import numpy as np import matplotlib.pyplot as plt learning_rate=1e-1 # 多次调整 epochs=1000 # input_features=1 # input_size=1000(and sum) # output_features=1 # output_size=1000(and sum) w=np.ones((1000,)) b=np.ones((1000,)) x=np.random.randn(1000,) y=np.array([xi**3 for xi in x]) print(x.shape,y.shape) plt.scatter(x,y) plt.show()
(1000,) (1000,)
l o s s = 1 n ( w x + b − y ) 2 δ l o s s δ w = 2 x n [ w x + ( b − y ) ] δ l o s s δ b = 2 n [ w x + b − y ] loss=frac{1}{n}(wx+b-y)^2\frac{delta loss}{delta w}=frac{2x}{n}[wx+(b-y)]\frac{delta loss}{delta b}=frac{2}{n}[wx+b-y] \ loss=n1(wx+b−y)2δwδloss=n2x[wx+(b−y)]δbδloss=n2[wx+b−y]
def getloss(pred,label):
"""
pred:prediction array whose shape is (n,)
label:label array whose shape is (n,)
"""
# using MAE loss function
n=len(pred)
loss=np.sum((pred-label))/n
return loss
def gradient_decent(init_weight,init_bias,x_train,y_train,epochs,lr):
loss=0.
pred=0.
grad_b=0.
grad_w=0.
w=init_weight
b=init_bias
n=len(x_train)
loss_list=[]
for epoch in range(epochs):
if (epoch+1)%50==0:
print("Epoch {}/{}:".format(epoch+1,epochs))
# 前向传播
pred=w*x_train+b
loss=getloss(pred,y_train)
loss_list.append(loss)
# 后向传播
grad_w=np.sum((pred-y_train)*(2*x_train)/n)
grad_b=np.sum((pred-y_train)*(2/n))
w=w-learning_rate*grad_w
b=b-learning_rate*grad_b
if (epoch+1)%50==0:
print("Loss:{}".format(loss))
return w,b,loss_list
w,b,loss=gradient_decent(w,b,x,y,epochs,learning_rate)
loss=np.array(loss)
Epochs=np.array(range(1,epochs+1))
plot_x=np.linspace(-3,3,1000)
prediction=w*plot_x+b
print(plot_x.shape,prediction.shape)
plt.plot(plot_x,prediction,c='r')
plt.scatter(x,y)
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
plt.plot(Epochs,loss)
plt.xlabel("Epoch")
plt.ylabel("Loss")
plt.show()
Epoch 50/1000: Loss:0.017706093923100227 Epoch 100/1000: Loss:0.016060874992968197 Epoch 150/1000: Loss:0.014568561314171443 Epoch 200/1000: Loss:0.013214938732651933 Epoch 250/1000: Loss:0.011987114760282535 Epoch 300/1000: Loss:0.010873395653728185 Epoch 350/1000: Loss:0.009863174928349911 Epoch 400/1000: Loss:0.008946832243113071 Epoch 450/1000: Loss:0.008115641691495604 Epoch 500/1000: Loss:0.0073616886232058506 Epoch 550/1000: Loss:0.0066777942029764914 Epoch 600/1000: Loss:0.0060574469865672075 Epoch 650/1000: Loss:0.005494740861105241 Epoch 700/1000: Loss:0.004984318757650579 Epoch 750/1000: Loss:0.004521321598973595 Epoch 800/1000: Loss:0.0041013419955055926 Epoch 850/1000: Loss:0.003720382247745059 Epoch 900/1000: Loss:0.0033748162545040243 Epoch 950/1000: Loss:0.0030613549636569408 Epoch 1000/1000: Loss:0.002777015035862922 (1000,) (1000,)
