神经网络基础 logistic回归模型代码

初学思路

代码

1.人工生成数据集

import torch
from torch.autograd import Variable
import matplotlib.pyplot as plt

n_data = torch.ones(100, 2) 
x1 = torch.normal(2*n_data, 1)
y1 = torch.zeros(100,1)
x2 = torch.normal(-2*n_data, 1)
y2 = torch.ones(100,1)
x = torch.cat((x1, x2), 0).type(torch.FloatTensor)
y = torch.cat((y1, y2), 0).type(torch.FloatTensor) # labels

# 数据可视化
plt.scatter(x.data.numpy()[0:len(x1), 0], x.data.numpy()[0:len(x1), 1],s=100, lw=0) 
plt.scatter(x.data.numpy()[len(x1):len(x), 0], x.data.numpy()[len(x1):len(x), 1],s=100,lw=0)
plt.show()

数据集可视化

2.初始化参数w与b

w = torch.ones(2, 1, requires_grad = True)
b = torch.ones(1, 1, requires_grad = True)

3.logistic回归模型的sigmoid函数

def sigmoid(w,b):
    y_hat = 1/(1+torch.exp(-(torch.mm(x,w) + b)))
    return y_hat

4.loss交叉熵损失函数

def loss(y_hat,y):
    loss_func = -y*torch.log(y_hat) - (1-y)*torch.log(1-y_hat)
    return loss_func

5.迭代开始

lr = 0.2 
epoch_nums = 20 # 迭代次数
graph = [] # 最后要用到的可视化损失的数据
for i in range(epoch_nums):
    y_hat = sigmoid(w,b)
    J = torch.mean(loss(y_hat,y)) # 一共的代价函数
    graph.append(J)
    J.backward() # 反向传递
    w.data = w.data - lr * w.grad.data # 开始梯度下降方法更新w与b
    b.data = b.data - lr * b.grad.data
    w.grad.data.zero_()
    b.grad.data.zero_()
    print("epoch:{} loss:{:.4}".format(i + 1,J.item()))

plt.plot(graph)
plt.xlabel("epoch_nums")
plt.ylabel("loss")
plt.show

结果

epoch:1 loss:4.111
epoch:2 loss:2.619
epoch:3 loss:1.409
epoch:4 loss:0.714
epoch:5 loss:0.421
epoch:6 loss:0.2933
epoch:7 loss:0.2267
epoch:8 loss:0.1865
epoch:9 loss:0.1595
epoch:10 loss:0.1401
epoch:11 loss:0.1255
epoch:12 loss:0.1141
epoch:13 loss:0.1048
epoch:14 loss:0.09721
epoch:15 loss:0.09079
epoch:16 loss:0.08532
epoch:17 loss:0.08059
epoch:18 loss:0.07645
epoch:19 loss:0.0728
epoch:20 loss:0.06955

（可以观察到学习率为0.2时比较合适）