深度学习之pytorch实现逻辑斯蒂回归

解决的问题

logistic 适用于分类问题，这里案例( y为0和1 ，0和 1 分别代表一类）
于解决二分类（0 or 1）问题的机器学习方法，用于估计某种事物的可能性

数学公式

logiatic函数

损失值

代码

也是用y=wx+b的模型来举例，之前的输出y属于实数集合R，现在我们要输出一个一个概率，也就是在区间[0,1]之间。我们就想到需要找出一个映射，把我们之前的输出集合R映射到区间[0,1]，他就是函数Sigma，这样我们就轻松的实现了实数集合到0~1之间的映射

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]])

class LinearModel(torch.nn.Module):
    def __init__(self):
        super(LinearModel,self).__init__()
        self.linear = torch.nn.Linear(1,1)
    def forward(self, x):
        y_pred = F.sigmoid(self.linear(x))#这里需要把原来的输出y传给sigmoid，即实现的区间的映射
        return  y_pred

model = LinearModel()

criterion = torch.nn.BCELoss(size_average=False)
optimizer = torch.optim.SGD(model.parameters(),lr=0.01)

for epoch in range(1000):
    y_pred = model(x_data)
    loss = criterion(y_pred,y_data)
    print(epoch,loss.item())

    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

x = np.linspace(0,10,200)
x_t = torch.Tensor(x).view(200,1)#将数据变成一个二百行一列的矩阵
y_t = model(x_t)
y = y_t.data.numpy()

plt.plot(x,y)
plt.plot([0,10],[0.5,0.5],c='r')
plt.ylabel('probablility of pass')
plt.xlabel('hours')
plt.grid()#画出网格
plt.show()

与线性回归代码的区别

数据

x_data = torch.Tensor([[1.0],[2.0],[3.0]])
y_data = torch.Tensor([[0],[0],[1]])

#线性回归
#x_data = torch.Tensor([[1.0],[2.0],[3.0]])
#y_data = torch.Tensor([[2.0],[4.0],[=6.0]])

损失值

criterion = torch.nn.BCELoss(size_average=False)
#线性回归
#criterion = torch.nn.MSELoss(size_average=False)

构造回归的函数

import torch.nn.functional as F
y_pred = F.sigmoid(self.linear(x))

#线性回归
#y_pred = self.linear(x)

结果分析

部分结果数据
964 1.1182234287261963
965 1.1176648139953613
966 1.1171066761016846
967 1.1165491342544556
968 1.1159923076629639
969 1.1154361963272095
970 1.1148808002471924
971 1.1143261194229126
972 1.113771915435791
973 1.1132186651229858
974 1.1126658916473389
975 1.1121137142181396
976 1.1115622520446777
977 1.1110115051269531
978 1.1104612350463867
979 1.1099116802215576
980 1.1093629598617554
981 1.1088148355484009
982 1.1082673072814941
983 1.1077203750610352
984 1.1071741580963135
985 1.106628656387329
986 1.106083631515503
987 1.105539321899414
988 1.104995846748352
989 1.1044528484344482
990 1.1039104461669922
991 1.1033687591552734
992 1.1028276681900024
993 1.1022872924804688
994 1.1017472743988037
995 1.101208209991455
996 1.1006698608398438
997 1.1001317501068115
998 1.0995947122573853
999 1.0990580320358276