刘老师讲的十分细节，易于理解，大家可以去学习，课堂地址，废话不多说，直接上代码。
梯度下降算法课堂代码:
# 梯度下降算法
import matplotlib.pyplot as plt
x_data = [1.0,2.0,3.0]
y_data = [2.0,4.0,6.0]
w = 1.0
def forward(x):
return x * w
#计算损失函数MSE
def cost(xs,ys):
cost = 0
for x,y in zip(xs,ys):
y_pred = forward(x)
cost += (y_pred - y) ** 2
return cost / len(xs)
#计算梯度
def gradient(xs,ys):
grad = 0
for x,y in zip(xs,ys):
grad += 2 * x * (x * w - y)
return grad / len(xs)
print('Predict (before training)',4,forward(4))
epoch_list = []
cost_list = []
#进行一百轮的训练
for epoch in range(100):
cost_val = cost(x_data,y_data)
grad_val = gradient(x_data,y_data)
w -= 0.01 * grad_val
print('Epoch:',epoch,'w = ',w,'loss = ',cost_val)
epoch_list.append(epoch)
cost_list.append(cost_val)
print('Predict (after training)',4,forward(4))
plt.plot(epoch_list,cost_list)
plt.xlabel('Epoch')
plt.ylabel('Cost')
plt.grid()
plt.show()
结果图如下：
随机梯度下降算法：
基本思路：只通过一个随机选取的数据 ( x n , y n ) (x_n,y_n) (xn,yn) 来获取“梯度”，以此对 ω omega ω 进行更新，这种优化方法叫做随机梯度下降。
#随机梯度下降
import matplotlib.pyplot as plt
import matplotlib.pyplot as plt
x_data = [1.0,2.0,3.0]
y_data = [2.0,4.0,6.0]
w = 1.0
def forward(x):
return x * w
#计算损失函数MSE
def loss(x,y):
y_pred = forward(x)
return (y_pred - y) ** 2
#计算梯度
def gradient(x,y):
return 2 * x * (x * w - y)
print('Predict (before training)',4,forward(4))
epoch_list = []
loss_list = []
#进行一百轮的训练
for epoch in range(100):
for x,y in zip(x_data,y_data):
grad = gradient(x,y)
w -= 0.01 * grad
print('tgrad: ',x,y,grad)
l = loss(x,y)
print('progress:',epoch,'w = ',w,'loss = ',l)
epoch_list.append(epoch)
loss_list.append(l)
print('Predict (after training)',4,forward(4))
plt.plot(epoch_list,loss_list)
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.grid()
plt.show()
运行结果图：
