-color-background);
    }

    #sk-container-id-1 div.sk-container {
      /* jupyter's `normalize.less` sets `[hidden] { display: none; }`
         but bootstrap.min.css set `[hidden] { display: none !important; }`
         so we also need the `!important` here to be able to override the
         default hidden behavior on the sphinx rendered scikit-learn.org.
         See: https://github.com/scikit-learn/scikit-learn/issues/21755 */
      display: inline-block !important;
      position: relative;
    }

    #sk-container-id-1 div.sk-text-repr-fallback {
      display: none;
    }

    div.sk-parallel-item,
    div.sk-serial,
    div.sk-item {
      /* draw centered vertical line to link estimators */
      background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));
      background-size: 2px 100%;
      background-repeat: no-repeat;
      background-position: center center;
    }

    /* Parallel-specific style estimator block */

    #sk-container-id-1 div.sk-parallel-item::after {
      content: "";
      width: 100%;
      border-bottom: 2px solid var(--sklearn-color-text-on-default-background);
      flex-grow: 1;
    }

    #sk-container-id-1 div.sk-parallel {
      display: flex;
      align-items: stretch;
      justify-content: center;
      background-color: var(--sklearn-color-background);
      position: relative;
    }

    #sk-container-id-1 div.sk-parallel-item {
      display: flex;
      flex-direction: column;
    }

    #sk-container-id-1 div.sk-parallel-item:first-child::after {
      align-self: flex-end;
      width: 50%;
    }

    #sk-container-id-1 div.sk-parallel-item:last-child::after {
      align-self: flex-start;
      width: 50%;
    }

    #sk-container-id-1 div.sk-parallel-item:only-child::after {
      width: 0;
    }

    /* Serial-specific style estimator block */

    #sk-container-id-1 div.sk-serial {
      display: flex;
      flex-direction: column;
      align-items: center;
      background-color: var(--sklearn-color-background);
      padding-right: 1em;
      padding-left: 1em;
    }


    /* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is
    clickable and can be expanded/collapsed.
    - Pipeline and ColumnTransformer use this feature and define the default style
    - Estimators will overwrite some part of the style using the `sk-estimator` class
    */

    /* Pipeline and ColumnTransformer style (default) */

    #sk-container-id-1 div.sk-toggleable {
      /* Default theme specific background. It is overwritten whether we have a
      specific estimator or a Pipeline/ColumnTransformer */
      background-color: var(--sklearn-color-background);
    }

    /* Toggleable label */
    #sk-container-id-1 label.sk-toggleable__label {
      cursor: pointer;
      display: flex;
      width: 100%;
      margin-bottom: 0;
      padding: 0.5em;
      box-sizing: border-box;
      text-align: center;
      align-items: center;
      justify-content: center;
      gap: 0.5em;
    }

    #sk-container-id-1 label.sk-toggleable__label .caption {
      font-size: 0.6rem;
      font-weight: lighter;
      color: var(--sklearn-color-text-muted);
    }

    #sk-container-id-1 label.sk-toggleable__label-arrow:before {
      /* Arrow on the left of the label */
      content: "▸";
      float: left;
      margin-right: 0.25em;
      color: var(--sklearn-color-icon);
    }

    #sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {
      color: var(--sklearn-color-text);
    }

    /* Toggleable content - dropdown */

    #sk-container-id-1 div.sk-toggleable__content {
      display: none;
      text-align: left;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-1 div.sk-toggleable__content.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-1 div.sk-toggleable__content pre {
      margin: 0.2em;
      border-radius: 0.25em;
      color: var(--sklearn-color-text);
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-1 div.sk-toggleable__content.fitted pre {
      /* unfitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {
      /* Expand drop-down */
      display: block;
      width: 100%;
      overflow: visible;
    }

    #sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {
      content: "▾";
    }

    /* Pipeline/ColumnTransformer-specific style */

    #sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator-specific style */

    /* Colorize estimator box */
    #sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    #sk-container-id-1 div.sk-label label.sk-toggleable__label,
    #sk-container-id-1 div.sk-label label {
      /* The background is the default theme color */
      color: var(--sklearn-color-text-on-default-background);
    }

    /* On hover, darken the color of the background */
    #sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    /* Label box, darken color on hover, fitted */
    #sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator label */

    #sk-container-id-1 div.sk-label label {
      font-family: monospace;
      font-weight: bold;
      line-height: 1.2em;
    }

