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


稳健线性估计拟合
===============================

这里使用三阶多项式拟合接近零值的正弦函数。

在不同情况下演示了稳健拟合：

- 没有测量误差，只有建模误差（用多项式拟合正弦函数）

- X中的测量误差

- y中的测量误差

使用对非损坏新数据的中位绝对偏差来判断预测质量。

我们可以看到：

- RANSAC适用于y方向上的强异常值

- TheilSen适用于X和y方向上的小异常值，但有一个临界点，超过该点后其表现不如OLS。

- HuberRegressor的评分不能直接与TheilSen和RANSAC比较，因为它不试图完全过滤异常值，而是减轻它们的影响。

.. GENERATED FROM PYTHON SOURCE LINES 26-111



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


    *

      .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_001.png
         :alt: Modeling Errors Only
         :srcset: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_002.png
         :alt: Corrupt X, Small Deviants
         :srcset: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_003.png
         :alt: Corrupt y, Small Deviants
         :srcset: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_004.png
         :alt: Corrupt X, Large Deviants
         :srcset: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_005.png
         :alt: Corrupt y, Large Deviants
         :srcset: /auto_examples/linear_model/images/sphx_glr_plot_robust_fit_005.png
         :class: sphx-glr-multi-img





.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    from sklearn.linear_model import (
        HuberRegressor,
        LinearRegression,
        RANSACRegressor,
        TheilSenRegressor,
    )
    from sklearn.metrics import mean_squared_error
    from sklearn.pipeline import make_pipeline
    from sklearn.preprocessing import PolynomialFeatures

    np.random.seed(42)

    X = np.random.normal(size=400)
    y = np.sin(X)
    # 确保它 X 是二维的
    X = X[:, np.newaxis]

    X_test = np.random.normal(size=200)
    y_test = np.sin(X_test)
    X_test = X_test[:, np.newaxis]

    y_errors = y.copy()
    y_errors[::3] = 3

    X_errors = X.copy()
    X_errors[::3] = 3

    y_errors_large = y.copy()
    y_errors_large[::3] = 10

    X_errors_large = X.copy()
    X_errors_large[::3] = 10

    estimators = [
        ("OLS", LinearRegression()),
        ("Theil-Sen", TheilSenRegressor(random_state=42)),
        ("RANSAC", RANSACRegressor(random_state=42)),
        ("HuberRegressor", HuberRegressor()),
    ]
    colors = {
        "OLS": "turquoise",
        "Theil-Sen": "gold",
        "RANSAC": "lightgreen",
        "HuberRegressor": "black",
    }
    linestyle = {"OLS": "-", "Theil-Sen": "-.", "RANSAC": "--", "HuberRegressor": "--"}
    lw = 3

    x_plot = np.linspace(X.min(), X.max())
    for title, this_X, this_y in [
        ("Modeling Errors Only", X, y),
        ("Corrupt X, Small Deviants", X_errors, y),
        ("Corrupt y, Small Deviants", X, y_errors),
        ("Corrupt X, Large Deviants", X_errors_large, y),
        ("Corrupt y, Large Deviants", X, y_errors_large),
    ]:
        plt.figure(figsize=(5, 4))
        plt.plot(this_X[:, 0], this_y, "b+")

        for name, estimator in estimators:
            model = make_pipeline(PolynomialFeatures(3), estimator)
            model.fit(this_X, this_y)
            mse = mean_squared_error(model.predict(X_test), y_test)
            y_plot = model.predict(x_plot[:, np.newaxis])
            plt.plot(
                x_plot,
                y_plot,
                color=colors[name],
                linestyle=linestyle[name],
                linewidth=lw,
                label="%s: error = %.3f" % (name, mse),
            )

        legend_title = "Error of Mean\nAbsolute Deviation\nto Non-corrupt Data"
        legend = plt.legend(
            loc="upper right", frameon=False, title=legend_title, prop=dict(size="x-small")
        )
        plt.xlim(-4, 10.2)
        plt.ylim(-2, 10.2)
        plt.title(title)
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.952 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_robust_fit.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/linear_model/plot_robust_fit.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_robust_fit.recommendations


.. only:: html

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

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