11、机器学习实战案例：普通最小二乘法求线性回归_笔记

fglbee

this is good idea

fglbee

this is good idea

东方耀

1. import numpy as np
   
2. from .metrics import r2_score
   
3. 
   
4. class LinearRegression:
   
5. 
   
6.     def __init__(self):
   
7.         """初始化Linear Regression模型"""
   
8.         self.coef_ = None
   
9.         self.intercept_ = None
   
10.         self._theta = None
    
11. 
    
12.     def fit_normal(self, X_train, y_train):
    
13.         """根据训练数据集X_train, y_train训练Linear Regression模型"""
    
14.         assert X_train.shape[0] == y_train.shape[0], \
    
15.             "the size of X_train must be equal to the size of y_train"
    
16. 
    
17.         X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
    
18.         self._theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y_train)
    
19. 
    
20.         self.intercept_ = self._theta[0]
    
21.         self.coef_ = self._theta[1:]
    
22. 
    
23.         return self
    
24. 
    
25.     def fit_gd(self, X_train, y_train, eta=0.01, n_iters=1e4):
    
26.         """根据训练数据集X_train, y_train, 使用梯度下降法训练Linear Regression模型"""
    
27.         assert X_train.shape[0] == y_train.shape[0], \
    
28.             "the size of X_train must be equal to the size of y_train"
    
29. 
    
30.         def J(theta, X_b, y):
    
31.             try:
    
32.                 return np.sum((y - X_b.dot(theta)) ** 2) / len(y)
    
33.             except:
    
34.                 return float('inf')
    
35. 
    
36.         def dJ(theta, X_b, y):
    
37.             # res = np.empty(len(theta))
    
38.             # res[0] = np.sum(X_b.dot(theta) - y)
    
39.             # for i in range(1, len(theta)):
    
40.             #     res[i] = (X_b.dot(theta) - y).dot(X_b[:, i])
    
41.             # return res * 2 / len(X_b)
    
42.             return X_b.T.dot(X_b.dot(theta) - y) * 2. / len(X_b)
    
43. 
    
44.         def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8):
    
45. 
    
46.             theta = initial_theta
    
47.             cur_iter = 0
    
48. 
    
49.             while cur_iter < n_iters:
    
50.                 gradient = dJ(theta, X_b, y)
    
51.                 last_theta = theta
    
52.                 theta = theta - eta * gradient
    
53.                 if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):
    
54.                     break
    
55. 
    
56.                 cur_iter += 1
    
57. 
    
58.             return theta
    
59. 
    
60.         X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
    
61.         initial_theta = np.zeros(X_b.shape[1])
    
62.         self._theta = gradient_descent(X_b, y_train, initial_theta, eta, n_iters)
    
63. 
    
64.         self.intercept_ = self._theta[0]
    
65.         self.coef_ = self._theta[1:]
    
66. 
    
67.         return self
    
68. 
    
69.     def fit_sgd(self, X_train, y_train, n_iters=5, t0=5, t1=50):
    
70.         """根据训练数据集X_train, y_train, 使用梯度下降法训练Linear Regression模型"""
    
71.         assert X_train.shape[0] == y_train.shape[0], \
    
72.             "the size of X_train must be equal to the size of y_train"
    
73.         assert n_iters >= 1
    
74. 
    
75.         def dJ_sgd(theta, X_b_i, y_i):
    
76.             return X_b_i * (X_b_i.dot(theta) - y_i) * 2.
    
77. 
    
78.         def sgd(X_b, y, initial_theta, n_iters, t0=5, t1=50):
    
79. 
    
80.             def learning_rate(t):
    
81.                 return t0 / (t + t1)
    
82. 
    
83.             theta = initial_theta
    
84.             m = len(X_b)
    
85. 
    
86.             for cur_iter in range(n_iters):
    
87.                 indexes = np.random.permutation(m)
    
88.                 X_b_new = X_b[indexes]
    
89.                 y_new = y[indexes]
    
90.                 for i in range(m):
    
91.                     gradient = dJ_sgd(theta, X_b_new[i], y_new[i])
    
92.                     theta = theta - learning_rate(cur_iter * m + i) * gradient
    
93. 
    
94.             return theta
    
95. 
    
96.         X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
    
97.         initial_theta = np.random.randn(X_b.shape[1])
    
98.         self._theta = sgd(X_b, y_train, initial_theta, n_iters, t0, t1)
    
99. 
    
100.         self.intercept_ = self._theta[0]
     
101.         self.coef_ = self._theta[1:]
     
102. 
     
103.         return self
     
104. 
     
105.     def predict(self, X_predict):
     
106.         """给定待预测数据集X_predict，返回表示X_predict的结果向量"""
     
107.         assert self.intercept_ is not None and self.coef_ is not None, \
     
108.             "must fit before predict!"
     
109.         assert X_predict.shape[1] == len(self.coef_), \
     
110.             "the feature number of X_predict must be equal to X_train"
     
111. 
     
112.         X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])
     
113.         return X_b.dot(self._theta)
     
114. 
     
115.     def score(self, X_test, y_test):
     
116.         """根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""
     
117. 
     
118.         y_predict = self.predict(X_test)
     
119.         return r2_score(y_test, y_predict)
     
120. 
     
121.     def __repr__(self):
     
122.         return "LinearRegression()"

复制代码