    #sk-container-id-1 div.sk-label-container {
      text-align: center;
    }

    /* Estimator-specific */
    #sk-container-id-1 div.sk-estimator {
      font-family: monospace;
      border: 1px dotted var(--sklearn-color-border-box);
      border-radius: 0.25em;
      box-sizing: border-box;
      margin-bottom: 0.5em;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-1 div.sk-estimator.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    /* on hover */
    #sk-container-id-1 div.sk-estimator:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-1 div.sk-estimator.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Specification for estimator info (e.g. "i" and "?") */

    /* Common style for "i" and "?" */

    .sk-estimator-doc-link,
    a:link.sk-estimator-doc-link,
    a:visited.sk-estimator-doc-link {
      float: right;
      font-size: smaller;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-unfitted-level-0);
      border-radius: 1em;
      height: 1em;
      width: 1em;
      text-decoration: none !important;
      margin-left: 0.5em;
      text-align: center;
      /* unfitted */
      border: var(--sklearn-color-unfitted-level-3) 1pt solid;
      color: var(--sklearn-color-unfitted-level-3);
    }

    .sk-estimator-doc-link.fitted,
    a:link.sk-estimator-doc-link.fitted,
    a:visited.sk-estimator-doc-link.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3) 1pt solid;
      color: var(--sklearn-color-fitted-level-3);
    }

    /* On hover */
    div.sk-estimator:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover,
    div.sk-label-container:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      border: var(--sklearn-color-fitted-level-0) 1pt solid;
      color: var(--sklearn-color-unfitted-level-0);
      text-decoration: none;
    }

    div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover,
    div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
      border: var(--sklearn-color-fitted-level-0) 1pt solid;
      color: var(--sklearn-color-fitted-level-0);
      text-decoration: none;
    }

    /* Span, style for the box shown on hovering the info icon */
    .sk-estimator-doc-link span {
      display: none;
      z-index: 9999;
      position: relative;
      font-weight: normal;
      right: .2ex;
      padding: .5ex;
      margin: .5ex;
      width: min-content;
      min-width: 20ex;
      max-width: 50ex;
      color: var(--sklearn-color-text);
      box-shadow: 2pt 2pt 4pt #999;
      /* unfitted */
      background: var(--sklearn-color-unfitted-level-0);
      border: .5pt solid var(--sklearn-color-unfitted-level-3);
    }

    .sk-estimator-doc-link.fitted span {
      /* fitted */
      background: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3);
    }

    .sk-estimator-doc-link:hover span {
      display: block;
    }

    /* "?"-specific style due to the `<a>` HTML tag */

    #sk-container-id-1 a.estimator_doc_link {
      float: right;
      font-size: 1rem;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-unfitted-level-0);
      border-radius: 1rem;
      height: 1rem;
      width: 1rem;
      text-decoration: none;
      /* unfitted */
      color: var(--sklearn-color-unfitted-level-1);
      border: var(--sklearn-color-unfitted-level-1) 1pt solid;
    }

    #sk-container-id-1 a.estimator_doc_link.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-1) 1pt solid;
      color: var(--sklearn-color-fitted-level-1);
    }

    /* On hover */
    #sk-container-id-1 a.estimator_doc_link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    #sk-container-id-1 a.estimator_doc_link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
    }

    .estimator-table {
        font-family: monospace;
    }

    .estimator-table summary {
        padding: .5rem;
        cursor: pointer;
    }

    .estimator-table summary::marker {
        font-size: 0.7rem;
    }

    .estimator-table details[open] {
        padding-left: 0.1rem;
        padding-right: 0.1rem;
        padding-bottom: 0.3rem;
    }

    .estimator-table .parameters-table {
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        display: none;
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        max-height: 10em;
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    </style><body><div id="sk-container-id-1" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),
                    (&#x27;logisticregression&#x27;,
                     LogisticRegression(C=10, random_state=0))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label  sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-1" type="checkbox" ><label for="sk-estimator-id-1" class="sk-toggleable__label  sk-toggleable__label-arrow"><div><div>Pipeline</div></div><div><a class="sk-estimator-doc-link " rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.pipeline.Pipeline.html">?<span>Documentation for Pipeline</span></a><span class="sk-estimator-doc-link ">i<span>Not fitted</span></span></div></label><div class="sk-toggleable__content " data-param-prefix="">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('steps',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=steps,-list%20of%20tuples">
                steps
                <span class="param-doc-description">steps: list of tuples<br><br>List of (name of step, estimator) tuples that are to be chained in<br>sequential order. To be compatible with the scikit-learn API, all steps<br>must define `fit`. All non-last steps must also define `transform`. See<br>:ref:`Combining Estimators <combining_estimators>` for more details.</span>
            </a>
        </td>
                <td class="value">[(&#x27;standardscaler&#x27;, ...), (&#x27;logisticregression&#x27;, ...)]</td>
            </tr>
    

