代码实现

import numpy as np
import matplotlib.pyplot as plt


x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]


def forward(x):
    return x * w


def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) * (y_pred - y)


w_list = []
mse_list = []
for w in np.arange(0.0, 4.1, 0.1):
    print("w=", w)
    l_sum = 0
    for x_val, y_val in zip(x_data, y_data):
        y_pred_val = forward(x_val)
        loss_val = loss(x_val, y_val)
        l_sum += loss_val
        print('\t', x_val, y_val, y_pred_val, loss_val)
    print('MSE=', l_sum / 3)
    w_list.append(w)
    mse_list.append(l_sum / 3)


if __name__ == "__main__":
    plt.plot(w_list, mse_list)
    plt.ylabel('Loss')
    plt.xlabel('w')
    plt.show()

实验分析

由上面实验结果可以看出，当 w = 2 时，损失函数降到最低。因此这个时候找到了最优的线性模

型即为 y^ = 2x

拓展