手写二元线性回归梯度下降—Python代码

代码思路

1. 导入所需库
2. 导入所需数据
3. 数据转换—提取X,Y
4. 设置初始值
   事先指定系数值、学习率、迭代次数
5. 定义损失函数(二元线性回归)
   $$J({\theta }_i)=\frac{1}{2m}\sum _{i=1}^m[h_{\theta }(x^{(i)})-y^{(i)}{]}^2$$其中$$h_{\theta }(x^{(i)})={\theta }_0+{\theta }_1{x}^{(1)}+{\theta }_2{x}^{(2)}$$
6. 求解梯度下降
   $$\frac{\partial J({\theta }_i)}{\partial {\theta }_i}=\frac{1}{m}\sum _{i=1}^m(h_{\theta }(x^{(i)})-y^{(i)})\ast x^{(i)}=\frac{1}{m}\sum _{i=1}^m({\theta }_0+{\theta }_1{x}^{(1)}+{\theta }_2{x}^{(2)}-y^{(i)})\ast x^{(i)}$$

代码实现

1. 导入所需库

import numpy as np 

2. 导入所需数据

data = np.genfromtxt("线性回归/data/Delivery.csv",delimiter=',')

3. 数据转换——提取X,Y

X = data[:,:-1]
Y = data[:,-1]

4. 设置初始值

theta0 = 0
theta1 = 0
theta2 = 0
epochs = 100
alpha = 0.001

5. 定义损失函数（根据上述公式编写）

def cost(X,Y,theta0,theta1,theta2):
    loss = 0
    m = len(Y)
    for i in range(m):
        loss += (theta0+theta1*X[i,0]+theta2*X[i,1]-Y[i])**2
    loss = loss/(2*m)
    return loss

6. 定义梯度下降（根据上述公式编写）

def grad_des(X,Y,theta0,theta1,theta2,alpha,epochs):
    m = len(Y)
    for z in range(epochs):
        theta0_grad = 0
        theta1_grad = 0
        theta2_grad = 0
        for i in range(m):
            theta0_grad = (theta0+theta1*X[i,0]+theta2*X[i,1]-Y[i])
            theta1_grad = (theta0+theta1*X[i,0]+theta2*X[i,1]-Y[i])*X[i,0]
            theta2_grad = (theta0+theta1*X[i,0]+theta2*X[i,1]-Y[i])*X[i,1]
        theta0_grad = theta0_grad/m
        theta1_grad = theta1_grad/m
        theta2_grad = theta2_grad/m
    theta0 -=alpha*theta0_grad
    theta1 -=alpha*theta1_grad
    theta2 -=alpha*theta2_grad
    return theta0,theta1,theta2

7. 输出结果（系数值和损失值）

print('begin...theta0={},theta1={},theta2={},loss={}'.format(theta0,theta1,theta2,cost(X,Y,theta0,theta1,theta2)))
print('running...')
theta0,theta1,theta2 = grad_des(X,Y,theta0,theta1,theta2,alpha,epochs)
print('end...theta0={},theta1={},theta2={},loss={}'.format(theta0,theta1,theta2,cost(X,Y,theta0,theta1,theta2)))

数据资料

X1	X2	Y
100	4	9.3
50	3	4.8
100	4	8.9
100	2	6.5
50	2	4.2
80	2	6.2
75	3	7.4
65	4	6
90	3	7.6
90	2	6.1