接下来我们将用波士顿房价数据集来介绍我们的回归模型，波士顿总共有506条数据，所以样本数小于100K，依据地图可以先使用Lasso回归-弹性网络回归-岭回归-线性支持向量回归-核支持向量回归-决策树回归-随机森林回归
| import numpy as np |
| import pandas as pd |
| import matplotlib.pyplot as plt |
| from matplotlib.font_manager import FontProperties |
| from sklearn import datasets |
| %matplotlib inline |
| font = FontProperties(fname='/Library/Fonts/Heiti.ttc') |
| |
| np.set_printoptions(precision=4, suppress=True) |
| boston = datasets.load_boston() |
| len(boston.target) |
| array([[ 0.0063, 18. , 2.31 , 0. , 0.538 , 6.575 , |
| 65.2 , 4.09 , 1. , 296. , 15.3 , 396.9 , |
| 4.98 ], |
| [ 0.0273, 0. , 7.07 , 0. , 0.469 , 6.421 , |
| 78.9 , 4.9671, 2. , 242. , 17.8 , 396.9 , |
| 9.14 ], |
| [ 0.0273, 0. , 7.07 , 0. , 0.469 , 7.185 , |
| 61.1 , 4.9671, 2. , 242. , 17.8 , 392.83 , |
| 4.03 ], |
| [ 0.0324, 0. , 2.18 , 0. , 0.458 , 6.998 , |
| 45.8 , 6.0622, 3. , 222. , 18.7 , 394.63 , |
| 2.94 ], |
| [ 0.0691, 0. , 2.18 , 0. , 0.458 , 7.147 , |
| 54.2 , 6.0622, 3. , 222. , 18.7 , 396.9 , |
| 5.33 ]]) |
| array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. , |
| 18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6, |
| 15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2, |
| 13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7, |
| 21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9, |
| 35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5, |
| 19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. , |
| 20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2, |
| 23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8, |
| 33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4, |
| 21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. , |
| 20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6, |
| 23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4, |
| 15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4, |
| 17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7, |
| 25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4, |
| 23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. , |
| 32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3, |
| 34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4, |
| 20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. , |
| 26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3, |
| 31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1, |
| 22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6, |
| 42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. , |
| 36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4, |
| 32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. , |
| 20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1, |
| 20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2, |
| 22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1, |
| 21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6, |
| 19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7, |
| 32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1, |
| 18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8, |
| 16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8, |
| 13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3, 8.8, |
| 7.2, 10.5, 7.4, 10.2, 11.5, 15.1, 23.2, 9.7, 13.8, 12.7, 13.1, |
| 12.5, 8.5, 5. , 6.3, 5.6, 7.2, 12.1, 8.3, 8.5, 5. , 11.9, |
| 27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3, 7. , 7.2, 7.5, 10.4, |
| 8.8, 8.4, 16.7, 14.2, 20.8, 13.4, 11.7, 8.3, 10.2, 10.9, 11. , |
| 9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4, 9.6, 8.7, 8.4, 12.8, |
| 10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4, |
| 15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7, |
| 19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2, |
| 29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8, |
