机器学习-李宏毅-01

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Gradient Descent Demo

x_data = [338.,333.,207.,226.,25.,179.,60.,208.,606.]
y_data = [640.,633.,619.,393.,428.,27.,66.,226.,1591.]
import numpy as np
import matplotlib
import matplotlib.pyplot as plt

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[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) 

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] - w*x_data[n])*1.0
        w_grad = w_grad - 2.0*(y_data[n] - w*x_data[n])*x_data[n]
    
    lr_b = lr_b + b_grad**2
    lr_w = 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='black')
plt.xlim(-200,-100)
plt.ylim(-5,5)
plt.xlabel(r'$b$',fontsize=16)
plt.xlabel(r'$w$',fontsize=16)
plt.show()