python实现线性回归的两种算法

小锟

1. import numpy as np
   
2. 
   
3. #y=3*x0 + 2 * (x1) + (x2)
   
4. # x0 = 1
   
5. x_train = np.array([    [1, 2],    [2, 1],    [2, 3],    [3, 5],    [1, 3],    [4, 2],    [7, 3],    [4, 5],    [11, 3],    [8, 7]    ])
   
6. y_train = np.array([[7, 8, 10, 14, 8, 13, 20, 16, 28, 26]])
   
7. x_test  = np.array([    [1, 4],    [2, 2],    [2, 5],    [5, 3],    [1, 5],    [4, 1]    ])
   
8. 
   
9. 
   
10. ###最小二乘法  系数 = (X.T * X)^-1 * X.T * Y
    
11. def function1(x_train,y_train):
    
12.     m,n = x_train.shape
    
13.     x = np.ones((m,1))
    
14.     x_train = np.hstack((x,x_train)) ###增加x0 = 1这个特征
    
15.     x_train_T = x_train.T
    
16.     x_x_t = x_train_T.dot(x_train)  
    
17.     x_x_t_ = np.linalg.inv(x_x_t)
    
18.     x_x_t_t = x_x_t_.dot(x_train_T)
    
19.     y_train = y_train.T
    
20.     theat = x_x_t_t.dot(y_train)
    
21.     return theat
    
22. 
    
23. ###梯度下降法
    
24. # rate表示学习速率，不可太大，也不可太小
    
25. # theat表示初始化的系数，颗随便给
    
26. # num表示有几组数据
    
27. # minnum表示当原来的theat与求出的theat相差多少时，认为收敛
    
28. def function2(x_train,y_train,rate,theat,num,minnum=0.000001):
    
29.     m,n = x_train.shape
    
30.     x = np.ones((m,1))
    
31.     x_train = np.hstack((x,x_train)) ###增加x0 = 1这个特征
    
32.     x_train_T = x_train.T
    
33.     y_train = y_train.T
    
34.     theat = theat.reshape(n+1,1)
    
35.     while True:
    
36.         y = x_train.dot(theat)
    
37.         y_ = (y - y_train).T
    
38.         de = y_.dot(x_train) * rate / num
    
39.         theat = theat - de.T
    
40.         f = abs(de) < minnum
    
41.         if f.all():
    
42.             break
    
43.     return theat
    
44. theat = np.array([0,0,0])
    
45. 
    
46. 
    
47. print  function1(x_train,y_train)
    
48. print  function2(x_train,y_train,rate=0.01,theat=theat,num=10)

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Python 2.7