机器学习-线性回归python实现

1.梯度下降

1.1 线性回归函数：y=w*x+b，对于任意x，y包含两个未知参数w，b
1.2 梯度下降
loss

参数更新，a为学习率

2.python实现

# 数据
x = np.array([1,2,3,4,5,6,7,8,9,10])
y = 3*x+2

# 初始化参数
w1 = 0
w2 = 0

#训练
learning_rate = 1e-3  #学习率
for it in range(1):
    # Forward pass
    y_pred = x*w1+w2 
    
    # compute loss
    loss = np.square(y_pred - y).sum()   #平方和
    print(it, loss)
    
    # Backward pass
    # compute the gradient
    grad_w1 = (x * (y_pred - y)).sum()
    grad_w2 = (y_pred - y).sum()
    
    # update weights of w1 and w2
    w1 = w1 - learning_rate * grad_w1
    w2 = w2 - learning_rate * grad_w2