6. Logistic model

 

Logistic model To solve the problem of classification .

If the first 5 The problem with section Whether to pass , It is a binary classification problem .

The output is the probability of passing the exam P. probability P stay 0 To 1 Between .

The output range of the original linear model is R （ The set of real Numbers ）, The original output can be mapped to [0,1] Within the scope of .

 

 

It only needs two changes to change the linear model into the logistic model , Model plus sigmod() And the loss function is changed to BCELoss

Complete code ：

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

# 1. Prepare the data , Note that they are all in matrix form 
x_data = torch.Tensor([[1.0], [2.0], [3.0]])
y_data = torch.Tensor([[0], [0], [1]])


# 2. The design model （ class ）  Inherit nn.Module  In order to use its method 
class LogisticRegressionModel(torch.nn.Module):
    #  initialization 
    def __init__(self):
        super(LogisticRegressionModel, self).__init__()
        self.linear = torch.nn.Linear(1, 1)  # Linear Is a linear unit 

    #  Feedforward method 
    def forward(self, x):
        y_pred = F.sigmoid(self.linear(x))  #  In fact, the calling object linear Of __call__() Method ,linear Of __call__() Method execution forward feedforward 
        return y_pred


model = LogisticRegressionModel()

# 3 loss  and  optimizer( Optimizer )
criterion = torch.nn.BCELoss(size_average=False)  #  There is no need to find the mean 
#  Optimizer . model.parameters() Get the parameters that need to be optimized in the model ,lr（learning rate, Learning rate ）
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

# 4  Training process 
for epoch in range(1000):
    #  feedforward 
    y_pred = model(x_data)
    #  Calculate the loss 
    loss = criterion(y_pred, y_data)
    print("epoch={},loss={}".format(epoch, loss))

    optimizer.zero_grad()  #  Zeroing 
    #  Back propagation 
    loss.backward()
    #  to update 、 Optimization parameters 
    optimizer.step()

# Test,  Check the model parameters and test the training effect 
x_test = torch.Tensor([[4.0]])
y_test = model(x_test)
print('y_pred = {} for x = {}'.format(y_test.data, x_test.data))

# mapping 
x = np.linspace(0,10,200)
x_t = torch.Tensor(x).view((200, 1))
y_t = model(x_t)
y = y_t.data.numpy()
plt.plot(x, y)
plt.plot([0,10], [.5,.5], c='r')
plt.xlabel('Hours')
plt.ylabel('Probability of Pass')
plt.grid()
plt.show()