Regression 手动实现Gradient Descent

import numpy as np
import matplotlib.pyplot as plt

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

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)

b = -120 #初始化b
w = -4 #初始化w
lr = 0.0000001 #learning rate
iteration = 100000

#作图保留
b_history = [b]
w_history = [w]

for i in range(iteration):
    b_grad = 0.0
    w_grad = 0.0
    for n in range(len(x_data)):#求导的和
        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
    b = b - lr*b_grad
    w = w - lr*w_grad

    #store for plotting
    b_history.append(b)
    w_history.append(w)

#plot
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()

_

显然没有搞好

用adaGrad

import numpy as np
import matplotlib.pyplot as plt

x_data = [338.,333.,328.,207.,226.,25.,179.,60.,208.,606.]
y_data = [640.,633.,619.,393.,428.,27.,193.,66.,226.,1591.]
#y_data = w*x_data + b
#Z是整个data的loss值
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)

b = -120 #初始化b
w = -4 #初始化w
lr = 1 #learning rate
iteration = 100000

#作图保留
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)):#求导的和
        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 + b_grad ** 2
    lr_w = lr_w + w_grad ** 2

    #update
    b = b - lr/np.sqrt(lr_b)*b_grad
    w = w - lr/np.sqrt(lr_w)*w_grad

    #store for plotting
    b_history.append(b)
    w_history.append(w)

#plot
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()

ok