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


==========================================================================
Fitting an Elastic Net with a precomputed Gram Matrix and Weighted Samples
==========================================================================

The following example shows how to precompute the gram matrix
while using weighted samples with an :class:`~sklearn.linear_model.ElasticNet`.

If weighted samples are used, the design matrix must be centered and then
rescaled by the square root of the weight vector before the gram matrix
is computed.

.. note::
  `sample_weight` vector is also rescaled to sum to `n_samples`, see the
   documentation for the `sample_weight` parameter to
   :meth:`~sklearn.linear_model.ElasticNet.fit`.

.. GENERATED FROM PYTHON SOURCE LINES 19-23

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Let's start by loading the dataset and creating some sample weights.

.. GENERATED FROM PYTHON SOURCE LINES 25-38

.. code-block:: Python

    import numpy as np

    from sklearn.datasets import make_regression

    rng = np.random.RandomState(0)

    n_samples = int(1e5)
    X, y = make_regression(n_samples=n_samples, noise=0.5, random_state=rng)

    sample_weight = rng.lognormal(size=n_samples)
    # normalize the sample weights
    normalized_weights = sample_weight * (n_samples / (sample_weight.sum()))








.. GENERATED FROM PYTHON SOURCE LINES 39-42

To fit the elastic net using the `precompute` option together with the sample
weights, we must first center the design matrix,  and rescale it by the
normalized weights prior to computing the gram matrix.

.. GENERATED FROM PYTHON SOURCE LINES 42-47

.. code-block:: Python

    X_offset = np.average(X, axis=0, weights=normalized_weights)
    X_centered = X - np.average(X, axis=0, weights=normalized_weights)
    X_scaled = X_centered * np.sqrt(normalized_weights)[:, np.newaxis]
    gram = np.dot(X_scaled.T, X_scaled)








.. GENERATED FROM PYTHON SOURCE LINES 48-52

We can now proceed with fitting. We must passed the centered design matrix to
`fit` otherwise the elastic net estimator will detect that it is uncentered
and discard the gram matrix we passed. However, if we pass the scaled design
matrix, the preprocessing code will incorrectly rescale it a second time.

.. GENERATED FROM PYTHON SOURCE LINES 52-56

.. code-block:: Python

    from sklearn.linear_model import ElasticNet

    lm = ElasticNet(alpha=0.01, precompute=gram)
    lm.fit(X_centered, y, sample_weight=normalized_weights)





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    </style><body><div id="sk-container-id-40" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>ElasticNet(alpha=0.01,
               precompute=array([[ 9.98809919e+04, -4.48938813e+02, -1.03237920e+03, ...,
            -2.25349312e+02, -3.53959628e+02, -1.67451144e+02],
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           [-1.03237920e+03,  1.19112072e+02,  1.00393284e+05, ...,
            -3.07582983e+02,  6.66670169e+02,  2.65799352e+02],
           ...,
           [-2.25349312e+02, -1.07963978e+03, -3.07582983e+02, ...,
             9.99891212e+04, -4.58195950e+02, -1.58667835e+02],
           [-3.53959628e+02,  7.47987268e+01,  6.66670169e+02, ...,
            -4.58195950e+02,  9.98350372e+04,  5.60836363e+02],
           [-1.67451144e+02, -5.76195467e+02,  2.65799352e+02, ...,
            -1.58667835e+02,  5.60836363e+02,  1.00911944e+05]],
          shape=(100, 100)))</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"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-163" type="checkbox" checked><label for="sk-estimator-id-163" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>ElasticNet</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.ElasticNet.html">?<span>Documentation for ElasticNet</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('alpha',
                              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.ElasticNet.html#:~:text=alpha,-float%2C%20default%3D1.0">
                alpha
                <span class="param-doc-description">alpha: float, default=1.0<br><br>Constant that multiplies the penalty terms. Defaults to 1.0.<br>See the notes for the exact mathematical meaning of this<br>parameter. ``alpha = 0`` is equivalent to an ordinary least square,<br>solved by the :class:`LinearRegression` object. For numerical<br>reasons, using ``alpha = 0`` with the ``Lasso`` object is not advised.<br>Given this, you should use the :class:`LinearRegression` object.</span>
            </a>
        </td>
                <td class="value">0.01</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.ElasticNet.html#:~:text=l1_ratio,-float%2C%20default%3D0.5">
                l1_ratio
                <span class="param-doc-description">l1_ratio: float, default=0.5<br><br>The ElasticNet mixing parameter, with ``0 <= l1_ratio <= 1``. For<br>``l1_ratio = 0`` the penalty is an L2 penalty. ``For l1_ratio = 1`` it<br>is an L1 penalty.  For ``0 < l1_ratio < 1``, the penalty is a<br>combination of L1 and L2.</span>
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                <td class="value">0.5</td>
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            <tr class="default">
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                     onclick="copyToClipboard('fit_intercept',
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                fit_intercept
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                <td class="value">True</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('precompute',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
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                precompute
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                <td class="value">array([[ 9.98...pe=(100, 100))</td>
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            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_iter',
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                ></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.ElasticNet.html#:~:text=max_iter,-int%2C%20default%3D1000">
                max_iter
                <span class="param-doc-description">max_iter: int, default=1000<br><br>The maximum number of iterations.</span>
            </a>
        </td>
                <td class="value">1000</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('copy_X',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
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                copy_X
                <span class="param-doc-description">copy_X: bool, default=True<br><br>If ``True``, X will be copied; else, it may be overwritten.</span>
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                <td class="value">True</td>
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            <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.ElasticNet.html#:~:text=tol,-float%2C%20default%3D1e-4">
                tol
                <span class="param-doc-description">tol: float, default=1e-4<br><br>The tolerance for the optimization: if the updates are smaller or equal to<br>``tol``, the optimization code checks the dual gap for optimality and continues<br>until it is smaller or equal to ``tol``, see Notes below.</span>
            </a>
        </td>
                <td class="value">0.0001</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.ElasticNet.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>See :term:`the Glossary <warm_start>`.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('positive',
                              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.ElasticNet.html#:~:text=positive,-bool%2C%20default%3DFalse">
                positive
                <span class="param-doc-description">positive: bool, default=False<br><br>When set to ``True``, forces the coefficients to be positive.</span>
            </a>
        </td>
                <td class="value">False</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.ElasticNet.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>The seed of the pseudo random number generator that selects a random<br>feature to update. Used when ``selection`` == 'random'.<br>Pass an int for reproducible output across multiple function calls.<br>See :term:`Glossary <random_state>`.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('selection',
                              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.ElasticNet.html#:~:text=selection,-%7B%27cyclic%27%2C%20%27random%27%7D%2C%20default%3D%27cyclic%27">
                selection
                <span class="param-doc-description">selection: {'cyclic', 'random'}, default='cyclic'<br><br>If set to 'random', a random coefficient is updated every iteration<br>rather than looping over features sequentially by default. This<br>(setting to 'random') often leads to significantly faster convergence<br>especially when tol is higher than 1e-4.</span>
            </a>
        </td>
                <td class="value">&#x27;cyclic&#x27;</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
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