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


============================
欠拟合与过拟合
============================

本示例演示了欠拟合和过拟合的问题，以及如何使用带有多项式特征的线性回归来逼近非线性函数。图中显示了我们想要逼近的函数，它是余弦函数的一部分。此外，还显示了真实函数的样本和不同模型的逼近结果。这些模型具有不同次数的多项式特征。我们可以看到，线性函数（次数为1的多项式）不足以拟合训练样本。这被称为 **欠拟合** 。次数为4的多项式几乎完美地逼近了真实函数。然而，对于更高次数的多项式，模型会对训练数据 **过拟合** ，即它学习了训练数据的噪声。
我们通过使用交叉验证定量评估 **过拟合** / **欠拟合** 。我们计算验证集上的均方误差（MSE），误差越高，模型从训练数据中正确泛化的可能性就越小。

.. GENERATED FROM PYTHON SOURCE LINES 10-67



.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_underfitting_overfitting_001.png
   :alt: Degree 1 MSE = 4.08e-01(+/- 4.25e-01), Degree 4 MSE = 4.32e-02(+/- 7.08e-02), Degree 15 MSE = 1.83e+08(+/- 5.48e+08)
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_underfitting_overfitting_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.linear_model import LinearRegression
    from sklearn.model_selection import cross_val_score
    from sklearn.pipeline import Pipeline
    from sklearn.preprocessing import PolynomialFeatures


    def true_fun(X):
        return np.cos(1.5 * np.pi * X)


    np.random.seed(0)

    n_samples = 30
    degrees = [1, 4, 15]

    X = np.sort(np.random.rand(n_samples))
    y = true_fun(X) + np.random.randn(n_samples) * 0.1

    plt.figure(figsize=(14, 5))
    for i in range(len(degrees)):
        ax = plt.subplot(1, len(degrees), i + 1)
        plt.setp(ax, xticks=(), yticks=())

        polynomial_features = PolynomialFeatures(degree=degrees[i], include_bias=False)
        linear_regression = LinearRegression()
        pipeline = Pipeline(
            [
                ("polynomial_features", polynomial_features),
                ("linear_regression", linear_regression),
            ]
        )
        pipeline.fit(X[:, np.newaxis], y)

        # 使用交叉验证评估模型
        scores = cross_val_score(
            pipeline, X[:, np.newaxis], y, scoring="neg_mean_squared_error", cv=10
        )

        X_test = np.linspace(0, 1, 100)
        plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label="Model")
        plt.plot(X_test, true_fun(X_test), label="True function")
        plt.scatter(X, y, edgecolor="b", s=20, label="Samples")
        plt.xlabel("x")
        plt.ylabel("y")
        plt.xlim((0, 1))
        plt.ylim((-2, 2))
        plt.legend(loc="best")
        plt.title(
            "Degree {}\nMSE = {:.2e}(+/- {:.2e})".format(
                degrees[i], -scores.mean(), scores.std()
            )
        )
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.102 seconds)


.. _sphx_glr_download_auto_examples_model_selection_plot_underfitting_overfitting.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/main?urlpath=lab/tree/notebooks/auto_examples/model_selection/plot_underfitting_overfitting.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_underfitting_overfitting.recommendations


.. only:: html

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

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