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


============================================
使用贝叶斯岭回归进行曲线拟合
============================================

计算正弦曲线的贝叶斯岭回归。

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

通常，在使用贝叶斯岭回归通过多项式拟合曲线时，正则化参数（alpha, lambda）的初始值选择可能很重要。这是因为正则化参数是通过依赖初始值的迭代过程确定的。

在此示例中，使用不同的初始值对来通过多项式逼近正弦曲线。

当从默认值（alpha_init = 1.90, lambda_init = 1.）开始时，结果曲线的偏差较大，方差较小。因此，lambda_init 应相对较小（1.e-3），以减少偏差。

此外，通过评估这些模型的对数边际似然（L），我们可以确定哪个模型更好。可以得出结论，L 较大的模型更有可能。

.. GENERATED FROM PYTHON SOURCE LINES 19-22

.. code-block:: Python


    # Author: Yoshihiro Uchida <nimbus1after2a1sun7shower@gmail.com>








.. GENERATED FROM PYTHON SOURCE LINES 23-25

生成带噪声的正弦数据
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 25-40

.. code-block:: Python


    import numpy as np


    def func(x):
        return np.sin(2 * np.pi * x)


    size = 25
    rng = np.random.RandomState(1234)
    x_train = rng.uniform(0.0, 1.0, size)
    y_train = func(x_train) + rng.normal(scale=0.1, size=size)
    x_test = np.linspace(0.0, 1.0, 100)









.. GENERATED FROM PYTHON SOURCE LINES 41-43

按三次多项式拟合
-------------------

.. GENERATED FROM PYTHON SOURCE LINES 43-51

.. code-block:: Python


    from sklearn.linear_model import BayesianRidge

    n_order = 3
    X_train = np.vander(x_train, n_order + 1, increasing=True)
    X_test = np.vander(x_test, n_order + 1, increasing=True)
    reg = BayesianRidge(tol=1e-6, fit_intercept=False, compute_score=True)








.. GENERATED FROM PYTHON SOURCE LINES 52-54

绘制真实和预测曲线与对数边际似然 (L)
-------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 54-86

.. code-block:: Python

    import matplotlib.pyplot as plt

    fig, axes = plt.subplots(1, 2, figsize=(8, 4))
    for i, ax in enumerate(axes):
        # 不同初始值对的贝叶斯岭回归
        if i == 0:
            init = [1 / np.var(y_train), 1.0]  # Default values
        elif i == 1:
            init = [1.0, 1e-3]
            reg.set_params(alpha_init=init[0], lambda_init=init[1])
        reg.fit(X_train, y_train)
        ymean, ystd = reg.predict(X_test, return_std=True)

        ax.plot(x_test, func(x_test), color="blue", label="sin($2\\pi x$)")
        ax.scatter(x_train, y_train, s=50, alpha=0.5, label="observation")
        ax.plot(x_test, ymean, color="red", label="predict mean")
        ax.fill_between(
            x_test, ymean - ystd, ymean + ystd, color="pink", alpha=0.5, label="predict std"
        )
        ax.set_ylim(-1.3, 1.3)
        ax.legend()
        title = "$\\alpha$_init$={:.2f},\\ \\lambda$_init$={}$".format(init[0], init[1])
        if i == 0:
            title += " (Default)"
        ax.set_title(title, fontsize=12)
        text = "$\\alpha={:.1f}$\n$\\lambda={:.3f}$\n$L={:.1f}$".format(
            reg.alpha_, reg.lambda_, reg.scores_[-1]
        )
        ax.text(0.05, -1.0, text, fontsize=12)

    plt.tight_layout()
    plt.show()



.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_bayesian_ridge_curvefit_001.png
   :alt: $\alpha$_init$=1.90,\ \lambda$_init$=1.0$ (Default), $\alpha$_init$=1.00,\ \lambda$_init$=0.001$
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_bayesian_ridge_curvefit_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.133 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_bayesian_ridge_curvefit.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_bayesian_ridge_curvefit.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_bayesian_ridge_curvefit.recommendations


.. only:: html

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

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