李宏毅 机器学习 回归demo代码

import numpy as np
import matplotlib.pyplot as plt

x_data=[338.,333.,328.,207.,226.,25.,170.,60.,208.,606.]
y_data=[640.,633.,619.,393.,428.,27.,193.,66.,226.,1591.]
x=np.arange(-200,-100,1)#bias
y=np.arange(-5,5,0.1)#weight
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[i]
  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)

#ydata = b + w*xdata
b = -120 #initial b
w = -4
lr = 0.0000001 #learning rate
iteration = 1000000

#store initial values for plotting.
b_history = [b]
w_history = [w]

#iteration
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]

    #updata parameters
    b = b - lr*b_grad
    w = w - lr*w_grad
    
    #store parameters for plotting
    b_history.append(b)
    w_history.append(w)

#plot the figure
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='black')
plt.xlim(-200,-100)
plt.ylim(-5,5)
plt.xlabel(r'$b$',fontsize=16)
plt.ylabel(r'$w$',fontsize=16)
plt.show()

将迭代次数iteration 设置为1000000后仍未到达最优解

故用了李老师的“大招”，中间做了一点修改如下：

lr_b = 0
lr_w = 0
#iteration
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 = lr_b + 2.0*b_grad**2
    lr_w = lr_w + 2.0*w_grad**2
    #updata parameters
    b = b - lr/np.sqrt(lr_b)*b_grad
    w = w - lr/np.sqrt(lr_w)*w_grad
    ```

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