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本文用机器学习中的决策树回归模型对美国波士顿房价进行分析预测。
关于决策树的详细介绍及原理参见前之前博文【阿旭机器学习实战】【12】决策树基本原理及其构造与使用方法.
目录
决策树回归模型：对美国波士顿房价进行分析导入数据建立模型回归问题的性能检测与线性回归做对比决策树回归模型：对美国波士顿房价进行分析
导入数据
boston = datasets.load_boston()boston
{'data': array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,4.9800e+00],[2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,9.1400e+00],[2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9283e+02,4.0300e+00],...,[6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,5.6400e+00],[1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9345e+02,6.4800e+00],[4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,7.8800e+00]]),'target': 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]),'feature_names': array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD','TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7'),'DESCR': "Boston House Prices dataset\n===========================\n\nNotes\n------\nData Set Characteristics: \n\n :Number of Instances: 506 \n\n :Number of Attributes: 13 numeric/categorical predictive\n \n :Median Value (attribute 14) is usually the target\n\n :Attribute Information (in order):\n - CRIMper capita crime rate by town\n - ZN proportion of residential land zoned for lots over 25,000 sq.ft.\n - INDUS proportion of non-retail business acres per town\n - CHASCharles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n - NOXnitric oxides concentration (parts per 10 million)\n - RM average number of rooms per dwelling\n - AGEproportion of owner-occupied units built prior to 1940\n - DISweighted distances to five Boston employment centres\n - RADindex of accessibility to radial highways\n - TAXfull-value property-tax rate per $10,000\n - PTRATIO pupil-teacher ratio by town\n - B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n - LSTAT % lower status of the population\n - MEDVMedian value of owner-occupied homes in $1000's\n\n :Missing Attribute Values: None\n\n :Creator: Harrison, D. and Rubinfeld, D.L.\n\nThis is a copy of UCI ML housing dataset.\nhttp://archive.ics.uci.edu/ml/datasets/Housing\n\n\nThis dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n\nThe Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\nprices and the demand for clean air', J. Environ. Economics & Management,\nvol.5, 81-102, 1978. Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n...', Wiley, 1980. N.B. Various transformations are used in the table on\npages 244-261 of the latter.\n\nThe Boston house-price data has been used in many machine learning papers that address regression\nproblems. \n\n**References**\n\n - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)\n"}
data = boston.datatarget = boston.target
data.shape
(506, 13)
x_train,x_test,y_train,y_test = train_test_split(data,target,test_size=0.25)
建立模型
# 导入决策树回归器from sklearn.tree import DecisionTreeRegressordt = DecisionTreeRegressor()
dt.fit(x_train,y_train)
DecisionTreeRegressor(criterion='mse', max_depth=None, max_features=None,max_leaf_nodes=None, min_impurity_decrease=0.0,min_impurity_split=None, min_samples_leaf=1,min_samples_split=2, min_weight_fraction_leaf=0.0,presort=False, random_state=None, splitter='best')
y_pre = dt.predict(x_test)
y_pre[:10],y_test[:10]
(array([32.7, 23.8, 8.7, 24.6, 48.3, 29.6, 29.9, 16.1, 22.7, 50. ]),array([33.3, 27.1, 13.4, 22.2, 46.7, 26.4, 28.2, 14.1, 23. , 38.7]))
dt.score(x_test,y_test)
0.7430965111047945
回归问题的性能检测
# 平均绝对误差,#记为MAE = [|y_pre[0]-avg_y| + |y_pre[1]-avg_y| +...+|y_pre[n-1]-avg_y|]/n,其中avg_y代表y的平均值from sklearn.metrics import mean_absolute_errormean_absolute_error(y_pre,y_test)
3.089763779527559
# 均方误差# 记为MSE = [(y1-avg_y)^2+...+(yn-avg_y)^2]from sklearn.metrics import mean_squared_errormean_squared_error(y_pre,y_test)
20.925984251968504
与线性回归做对比
from sklearn.linear_model import LinearRegression
lgr = LinearRegression()
lgr.fit(x_train,y_train)
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)
y_ = lgr.predict(x_test)
mean_absolute_error(y_,y_test)
3.364403770795325
mean_squared_error(y_,y_test)
25.399771785084596
lgr.score(x_test,y_test)
0.6881728519834664
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