BGD线性回归(批量梯度下降算法)实例

BGD线性回归

批量梯度下降算法 简写BGD

一个特征（n），两个未知量（n+1）

#1.生成回归数据
from sklearn.datasets import make_regression
X,y=make_regression(n_samples=100,n_features=1,noise=50,random_state=8)
plt.scatter(X,y)

#2.拆分训练集和测试集
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.3,random_state=8)
plt.subplot(1,2,1)
plt.scatter(X_train,y_train,c='g')
plt.title("训练集散点图")
plt.subplot(1,2,2)
plt.scatter(X_test,y_test,c='orange')
plt.title("训练集散点图")

Text(0.5, 1.0, '训练集散点图')

#3,拟合直线y=wx+b
#3.1参数初始化
w=1 #直线斜率
b=-100#直线截距
lr=0.001#学习率learning rate

#3.2针对参数w和b，先分别计算求和号的值
sum_w=0
sum_b=0
for i in range(len(X_train)):
    y_hat=w*X_train[i]+b
    sum_w+=(y_train[i]-y_hat)*X_train[i]
    sum_b+=y_train[i]-y_hat

#3.3 更新参数w与b的值
w+=lr*sum_w
b+=lr*sum_b

w

array([8.47987404])

b

array([-92.20644646])

#3.4 将3.2与3.3重复迭代epochs次'
epochs=1000
for j in range(epochs):
    sum_w=0
    sum_b=0
    for i in range(len(X_train)):
        y_hat=w*X_train[i]+b
        sum_w+=(y_train[i]-y_hat)*X_train[i]
        sum_b+=y_train[i]-y_hat
    #更新参数w与b的值
    w+=lr*sum_w
    b+=lr*sum_b

#3.5 将迭代结果可视化
xx=np.linspace(-4,4,100)
yy=w*xx+b
plt.scatter(X_train,y_train,c='g')
plt.plot(xx,yy)
plt.title("线性回归拟合图")
plt.legend(("拟合直线",'训练集散点'))

#3.6 计算在训练集和测试集上的均方误差
total_loss_train=0
for i in range(len(X_train)):
    y_hat =y_hat=w*X_train[i]+b
    total_loss_train+=(y_hat-y_train[i])**2
    
total_loss_test=0
for i in range(len(X_test)):
    y_hat =y_hat=w*X_test[i]+b
    total_loss_train+=(y_hat-y_test[i])**2
    
print(total_loss_train/len(X_train),total_loss_test/len(X_test))

[3859.46923139] 0.0