基于sklearn的线性回归器理论代码实现

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)    

from sklearn.model_selection import train_test_split
x_train,x_test,y_train,y_test = train_test_split(x_data,boston.target,random_state=33,test_size=0.25)

# print(type(y_test))
from sklearn.preprocessing import StandardScaler
ss_x = StandardScaler()
ss_y = 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,) 

from sklearn.linear_model import LinearRegression
lr = LinearRegression()
lr.fit(x_train,y_train)

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)

from sklearn.linear_model import SGDRegressor
sgd = SGDRegressor()
sgd.fit(x_train,y_train)

c:\users\qiank\appdata\local\programs\python\python35\lib\site-packages\sklearn\linear_model\stochastic_gradient.py:84: FutureWarning: max_iter and tol parameters have been added in <class 'sklearn.linear_model.stochastic_gradient.SGDRegressor'> in 0.19. If both are left unset, they default to max_iter=5 and tol=None. If tol is not None, max_iter defaults to max_iter=1000. From 0.21, default max_iter will be 1000, and default tol will be 1e-3.
  "and default tol will be 1e-3." % type(self), FutureWarning)

SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.01,
       fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',
       loss='squared_loss', max_iter=5, n_iter=None, penalty='l2',
       power_t=0.25, random_state=None, shuffle=True, tol=None, verbose=0,
       warm_start=False)

lr.score(x_test,y_test)

0.67634038309987021

sgd.score(x_test,y_test)

0.65777103520375069

from sklearn.metrics import mean_absolute_error
print("lr:",mean_absolute_error(ss_y.inverse_transform(y_test),ss_y.inverse_transform(lr.predict(x_test))))
print("sgd:",mean_absolute_error(ss_y.inverse_transform(y_test),ss_y.inverse_transform(sgd.predict(x_test))))

lr: 0.379976703913
sgd: 0.377629585475

from sklearn.metrics import mean_squared_error
print("lr:",mean_squared_error(ss_y.inverse_transform(y_test),ss_y.inverse_transform(lr.predict(x_test))))
print("sgd:",mean_squared_error(ss_y.inverse_transform(y_test),ss_y.inverse_transform(sgd.predict(x_test))))

lr: 0.29143408577
sgd: 0.30815455581

from sklearn.metrics import r2_score
print("lr:",r2_score(ss_y.inverse_transform(y_test),ss_y.inverse_transform(lr.predict(x_test))))
print("sgd:",r2_score(ss_y.inverse_transform(y_test),ss_y.inverse_transform(sgd.predict(x_test))))

lr: 0.6763403831
sgd: 0.657771035204