分类模型

需要找到一个函数，将实数域映射到[0,1]-->logistic function=

饱和函数-->导数如图中红线   （sigmoid）

logistic regression model:

对二分类问题，损失函数loss=-(y*log y_hat + (1-y)*log(1-y_hat))  类似交叉熵算法，评价两种分布之间的差异程度   BCE

对于mini-batch的BCE，求平均

下面是代码实现简单的二分类问题

import torch
import torch.nn.functional as F
import numpy as np
import matplotlib.pyplot as plt
x_data=torch.Tensor([[1.0],[2.0],[3.0]])
y_data=torch.Tensor([[0],[0],[1]])
##########################################dataset prepare
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))
        return y_pred
model=LogisticRegressionModel()
#########################################design model using class
criterion=torch.nn.BCELoss(size_average=False)
optimizer=torch.optim.SGD(model.parameters(),lr=0.01)
########################################搭建loss和optimizer
for epoch in range(100):
    y_pred=model(x_data)
    loss=criterion(y_pred,y_data)
    print(epoch,loss.item())
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
########################################training cycle
# x_test=torch.Tensor([4.0])
# y_test=model(x_test)
# print(y_test)
x=np.linspace(0,10,200)
x_t=torch.Tensor(x).view((200,1))
y_t=model(x_t)
y = y_t.detach().numpy()

plt.plot(x,y)
plt.plot([0,10],[0.5,0.5],c='r')
plt.xlabel('Hours')
plt.ylabel('probability')
plt.grid()
plt.show()