.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/linear_model/plot_lasso_lars_ic.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_lasso_lars_ic.py>`
        to download the full example code. or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_linear_model_plot_lasso_lars_ic.py:


==============================================
通过信息准则进行Lasso模型选择
==============================================

本示例重现了[ZHT2007]_中图2的示例。一个
:class:`~sklearn.linear_model.LassoLarsIC` 估计器在糖尿病数据集上进行拟合，并使用AIC和BIC准则选择最佳模型。

.. NOTE::
    需要注意的是，使用:class:`~sklearn.linear_model.LassoLarsIC` 找到 `alpha` 的优化依赖于在样本内计算的AIC或BIC准则，因此直接在训练集上进行。这种方法不同于交叉验证程序。关于这两种方法的比较，可以参考以下示例：
    :ref:`sphx_glr_auto_examples_linear_model_plot_lasso_model_selection.py` .

.. rubric:: References

.. [ZHT2007] :arxiv:`Zou, Hui, Trevor Hastie, and Robert Tibshirani.
    "On the degrees of freedom of the lasso."
    The Annals of Statistics 35.5 (2007): 2173-2192.
    <0712.0881>` 

.. GENERATED FROM PYTHON SOURCE LINES 20-24

.. code-block:: Python


    # 作者：scikit-learn 开发者
    # SPDX 许可证标识符：BSD-3-Clause








.. GENERATED FROM PYTHON SOURCE LINES 25-26

我们将使用糖尿病数据集。

.. GENERATED FROM PYTHON SOURCE LINES 26-33

.. code-block:: Python


    from sklearn.datasets import load_diabetes

    X, y = load_diabetes(return_X_y=True, as_frame=True)
    n_samples = X.shape[0]
    X.head()






.. raw:: html

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

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

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>age</th>
          <th>sex</th>
          <th>bmi</th>
          <th>bp</th>
          <th>s1</th>
          <th>s2</th>
          <th>s3</th>
          <th>s4</th>
          <th>s5</th>
          <th>s6</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.038076</td>
          <td>0.050680</td>
          <td>0.061696</td>
          <td>0.021872</td>
          <td>-0.044223</td>
          <td>-0.034821</td>
          <td>-0.043401</td>
          <td>-0.002592</td>
          <td>0.019907</td>
          <td>-0.017646</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-0.001882</td>
          <td>-0.044642</td>
          <td>-0.051474</td>
          <td>-0.026328</td>
          <td>-0.008449</td>
          <td>-0.019163</td>
          <td>0.074412</td>
          <td>-0.039493</td>
          <td>-0.068332</td>
          <td>-0.092204</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.085299</td>
          <td>0.050680</td>
          <td>0.044451</td>
          <td>-0.005670</td>
          <td>-0.045599</td>
          <td>-0.034194</td>
          <td>-0.032356</td>
          <td>-0.002592</td>
          <td>0.002861</td>
          <td>-0.025930</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-0.089063</td>
          <td>-0.044642</td>
          <td>-0.011595</td>
          <td>-0.036656</td>
          <td>0.012191</td>
          <td>0.024991</td>
          <td>-0.036038</td>
          <td>0.034309</td>
          <td>0.022688</td>
          <td>-0.009362</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.005383</td>
          <td>-0.044642</td>
          <td>-0.036385</td>
          <td>0.021872</td>
          <td>0.003935</td>
          <td>0.015596</td>
          <td>0.008142</td>
          <td>-0.002592</td>
          <td>-0.031988</td>
          <td>-0.046641</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 34-37

Scikit-learn 提供了一个名为 :class:`~sklearn.linear_model.LassoLarsIC` 的估计器，该估计器使用赤池信息准则 (AIC) 或贝叶斯信息准则 (BIC) 来选择最佳模型。在拟合此模型之前，我们将对数据集进行缩放。

接下来，我们将拟合两个模型，以比较AIC和BIC报告的值。

.. GENERATED FROM PYTHON SOURCE LINES 37-44

.. code-block:: Python

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

    lasso_lars_ic = make_pipeline(StandardScaler(), LassoLarsIC(criterion="aic")).fit(X, y)









.. GENERATED FROM PYTHON SOURCE LINES 45-46

为了与 [ZHT2007]_ 中的定义保持一致，我们需要重新调整 AIC 和 BIC 的尺度。实际上，Zou 等人忽略了一些常数项，这些常数项与从线性模型的最大对数似然推导出的 AIC 原始定义相比。您可以参考 :ref:`用户指南的数学细节部分 <lasso_lars_ic>` 。

.. GENERATED FROM PYTHON SOURCE LINES 46-52

.. code-block:: Python


    def zou_et_al_criterion_rescaling(criterion, n_samples, noise_variance):
        """将信息准则重新调整为符合Zou等人的定义。"""
        return criterion - n_samples * np.log(2 * np.pi * noise_variance) - n_samples









.. GENERATED FROM PYTHON SOURCE LINES 53-65

.. code-block:: Python

    import numpy as np

    aic_criterion = zou_et_al_criterion_rescaling(
        lasso_lars_ic[-1].criterion_,
        n_samples,
        lasso_lars_ic[-1].noise_variance_,
    )

    index_alpha_path_aic = np.flatnonzero(
        lasso_lars_ic[-1].alphas_ == lasso_lars_ic[-1].alpha_
    )[0]








.. GENERATED FROM PYTHON SOURCE LINES 66-78

.. code-block:: Python

    lasso_lars_ic.set_params(lassolarsic__criterion="bic").fit(X, y)

    bic_criterion = zou_et_al_criterion_rescaling(
        lasso_lars_ic[-1].criterion_,
        n_samples,
        lasso_lars_ic[-1].noise_variance_,
    )

    index_alpha_path_bic = np.flatnonzero(
        lasso_lars_ic[-1].alphas_ == lasso_lars_ic[-1].alpha_
    )[0]








.. GENERATED FROM PYTHON SOURCE LINES 79-80

现在我们已经收集了AIC和BIC，我们可以检查两个准则的最小值是否发生在相同的alpha值处。然后，我们可以简化下面的图表。

.. GENERATED FROM PYTHON SOURCE LINES 80-83

.. code-block:: Python


    index_alpha_path_aic == index_alpha_path_bic





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

 .. code-block:: none


    np.True_



.. GENERATED FROM PYTHON SOURCE LINES 84-85

最终，我们可以绘制AIC和BIC准则以及随后的选择正则化参数。

.. GENERATED FROM PYTHON SOURCE LINES 85-102

.. code-block:: Python


    import matplotlib.pyplot as plt

    plt.plot(aic_criterion, color="tab:blue", marker="o", label="AIC criterion")
    plt.plot(bic_criterion, color="tab:orange", marker="o", label="BIC criterion")
    plt.vlines(
        index_alpha_path_bic,
        aic_criterion.min(),
        aic_criterion.max(),
        color="black",
        linestyle="--",
        label="Selected alpha",
    )
    plt.legend()
    plt.ylabel("Information criterion")
    plt.xlabel("Lasso model sequence")
    _ = plt.title("Lasso model selection via AIC and BIC")



.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_lars_ic_001.png
   :alt: Lasso model selection via AIC and BIC
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_lasso_lars_ic_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.045 seconds)


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