理论
支持向量机回归器
支持向量机回归器与分类器相似，关键在于从大量样本中选出对模型训练最有用的一部分向量。回归器和分类器的区别仅在于label为连续值
K临近回归器
K临近回归器任然是取特征向量最接近的k个训练样本，计算这几个样本的平均值获得结果（分类器是投票）
回归树
回归树相对于分类树的最大区别在于叶子节点的值时“连续值”，理论上来书回归树也是一种分类器，只是分的类别较多
集成回归器
随机森林和提升树本质上来说都是决策树的衍生，回归树也可以衍生出回归版本的随机森林和提升树。另外，随机森林还可以衍生出极端随机森林，其每个节点的特征划分并不是完全随机的
代码实现
数据预处理
数据获取
from sklearn.datasets import load_boston
boston = load_boston()
print(boston.DESCR)
Boston House Prices dataset
===========================
Notes
------
Data Set Characteristics:
:Number of Instances: 506
:Number of Attributes: 13 numeric/categorical predictive
:Median Value (attribute 14) is usually the target
:Attribute Information (in order):
- CRIM per capita crime rate by town
- ZN proportion of residential land zoned for lots over 25,000 sq.ft.
- INDUS proportion of non-retail business acres per town
- CHAS Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)
- NOX nitric oxides concentration (parts per 10 million)
- RM average number of rooms per dwelling
- AGE proportion of owner-occupied units built prior to 1940
- DIS weighted distances to five Boston employment centres
- RAD index of accessibility to radial highways
- TAX full-value property-tax rate per $10,000
- PTRATIO pupil-teacher ratio by town
- B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town
- LSTAT % lower status of the population
- MEDV Median value of owner-occupied homes in $1000's
:Missing Attribute Values: None
:Creator: Harrison, D. and Rubinfeld, D.L.
This is a copy of UCI ML housing dataset.
http://archive.ics.uci.edu/ml/datasets/Housing
This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.
The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic
prices and the demand for clean air', J. Environ. Economics & Management,
vol.5, 81-102, 1978. Used in Belsley, Kuh & Welsch, 'Regression diagnostics
...', Wiley, 1980. N.B. Various transformations are used in the table on
pages 244-261 of the latter.
The Boston house-price data has been used in many machine learning papers that address regression
problems.
**References**
- Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.
- 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.
- many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)
数据分割
from sklearn.model_selection import train_test_split
x_train,x_test,y_train,y_test = train_test_split(boston.data,boston.target,random_state=33,test_size=0.25)
print(x_test.shape)
(127, 13)
标准化
from sklearn.preprocessing import StandardScaler
ss_x,ss_y = StandardScaler(),StandardScaler()
x_train = ss_x.fit_transform(x_train)
x_test = ss_x.transform(x_test)
y_train = ss_y.fit_transform(y_train.reshape([-1,1])).reshape(-1)
y_test = ss_y.transform(y_test.reshape([-1,1])).reshape(-1)
print(y_train.shape)
(379,)
模型训练与评估
支持向量机回归器
from sklearn.svm import SVR
线性核函数
l_svr = SVR(kernel='linear')
l_svr.fit(x_train,y_train)
l_svr.score(x_test,y_test)
0.65171709742960804
多项式核函数
n_svr = SVR(kernel="poly")
n_svr.fit(x_train,y_train)
n_svr.score(x_test,y_test)
0.40445405800289286
径向基核函数
r_svr = SVR(kernel="rbf")
r_svr.fit(x_train,y_train)
r_svr.score(x_test,y_test)
0.75640689122739346
K临近回归器
from sklearn.neighbors import KNeighborsRegressor
knn = KNeighborsRegressor(weights="uniform")
knn.fit(x_train,y_train)
knn.score(x_test,y_test)
0.69034545646065615
回归树
from sklearn.tree import DecisionTreeRegressor
dt = DecisionTreeRegressor()
dt.fit(x_train,y_train)
dt.score(x_test,y_test)
0.68783308418825428
集成模型
随机森林
from sklearn.ensemble import RandomForestRegressor
rfr = RandomForestRegressor()
rfr.fit(x_train,y_train)
rfr.score(x_test,y_test)
0.79055864833158895
极端森林
from sklearn.ensemble import ExtraTreesRegressor
etr = ExtraTreesRegressor()
etr.fit(x_train,y_train)
etr.score(x_test,y_test)
0.7349024110033624
提升树
from sklearn.ensemble import GradientBoostingRegressor
gbr = GradientBoostingRegressor()
gbr.fit(x_train,y_train)
gbr.score(x_test,y_test)
0.84501318676123161
