李宏毅老师视频讲解 Regression：Case Study 中的Gradient Deescent Demo，供大家参考
// An highlighted block var foo = 'bar'; import matplotlib.pyplot as plt import numpy as np # 以上import导入视频中demo没有出现，但为必要 # 数据 x_data = [338.,333.,328.,207.,226.,25.,179.,60.,208.,606.] y_data = [640.,633.,619.,393.,428.,27.,193.,66.,226.,1591.] # ydata = b + w * xdata 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 # initial w lr = 0.0000001 # learning rate #lr=1 #Adagard中lr=1 iteration = 100000 # 迭代次数 # store initial values for plotting b_history = [b] w_history = [w] lr_b = 0 lr_w = 0 # Iterations 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] #update parameters b = b - lr * b_grad w = w - lr * w_grad # Adagard #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 #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') #xlim, ylim 表示横纵坐标轴 plt.xlim(-200,-100) plt.ylim(-5,5) plt.xlabel(r'$b$',fontsize=16) plt.ylabel(r'$w$',fontsize=16) plt.show()当lr = 0.0000001时，即学习效率（learning rate）为0.0000001 增大学习效率，当lr =0.000001时，即学习效率（learning rate）为0.000001，此时代码中为 lr = 0.0000001 # learning rate 再次增加，此时learning rate 过大，已经超出我们所设置的图像，此时代码中为 lr = 0.00001 # learning rate 最后，采用Adagard，代码中 # Adagard 那部分(#update parameters这部分隐去)，此时，可以设置lr=1 That is all,Thank you!
