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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_plot_sparse_recovery.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_plot_sparse_recovery.py:


=======================================================
Comparison with Tikhonov in L1 use for support recovery
=======================================================

This example compares Tikhonov and iterative regularization to identify the
support of a linear model.

.. GENERATED FROM PYTHON SOURCE LINES 9-24

.. code-block:: default


    import numpy as np
    from numpy.linalg import norm
    import matplotlib.pyplot as plt
    from sklearn.metrics import f1_score, mean_squared_error
    from sklearn.model_selection import train_test_split
    from celer.datasets import make_correlated_data
    from celer.homotopy import celer_path

    from iterreg.sparse import dual_primal
    from iterreg.utils import datadriven_ratio

    n_samples = 500
    n_features = 1_000








.. GENERATED FROM PYTHON SOURCE LINES 25-26

The function to compute CP, Lasso path and plot metrics:

.. GENERATED FROM PYTHON SOURCE LINES 26-87

.. code-block:: default



    def plot_varying_sigma(corr, density, snr, max_iter=100):
        np.random.seed(0)
        # true coefficient vector has entries equal to 0 or 1
        supp = np.random.choice(n_features, size=int(density * n_features),
                                replace=False)
        w_true = np.zeros(n_features)
        w_true[supp] = 1
        X_, y_, w_true = make_correlated_data(
            n_samples=int(n_samples * 4 / 3.), n_features=n_features,
            w_true=w_true,
            corr=corr, snr=snr, random_state=0)

        X, X_test, y, y_test = train_test_split(X_, y_, test_size=0.25)

        print('Starting computation for this setting')

        ratio = 10 * datadriven_ratio(X, y)
        _, _, _, all_w = dual_primal(
            X, y, step_ratio=ratio, rho=0.99, ret_all=True,
            max_iter=max_iter,
            f_store=1)

        fig, axarr = plt.subplots(2, 2, sharey='row', sharex='col',
                                  figsize=(4.2, 3.5), constrained_layout=True)

        scores = [f1_score(w != 0, w_true != 0) for w in all_w]
        mses = np.array([mean_squared_error(y_test, X_test @ w) for w in all_w])

        axarr[0, 0].plot(scores)
        axarr[1, 0].plot(mses / np.mean(y_test ** 2))

        axarr[0, 0].set_ylim(0, 1)
        axarr[0, 0].set_ylabel('F1 score')
        axarr[1, 0].set_ylabel("pred MSE left out")
        axarr[-1, 0].set_xlabel("CP iteration")
        axarr[0, 0].set_title('Iterative regularization')

        # last column: Lasso results
        alphas = norm(X.T @ y, ord=np.inf) / len(y) * np.geomspace(1, 1e-3)

        coefs = celer_path(X, y, 'lasso', alphas=alphas)[1].T
        axarr[0, 1].semilogx(
            alphas, [f1_score(coef != 0, w_true != 0) for coef in coefs])
        axarr[1, 1].semilogx(
            alphas,
            np.array([mean_squared_error(y_test, X_test @ coef) for coef in coefs])
            / np.mean(y_test ** 2))

        axarr[-1, 1].set_xlabel(r'$\lambda$')
        axarr[0, 1].set_title("Lasso path")

        axarr[0, 1].invert_xaxis()

        plt.show(block=False)
        return fig


    plt.close('all')








.. GENERATED FROM PYTHON SOURCE LINES 88-89

When there is noise in the data:

.. GENERATED FROM PYTHON SOURCE LINES 89-104

.. code-block:: default

    corr = 0.2
    density = 0.1
    snr = 5

    fig = plot_varying_sigma(corr, density, snr, max_iter=100)
    fig.savefig("vslasso1.pdf")

    # ###############################################################################
    # # Really difficult case
    corr = 0.8
    density = 0.1
    snr = 3

    fig = plot_varying_sigma(corr, density, snr, max_iter=100)
    fig.savefig("vslasso2.pdf")



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_sparse_recovery_001.png
         :alt: Iterative regularization, Lasso path
         :srcset: /auto_examples/images/sphx_glr_plot_sparse_recovery_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_sparse_recovery_002.png
         :alt: Iterative regularization, Lasso path
         :srcset: /auto_examples/images/sphx_glr_plot_sparse_recovery_002.png
         :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none

    Starting computation for this setting
    Starting computation for this setting





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

   **Total running time of the script:** ( 0 minutes  20.689 seconds)


.. _sphx_glr_download_auto_examples_plot_sparse_recovery.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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