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

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

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

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

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

            <tr class="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="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.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">0</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>
    

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                     onclick="copyToClipboard('max_iter',
                              this.parentElement.nextElementSibling)"
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                <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>
    

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                     onclick="copyToClipboard('n_jobs',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
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                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>
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.. GENERATED FROM PYTHON SOURCE LINES 228-236

DecisionTreeRegressor with `criterion="absolute_error"`
------------------------------------------------------
:class:`tree.DecisionTreeRegressor` with `criterion="absolute_error"`
now runs much faster. It has now `O(n * log(n))` complexity compared to
`O(n**2)` previously, which allows to scale to millions of data points.

As an illustration, on a dataset with 100_000 samples and 1 feature, doing a
single split takes of the order of 100 ms, compared to ~20 seconds before.

.. GENERATED FROM PYTHON SOURCE LINES 236-250

.. code-block:: Python


    import time

    from sklearn.datasets import make_regression
    from sklearn.tree import DecisionTreeRegressor

    X, y = make_regression(n_samples=100_000, n_features=1)
    tree = DecisionTreeRegressor(criterion="absolute_error", max_depth=1)

    tic = time.time()
    tree.fit(X, y)
    elapsed = time.time() - tic
    print(f"Fit took {elapsed:.2f} seconds")





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

 .. code-block:: none

    Fit took 0.17 seconds




.. GENERATED FROM PYTHON SOURCE LINES 251-261

ClassicalMDS
------------
Classical MDS, also known as "Principal Coordinates Analysis" (PCoA)
or "Torgerson's scaling" is now available within the `sklearn.manifold`
module. Classical MDS is close to PCA and instead of approximating
distances, it approximates pairwise scalar products, which has an exact
analytic solution in terms of eigendecomposition.

Let's illustrate this new addition by using it on an S-curve dataset to
get a low-dimensional representation of the data.

.. GENERATED FROM PYTHON SOURCE LINES 261-289

.. code-block:: Python


    import matplotlib.pyplot as plt
    from matplotlib import ticker

    from sklearn import datasets, manifold

    n_samples = 1500
    S_points, S_color = datasets.make_s_curve(n_samples, random_state=0)
    md_classical = manifold.ClassicalMDS(n_components=2)
    S_scaling = md_classical.fit_transform(S_points)

    fig = plt.figure(figsize=(8, 4))
    ax1 = fig.add_subplot(1, 2, 1, projection="3d")
    x, y, z = S_points.T
    ax1.scatter(x, y, z, c=S_color, s=50, alpha=0.8)
    ax1.set_title("Original S-curve samples", size=16)
    ax1.view_init(azim=-60, elev=9)
    for axis in (ax1.xaxis, ax1.yaxis, ax1.zaxis):
        axis.set_major_locator(ticker.MultipleLocator(1))

    ax2 = fig.add_subplot(1, 2, 2)
    x2, y2 = S_scaling.T
    ax2.scatter(x2, y2, c=S_color, s=50, alpha=0.8)
    ax2.set_title("Classical MDS", size=16)
    for axis in (ax2.xaxis, ax2.yaxis):
        axis.set_major_formatter(ticker.NullFormatter())

    plt.show()



.. image-sg:: /auto_examples/release_highlights/images/sphx_glr_plot_release_highlights_1_8_0_002.png
   :alt: Original S-curve samples, Classical MDS
   :srcset: /auto_examples/release_highlights/images/sphx_glr_plot_release_highlights_1_8_0_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 18.545 seconds)


.. _sphx_glr_download_auto_examples_release_highlights_plot_release_highlights_1_8_0.py:

.. only:: html

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

    .. container:: binder-badge

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        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/index.html?path=auto_examples/release_highlights/plot_release_highlights_1_8_0.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_release_highlights_1_8_0.ipynb <plot_release_highlights_1_8_0.ipynb>`

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

      :download:`Download Python source code: plot_release_highlights_1_8_0.py <plot_release_highlights_1_8_0.py>`

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

      :download:`Download zipped: plot_release_highlights_1_8_0.zip <plot_release_highlights_1_8_0.zip>`


.. include:: plot_release_highlights_1_8_0.recommendations


.. only:: html

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

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