回归算法比较【线性回归，Ridge回归，Lasso回归】

代码实现：

  1 # -*- coding: utf-8 -*-
  2 """
  3 Created on Mon Jul 16 09:08:09 2018
  4 
  5 @author: zhen
  6 """
  7 
  8 from sklearn.linear_model import LinearRegression, Ridge, Lasso
  9 import mglearn
 10 from sklearn.model_selection import train_test_split
 11 import matplotlib.pyplot as plt
 12 import numpy as np
 13 # 线性回归
 14 x, y = mglearn.datasets.load_extended_boston()
 15 x_train, x_test, y_train, y_test = train_test_split(x, y, random_state=0)
 16 
 17 linear_reg = LinearRegression()
 18 lr = linear_reg.fit(x_train, y_train)
 19 
 20 print("lr.coef_:{}".format(lr.coef_))  # 斜率
 21 print("lr.intercept_:{}".format(lr.intercept_))  # 截距
 22 
 23 print("="*25+"线性回归"+"="*25)
 24 print("Training set score:{:.2f}".format(lr.score(x_train, y_train)))
 25 print("Rest set score:{:.2f}".format(lr.score(x_test, y_test)))
 26 
 27 """
 28     总结：
 29         训练集和测试集上的分数非常接近，这说明可能存在欠耦合。
 30         训练集和测试集之间的显著性能差异是过拟合的明显标志。解决方式是使用岭回归！
 31 """
 32 print("="*25+"岭回归（默认值1.0）"+"="*25)
 33 # 岭回归
 34 ridge = Ridge().fit(x_train, y_train)
 35 
 36 print("Training set score:{:.2f}".format(ridge.score(x_train, y_train)))
 37 print("Test set score:{:.2f}".format(ridge.score(x_test, y_test)))
 38 
 39 print("="*25+"岭回归（alpha=10）"+"="*25)
 40 # 岭回归
 41 ridge_10 = Ridge(alpha=10).fit(x_train, y_train)
 42 
 43 print("Training set score:{:.2f}".format(ridge_10.score(x_train, y_train)))
 44 print("Test set score:{:.2f}".format(ridge_10.score(x_test, y_test)))
 45 
 46 print("="*25+"岭回归（alpha=0.1）"+"="*25)
 47 # 岭回归
 48 ridge_01 = Ridge(alpha=0.1).fit(x_train, y_train)
 49 
 50 print("Training set score:{:.2f}".format(ridge_01.score(x_train, y_train)))
 51 print("Test set score:{:.2f}".format(ridge_01.score(x_test, y_test)))
 52 
 53 
 54 # 可视化
 55 fig = plt.figure(10)
 56 plt.subplots_adjust(wspace =0, hspace =0.6)#调整子图间距
 57 ax1 = plt.subplot(2, 1, 1)
 58 
 59 ax2 = plt.subplot(2, 1, 2)
 60 
 61 ax1.plot(ridge_01.coef_, 'v', label="Ridge alpha=0.1")
 62 ax1.plot(ridge.coef_, 's', label="Ridge alpha=1")
 63 ax1.plot(ridge_10.coef_, '^', label="Ridge alpha=10")
 64 
 65 ax1.plot(lr.coef_, 'o', label="LinearRegression")
 66 
 67 
 68 ax1.set_ylabel("Cofficient magnitude")
 69 ax1.set_ylim(-25,25)
 70 ax1.hlines(0, 0, len(lr.coef_))
 71 ax1.legend(ncol=2, loc=(0.1, 1.05))
 72 
 73 print("="*25+"Lasso回归（默认配置）"+"="*25)
 74 lasso = Lasso().fit(x_train, y_train)
 75 
 76 print("Training set score:{:.2f}".format(lasso.score(x_train, y_train)))
 77 print("Test set score:{:.2f}".format(lasso.score(x_test, y_test)))
 78 print("Number of features used:{}".format(np.sum(lasso.coef_ != 0)))
 79 
 80 print("="*25+"Lasso回归（aplpha=0.01）"+"="*25)
 81 lasso_001 = Lasso(alpha=0.01, max_iter=1000).fit(x_train, y_train)
 82 
 83 print("Training set score:{:.2f}".format(lasso_001.score(x_train, y_train)))
 84 print("Test set score:{:.2f}".format(lasso_001.score(x_test, y_test)))
 85 print("Number of features used:{}".format(np.sum(lasso_001.coef_ != 0)))
 86 
 87 
 88 print("="*15+"Lasso回归（aplpha=0.0001）太小可能会过拟合"+"="*15)
 89 lasso_00001 = Lasso(alpha=0.0001, max_iter=1000).fit(x_train, y_train)
 90 
 91 print("Training set score:{:.2f}".format(lasso_00001.score(x_train, y_train)))
 92 print("Test set score:{:.2f}".format(lasso_00001.score(x_test, y_test)))
 93 print("Number of features used:{}".format(np.sum(lasso_00001.coef_ != 0)))
 94 
 95 
 96 # 可视化
 97 ax2.plot(ridge_01.coef_, 'o', label="Ridge alpha=0.1")
 98 ax2.plot(lasso.coef_, 's', label="lasso alpha=1")
 99 ax2.plot(lasso_001.coef_, '^', label="lasso alpha=0.001")
100 ax2.plot(lasso_00001.coef_, 'v', label="lasso alpha=0.00001")
101 
102 ax2.set_ylabel("Cofficient magnitude")
103 ax2.set_xlabel("Coefficient index")
104 ax2.set_ylim(-25,25)
105 ax2.legend(ncol=2, loc=(0.1, 1))