06逻辑斯蒂回归

逻辑斯蒂回归

Sigmoid 函数将任意实数映射到 (0, 1) 的范围内。数学表达式为：

$$\sigma (x)=\frac{1}{1+e^{-x}}$$

import torch
import numpy as np
import matplotlib.pyplot as plt
import torch.nn.functional as F

x_data = torch.tensor([[1.0], [2.0], [3.0]])
y_data = torch.tensor([[0], [0], [1]]).float()   # 分类，0或1

class LogisticRegressionModel(torch.nn.Module):
    def __init__(self):
        super(LogisticRegressionModel, self).__init__()
        self.linear = torch.nn.Linear(1, 1)

    def forward(self, x):
        y_pred = F.sigmoid(self.linear(x))   # F.sigmoid没有参数，所以不需要初始化
        return y_pred

model = LogisticRegressionModel()

# 二分类交叉熵损失
criterion = torch.nn.BCELoss(size_average=True)
# 优化器
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

for epoch in range(1000):
    y_pred = model(x_data)
    l = criterion(y_pred, y_data)

    print("epoch:{}\tloss: {}\t".format(epoch, l.item()))

    optimizer.zero_grad()  # 梯度清零
    l.backward()
    optimizer.step()


# 预测和画图
x = torch.tensor(np.linspace(0, 10, 200)).float()
x = x.view((200, 1))
y = model(x)

# 转为array
x = x.detach().numpy()
y = y.detach().numpy()

plt.plot(x, y)
plt.plot([0, 10], [0.5, 0.5], c='r')
plt.xlabel("Hours")
plt.ylabel("Probability of Pass")
plt.show()
plt.close()