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


====================
Theil-Sen 回归
====================

在一个合成数据集上计算 Theil-Sen 回归。

有关回归器的更多信息，请参见 :ref:`theil_sen_regression` 。

与 OLS（普通最小二乘）估计量相比，Theil-Sen 估计量对异常值具有鲁棒性。在简单线性回归的情况下，它的崩溃点约为 29.3%，这意味着它可以容忍高达 29.3% 的二维数据中的任意损坏数据（异常值）。

模型的估计是通过计算所有可能的 p 个子样本点组合的斜率和截距来完成的。如果拟合截距，p 必须大于或等于 n_features + 1。最终的斜率和截距定义为这些斜率和截距的空间中位数。

在某些情况下，Theil-Sen 的表现优于同样是鲁棒方法的 :ref:`RANSAC <ransac_regression>` 。这在下面的第二个示例中得到了说明，其中相对于 x 轴的异常值扰乱了 RANSAC。调整 RANSAC 的 ``residual_threshold`` 参数可以解决这个问题，但通常需要对数据和异常值的性质有先验知识。
由于 Theil-Sen 的计算复杂性，建议仅在样本数量和特征数量较少的小问题上使用它。对于较大的问题， ``max_subpopulation`` 参数限制了所有可能的 p 个子样本点组合的规模到一个随机选择的子集，因此也限制了运行时间。因此，Theil-Sen 适用于较大的问题，但代价是失去了一些数学特性，因为它在随机子集上工作。

.. GENERATED FROM PYTHON SOURCE LINES 18-37

.. code-block:: Python


    # 作者：scikit-learn 开发者
    # SPDX-License-Identifier：BSD-3-Clause

    import time

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.linear_model import LinearRegression, RANSACRegressor, TheilSenRegressor

    estimators = [
        ("OLS", LinearRegression()),
        ("Theil-Sen", TheilSenRegressor(random_state=42)),
        ("RANSAC", RANSACRegressor(random_state=42)),
    ]
    colors = {"OLS": "turquoise", "Theil-Sen": "gold", "RANSAC": "lightgreen"}
    lw = 2








.. GENERATED FROM PYTHON SOURCE LINES 38-40

仅在 y 方向上的异常值
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 40-73

.. code-block:: Python



    np.random.seed(0)
    n_samples = 200
    # 线性模型 y = 3*x + N(2, 0.1**2)
    x = np.random.randn(n_samples)
    w = 3.0
    c = 2.0
    noise = 0.1 * np.random.randn(n_samples)
    y = w * x + c + noise
    # 10% outliers
    y[-20:] += -20 * x[-20:]
    X = x[:, np.newaxis]

    plt.scatter(x, y, color="indigo", marker="x", s=40)
    line_x = np.array([-3, 3])
    for name, estimator in estimators:
        t0 = time.time()
        estimator.fit(X, y)
        elapsed_time = time.time() - t0
        y_pred = estimator.predict(line_x.reshape(2, 1))
        plt.plot(
            line_x,
            y_pred,
            color=colors[name],
            linewidth=lw,
            label="%s (fit time: %.2fs)" % (name, elapsed_time),
        )

    plt.axis("tight")
    plt.legend(loc="upper left")
    _ = plt.title("Corrupt y")




.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_theilsen_001.png
   :alt: Corrupt y
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_theilsen_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 74-76

X 方向上的异常值
-----------------

.. GENERATED FROM PYTHON SOURCE LINES 76-109

.. code-block:: Python



    np.random.seed(0)
    # 线性模型 y = 3*x + N(2, 0.1**2)
    x = np.random.randn(n_samples)
    noise = 0.1 * np.random.randn(n_samples)
    y = 3 * x + 2 + noise
    # 10% outliers
    x[-20:] = 9.9
    y[-20:] += 22
    X = x[:, np.newaxis]

    plt.figure()
    plt.scatter(x, y, color="indigo", marker="x", s=40)

    line_x = np.array([-3, 10])
    for name, estimator in estimators:
        t0 = time.time()
        estimator.fit(X, y)
        elapsed_time = time.time() - t0
        y_pred = estimator.predict(line_x.reshape(2, 1))
        plt.plot(
            line_x,
            y_pred,
            color=colors[name],
            linewidth=lw,
            label="%s (fit time: %.2fs)" % (name, elapsed_time),
        )

    plt.axis("tight")
    plt.legend(loc="upper left")
    plt.title("Corrupt x")
    plt.show()



.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_theilsen_002.png
   :alt: Corrupt x
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_theilsen_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.291 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_theilsen.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_theilsen.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_theilsen.recommendations


.. only:: html

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

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