机器学习-逻辑回归算法-基础数学原理版代码

`import numpy as np

x=[[1,5],[1,7],[1,3],[1,3],[1,5],[1,6],[1,9],[1,8],[1,7],[1,6]]
y=[0,1,0,0,0,1,1,1,1,1]

num_x=len(x)
num_fe=len(x[0])

初始化权重和Z

weight=[0.0 for _ in range (num_fe)]
Z=[0.0 for _ in range (num_x)]

设置学习率和训练次数

study=0.0001
train_item=500000000

开始训练

for i in range(train_item):
for a in range(num_x):
#正向传播 -净输入
Z[a]=weight[0]x[a][0]+weight[1]x[a][1]
#singmo -转换为激活函数的输出--将线性组合的结果转换为符合概率意义的预测值
y_two=[0.0 for _ in range (num_x)]
for b in range(num_x):
y_two[b]=(1/(1+np.exp(-Z[b])))
#反向传播 -gradient
gradient=[0.0 for _ in range (num_fe)]
for c in range(num_x):
gradient[0]=gradient[0]+(y_two[c]-y[c])x[c][0]
gradient[1]=gradient[1]+(y_two[c]-y[c])x[c][1]
gra_av=[0.0 for _ in range(num_fe) ]
gra_av[0]=gradient[0]/(num_x)
gra_av[1]=gradient[1]/(num_x)
#权重更新-梯度下降算法
weight[0]=weight[0]-gra_av[0]study
weight[1]=weight[1]-gra_av[1]study
#计算损失函数
if i % 50 ==0:
y_np=np.array(y)
y_two_np=np.array(y_two)
loss = -np.mean(y_np * np.log(y_two_np + 1e-8) + (1 - y_np) * np.log(1 - y_two_np + 1e-8))
print(f"{weight[0]}，{weight[1]},损失函数{loss}")

def pre (x,weight):
#样本个数
num_x=len(x)
#预测个数
pre_np=np.zeros(num_x)
z=np.zeros(num_x)
for i in range(num_x):
z[i]=weight[0]x[i][0]+weight[1]x[i][1]
pre_np[i]=(1/(1+np.exp(-z[i])))
return pre_np

x_test=[[1,5],[1,7]]
y_test=[0,1]

pre_test=pre(x_test,weight)
y_test_pre=(pre_test>0.5).astype(int)

print(f"预测结果{y_test_pre}")`