线性回归--实现西瓜书(3.11)公式

た入场券 2022-12-11 10:29 269阅读 0赞

## 实现西瓜书(3.11)公式 ##

一.工具  
1.Python3.8  
2.Jupyter NoteBook  
1和2请看:[安装Jupyter NoteBook][Jupyter NoteBook]  
3.Numpy  
命令行 : **pip3 install numpy**  
4.matplotlib  
命令行 : **pip3 install matplotlib**

import numpy as np
    import matplotlib.pyplot as plt

二.代码及注释  
1.需要线性回归的数据1

X = np.random.rand(100, 1)
    Y = 6 * X + np.random.randn(100, 1)

可视化:

plt.scatter(X, Y)
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zNzQ3NzAwOQ_size_16_color_FFFFFF_t_70_pic_center]  
2.西瓜书的公式及实现  
(1)  
![在这里插入图片描述][20200930103938541.png_pic_center]  
代码2:

X_b = np.c_[X, np.ones((100, 1))]

为便于讨论，我们把w和b吸收入向量形式W = (w；b),得Y = X·W

(2)  
![在这里插入图片描述][20200930104556788.png_pic_center]  
代码3:

theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(Y)

3.结果  
代码:

ansY = theta_best[0] * X + theta_best[1]
    plt.scatter(X, Y)
    plt.plot(X, ansY, color = "red")
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zNzQ3NzAwOQ_size_16_color_FFFFFF_t_70_pic_center 1]  
三.扩展阅读

--------------------

1.  [np.random.rand() 和 np.random.randn()讲解][np.random.rand_ _ np.random.randn] ↩︎
2.  [对numpy.c\_的理解][numpy.c] ↩︎
3.  [numpy, 计算矩阵的逆 + 计算两个数组的点积][numpy_ _ _] ↩︎

[Jupyter NoteBook]: https://blog.csdn.net/weixin_37477009/article/details/108846923
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zNzQ3NzAwOQ_size_16_color_FFFFFF_t_70_pic_center]: /images/20221123/1adce72e8dd447208e9830072faefdb2.png
[20200930103938541.png_pic_center]: /images/20221123/edc38c2a29134e6da470187a9563a57d.png
[20200930104556788.png_pic_center]: /images/20221123/d252af2453ab4ca6ac388cadb31317cc.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zNzQ3NzAwOQ_size_16_color_FFFFFF_t_70_pic_center 1]: /images/20221123/b813c70f7c304090920ec5ee2a319bf6.png
[np.random.rand_ _ np.random.randn]: https://blog.csdn.net/qq_40130759/article/details/79535575
[numpy.c]: https://blog.csdn.net/az9996/article/details/90231195
[numpy_ _ _]: http://ishero.net/NumPy%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0.html