python__regression-优快云博客

本文链接：https://blog.youkuaiyun.com/Miaulxixi/article/details/104821799

本文探讨了如何使用梯度下降法优化线性回归模型参数，通过迭代更新权重和偏置来最小化损失函数。展示了从数据准备到实现梯度下降法的全过程，并用Python代码进行了详细说明。

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x_data=[338.,333.,328.,207.,226.,25.,179.,60.,208.,606.]
y_data=[640.,633.,619.,393.,428.,27.,193.,66.,226.,1591.]

import numpy as np
x = np.arange(-200,-100,1)
y = np.arange(-5,5,0.1)
Z = np.zeros((len(x),len(y)))
X,Y = np.meshgrid(x,y)
for i in range(len(x)):
    for j in range(len(y)):
        b=x[j]
        w=y[j]
        Z[j][i]=0
        for n in range(len(x_data)):
            Z[j][i]=Z[j][i]+(y_data[n]-b-w*x_data[n])**2
        Z[j][i]=Z[j][i]/len(x_data)

from matplotlib import pyplot as plt
b=-120
w=-4
lr=1
iteration=100000

b_history=[b]
w_history=[w]

lr_b=0
lr_w=0



for i in range(iteration):
    
    b_grad=0.0
    w_grad=0.0
    for n in range(len(x_data)):
        b_grad=b_grad-2.0*(y_data[n]-b-w*x_data[n])*1.0
        w_grad=w_grad-2.0*(y_data[n]-b-w*x_data[n])*x_data[n]
    
    lr_b+=b_grad**2
    lr_w+=w_grad**2
    
    
    
    b=b-lr/np.sqrt(lr_b)*b_grad
    w=w-lr/np.sqrt(lr_w)*w_grad
    
    b_history.append(b)
    w_history.append(w)
    
    
plt.contourf(x,y,Z,50,alpha=0.5,cmap=plt.get_cmap('jet'))
plt.plot([-188.4],[2.67],'x',ms=12,markeredgewidth=3,color='orange')
plt.plot(b_history,w_history,'o-',ms=3,lw=1.5,color='green')
plt.xlim(-200,-100)
plt.ylim(-5,5)
plt.xlabel(r'$b$',fontsize=16)
plt.ylabel(r'$w$',fontsize=16)
plt.show()