1.8.1 使用Numpy实现 机器学习（梯度下降法）

import numpy as np
from matplotlib import pyplot as plt

np.random.seed(100)
x = np.linspace(-1, 1, 100).reshape(100, 1)
y = 3 * np.power(x, 2) + 2 + 0.2 * np.random.randn(x.size).reshape(100, 1)

# plt.scatter(list(x), list(y))
# plt.show()

w1 = np.random.rand(1, 1)
b1 = np.random.rand(1, 1)
# print(w1)   # [[0.40288033]]
# print(b1)   # [[0.3542983]]

lr = 0.001
for i in range(800):
    # 损失函数， 只作为收敛的观察，不参与后续的计算
    y_predict = w1 * np.power(x, 2) + b1
    loss = 0.5 * (y_predict - y) ** 2
    loss = loss.sum()

    # 计算梯度
    grad_w = np.sum((y_predict - y) * np.power(x, 2))
    grad_b = np.sum((y_predict - y))

    # 使用梯度下降法
    w1 -= lr * grad_w
    b1 -= lr * grad_b

plt.plot(x, y_predict, 'r-', label='predict')
plt.scatter(x, y, color='blue', marker='o', label='true')
plt.xlim(-1, 1)
plt.ylim(2, 6)
plt.legend()
plt.show()
print(w1, b1)