| 20.6, 21.2, 19.1, 20.6, 15.2, 7. , 8.1, 13.6, 20.1, 21.8, 24.5, |
| 23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9]) |
| from sklearn.model_selection import train_test_split |
| from sklearn.preprocessing import MinMaxScaler |
| |
| X_train, X_test, y_train, y_test = train_test_split( |
| X, y, test_size=0.3, random_state=1, shuffle=True) |
| print('训练集长度:{}'.format(len(y_train)), '测试集长度:{}'.format(len(y_test))) |
| |
| scaler = MinMaxScaler() |
| scaler = scaler.fit(X_train) |
| X_train, X_test = scaler.transform(X_train), scaler.transform(X_test) |
| print('标准化后的训练数据:\n{}'.format(X_train[:5])) |
| print('标准化后的测试数据:\n{}'.format(X_test[:5])) |
| 训练集长度:354 测试集长度:152 |
| 标准化后的训练数据: |
| [[0.0085 0. 0.2815 0. 0.3148 0.4576 0.5936 0.3254 0.1304 0.229 |
| 0.8936 1. 0.1802] |
| [0.0022 0.25 0.1712 0. 0.1399 0.4608 0.9298 0.5173 0.3043 0.1851 |
| 0.7553 0.9525 0.3507] |
| [0.1335 0. 0.6466 0. 0.5885 0.6195 0.9872 0.0208 1. 0.9141 |
| 0.8085 1. 0.5384] |
| [0.0003 0.75 0.0913 0. 0.0885 0.5813 0.1681 0.3884 0.087 0.124 |
| 0.6064 0.9968 0.0715] |
| [0.0619 0. 0.6466 0. 0.6852 0. 0.8713 0.044 1. 0.9141 |
| 0.8085 0.8936 0.1487]] |
| 标准化后的测试数据: |
| [[0.0006 0.33 0.063 0. 0.179 0.63 0.684 0.1867 0.2609 0.0668 |
| 0.617 1. 0.16 ] |
| [0.0003 0.55 0.1217 0. 0.2037 0.6007 0.5362 0.4185 0.1739 0.3492 |
| 0.5319 1. 0.1504] |
| [0.003 0. 0.2364 0. 0.1296 0.4731 0.8457 0.4146 0.087 0.0878 |
| 0.5638 0.9895 0.471 ] |
| [0.0007 0.125 0.2056 0. 0.0494 0.444 0.1638 0.4882 0.1304 0.3015 |
| 0.6702 0.9983 0.1758] |
| [0.0499 0. 0.6466 0. 0.7922 0.3451 0.9596 0.0886 1. 0.9141 |
| 0.8085 0.9594 0.2334]] |
| from sklearn.linear_model import Lasso |
| |
| |
| reg = Lasso() |
| reg = reg.fit(X_train, y_train) |
| y_pred = reg.predict(X_test) |
| print('所有样本误差率:\n{}'.format(np.abs(y_pred/y_test-1))) |
| 'Lasso回归R2分数:{}'.format(reg.score(X_test, y_test)) |
| 所有样本误差率: |
| [0.1634 0.0095 0.2647 0.0664 0.1048 0.0102 0.131 0.5394 0.0141 0.0309 |
| 0.0066 0.2222 0.1498 0.1839 0.1663 0.1924 0.4366 0.5148 0.0201 0.2684 |
| 0.3998 0.3775 0.0257 0.0433 0.032 1.374 0.5287 0.3086 0.4512 0.7844 |
| 0.0015 0.139 0.5067 0.7093 0.1734 0.0941 0.4246 0.3343 0.6761 0.1453 |
| 0.0459 0.1484 0.2167 0.4865 0.4501 1.391 0.5023 0.6975 0.0773 0.23 |
| 0.2403 0.0244 0.1593 0.0433 1.2819 0.071 1.9233 0.0837 0.254 0.4944 |
| 0.3093 0.1044 1.4394 0.4663 0.2188 0.3503 0.4062 0.4142 0.0567 0.0024 |
| 0.0396 0.7911 0.0091 0.0746 0.0823 0.0517 0.5071 0.0651 0.0139 0.3429 |
| 0.21 0.1955 0.3098 0.4897 0.0459 0.0748 0.6058 0.018 0.2064 0.1833 |
| 0.0054 0.517 0.556 0.0191 1.0166 0.1782 0.0312 0.0239 0.4559 0.0291 |
| 1.1285 0.3624 0.0518 0.0192 1.531 0.0605 0.8266 0.1089 0.2467 0.1109 |
| 0.4345 0.0151 0.8514 0.2863 0.3463 0.3223 0.2149 0.1205 0.2873 0.5277 |
| 0.1933 0.4103 0.0897 0.1084 0.0671 0.0542 0.023 0.1279 0.0502 0.139 |
| 0.1033 0.0069 0.0441 1.0007 0.0099 0.3426 0.4286 0.6492 0.4074 1.0538 |
| 0.1672 0.1838 0.0782 0.0069 0.1382 0.0446 0.0055 0.0687 0.1621 0.0338 |
| 0.316 0.4306] |
| |
| 'Lasso回归R2分数:0.21189040113362279' |
| from sklearn.linear_model import ElasticNet |
| |
| |
| reg = ElasticNet() |
| reg = reg.fit(X_train, y_train) |
| y_pred = reg.predict(X_test) |
| '弹性网络回归R2分数:{}'.format(reg.score(X_test, y_test)) |
| '弹性网络回归R2分数:0.1414319491120538' |
| from sklearn.linear_model import Ridge |
| |
| |
| reg = Ridge() |
| reg = reg.fit(X_train, y_train) |
| y_pred = reg.predict(X_test) |
| '岭回归R2分数:{}'.format(reg.score(X_test, y_test)) |
| '岭回归R2分数:0.7718570925003422' |
| from sklearn.svm import LinearSVR |
| |
| |
| reg = LinearSVR(C=100, max_iter=10000) |
| reg = reg.fit(X_train, y_train) |
| y_pred = reg.predict(X_test) |
| '线性支持向量回归R2分数:{}'.format(reg.score(X_test, y_test)) |
| '线性支持向量回归R2分数:0.7825143888611817' |
