经过几天水水的学习，利用波斯顿房价数据集做了一点小小练习，并写此笔记来记录自己点滴实验心得。新手实验，望有经验人士勿喷，本人抛砖引玉，望得到宝贵建议。如今后有新的体会，则会更新笔记。
1、线性回归+留出法与lasso+留出法
#波士顿房价from sklearn import datasetsfrom sklearn.linear_model import LinearRegressionfrom sklearn.model_selection import train_test_splitfrom sklearn.metrics import accuracy_scoreimport matplotlib.pyplot as pltimport numpy as npfrom sklearn.linear_model import Lassofrom sklearn.metrics import mean_squared_errorfrom sklearn.metrics import mean_absolute_errorfrom sklearn.metrics import r2_score#导入数据house_price = datasets.load_boston()house_price_feature = house_price.datahouse_price_target = house_price.target#导入数据#留出法house_price_feature_train, house_price_feature_test, house_price_target_train, house_price_target_test = train_test_split(house_price_feature,house_price_target,test_size=0.3)#留出法#创建分类器LR_model = LinearRegression()#创建线性回归分类器LR_model.fit(house_price_feature_train, house_price_target_train)#线性回归分类器训练LA_model = Lasso()#创建lassoLA_model.fit(house_price_feature_train, house_price_target_train)#lasso训练#创建分类器#预测predict_results_LR = LR_model.predict(house_price_feature_test)#线性回归分类器预测predict_results_LA = LA_model.predict(house_price_feature_test)#lasso预测#预测#指标分析print("LR's MSE is ",mean_squared_error(house_price_target_test,predict_results_LR))print("LR's MAE is ",mean_absolute_error(house_price_target_test,predict_results_LR))print("LR's R Squared is ",r2_score(house_price_target_test,predict_results_LR))print("LA's MSE is ",mean_squared_error(house_price_target_test,predict_results_LA))print("LA's MAE is ",mean_absolute_error(house_price_target_test,predict_results_LA))print("LA's R Squared is ",r2_score(house_price_target_test,predict_results_LA))#指标分析#画图#线性回归预测结果画图x = np.linspace(0,predict_results_LA.size,predict_results_LA.size)plt.plot(x,predict_results_LR,"r--",label="predict",alpha=0.5)plt.plot(x,house_price_target_test,"g-",label="real",alpha=0.5)plt.legend(loc="best")# plt.savefig("d:/image1",dpi=500,bbox_inches = 'tight')plt.title("linear")plt.show()#线性回归预测结果画图#lasso预测结果画图plt.plot(x,predict_results_LA,"r--",label="predict",alpha=0.5)plt.plot(x,house_price_target_test,"g-",label="real",alpha=0.5)plt.legend(loc="best")# plt.savefig("d:/image2",dpi=500,bbox_inches = 'tight')plt.title("lasso")plt.show()#lasso预测结果画图#画图
得到线性回归预测（留出法）图与lasso预测（留出法）图以及各项指标数据：
线性回归预测（留出法）图
lasso预测（留出法）图
指标数据图1
从各项指标数据可以看出，线性回归+留出法的各项指标都略胜一筹。
2、线性回归+k折交叉验证法与lasso+k折交叉验证法
（1）k=2时
#波士顿房价#k折交叉验证法from sklearn import datasetsfrom sklearn.linear_model import LinearRegressionfrom sklearn.metrics import accuracy_scoreimport matplotlib.pyplot as pltimport numpy as npfrom sklearn.model_selection import KFoldfrom sklearn.linear_model import Lasso#导入数据house_price = datasets.load_boston()house_price_feature = house_price.datahouse_price_target = house_price.target#导入数据#创建kf = KFold(n_splits=2)#创建k折交叉验证法LR_model = LinearRegression()#创建线性回归分类器LA_model = Lasso()#创建lasso#创建#指标变量定义MSE_LR=0.0MAE_LR=0.0RS_LR=0.0MSE_LA=0.0MAE_LA=0.0RS_LA=0.0#指标变量定义#k折交叉验证法循环i=1for train_index, test_index in kf.split(house_price_feature):#k折交叉验证法得到相应数据下标house_price_feature_train, house_price_feature_test = house_price_feature[train_index], house_price_feature[test_index]house_price_target_train, house_price_target_test = house_price_target[train_index], house_price_target[test_index]#训练与预测LR_model.fit(house_price_feature_train, house_price_target_train)#线性回归分类器训练predict_results_LR = LR_model.predict(house_price_feature_test)#线性回归分类器预测LA_model.fit(house_price_feature_train, house_price_target_train)#lasso训练predict_results_LA = LA_model.predict(house_price_feature_test)#lasso预测#训练与预测#计算各个循环的指标MSE_LR=MSE_LR+mean_squared_error(house_price_target_test,predict_results_LR)MAE_LR=MAE_LR+mean_absolute_error(house_price_target_test,predict_results_LR)RS_LR=RS_LR+r2_score(house_price_target_test,predict_results_LR)MSE_LA=MSE_LA+mean_squared_error(house_price_target_test,predict_results_LA)MAE_LA=MAE_LA+mean_absolute_error(house_price_target_test,predict_results_LA)RS_LA=RS_LA+r2_score(house_price_target_test,predict_results_LA)#计算各个循环的指标#画图i=i+1x = np.linspace(0,predict_results_LA.size,predict_results_LA.size)plt.plot(x,predict_results_LR,"r--",alpha=0.5)plt.plot(x,house_price_target_test,"g-",alpha=0.5)plt.title("LR")plt.savefig("d:/image"+str(i)+"1",dpi=500,bbox_inches = 'tight')plt.show()plt.plot(x,predict_results_LA,"r--",alpha=0.5)plt.plot(x,house_price_target_test,"g-",alpha=0.5)plt.title("LA")plt.savefig("d:/image"+str(i)+"2",dpi=500,bbox_inches = 'tight') plt.show()#画图#k折交叉验证法循环#指标分析print("LR's MSE is ",MSE_LR/2)print("LR's MAE is ",MAE_LR/2)print("LR's R Squared is ",RS_LR/2)print("LA's MSE is ",MSE_LA/2)print("LA's MAE is ",MAE_LA/2)print("LA's R Squared is ",RS_LA/2)#指标分析
得到线性回归预测（k折交叉验证法）图与lasso预测（k折交叉验证法）以及各项指标数据（k=2）：
此处因为k=2，因此各有两张图。
线性回归预测（k折交叉验证法）图
lasso预测（k折交叉验证法）图
指标数据图2
由于R Squared 为负，便不以R Squared为依据。以MSE和MAE的数据进行对比，lasso预测（k折交叉验证法）更胜一筹。
（2）k=22时
#波士顿房价#k折交叉验证法from sklearn import datasetsfrom sklearn.linear_model import LinearRegressionfrom sklearn.metrics import accuracy_scoreimport matplotlib.pyplot as pltimport numpy as npfrom sklearn.model_selection import KFoldfrom sklearn.linear_model import Lasso#导入数据house_price = datasets.load_boston()house_price_feature = house_price.datahouse_price_target = house_price.target#导入数据#创建kf = KFold(n_splits=22)#创建k折交叉验证法LR_model = LinearRegression()#创建线性回归分类器LA_model = Lasso()#创建lasso#创建#指标变量定义MSE_LR=0.0MAE_LR=0.0RS_LR=0.0MSE_LA=0.0MAE_LA=0.0RS_LA=0.0#指标变量定义#k折交叉验证法循环i=1for train_index, test_index in kf.split(house_price_feature):#k折交叉验证法得到相应数据下标house_price_feature_train, house_price_feature_test = house_price_feature[train_index], house_price_feature[test_index]house_price_target_train, house_price_target_test = house_price_target[train_index], house_price_target[test_index]#训练与预测LR_model.fit(house_price_feature_train, house_price_target_train)#线性回归分类器训练predict_results_LR = LR_model.predict(house_price_feature_test)#线性回归分类器预测LA_model.fit(house_price_feature_train, house_price_target_train)#lasso训练predict_results_LA = LA_model.predict(house_price_feature_test)#lasso预测#训练与预测#计算各个循环的指标MSE_LR=MSE_LR+mean_squared_error(house_price_target_test,predict_results_LR)MAE_LR=MAE_LR+mean_absolute_error(house_price_target_test,predict_results_LR)RS_LR=RS_LR+r2_score(house_price_target_test,predict_results_LR)MSE_LA=MSE_LA+mean_squared_error(house_price_target_test,predict_results_LA)MAE_LA=MAE_LA+mean_absolute_error(house_price_target_test,predict_results_LA)RS_LA=RS_LA+r2_score(house_price_target_test,predict_results_LA)#计算各个循环的指标#画图i=i+1x = np.linspace(0,predict_results_LA.size,predict_results_LA.size)plt.plot(x,predict_results_LR,"r--",alpha=0.5)plt.plot(x,house_price_target_test,"g-",alpha=0.5)plt.title("LR")plt.savefig("d:/image"+str(i)+"1",dpi=500,bbox_inches = 'tight')plt.show()plt.plot(x,predict_results_LA,"r--",alpha=0.5)plt.plot(x,house_price_target_test,"g-",alpha=0.5)plt.title("LA")plt.savefig("d:/image"+str(i)+"2",dpi=500,bbox_inches = 'tight') plt.show()#画图#k折交叉验证法循环#指标分析print("LR's MSE is ",MSE_LR/22)print("LR's MAE is ",MAE_LR/22)print("LR's R Squared is ",RS_LR/22)print("LA's MSE is ",MSE_LA/22)print("LA's MAE is ",MAE_LA/22)print("LA's R Squared is ",RS_LA/22)#指标分析
得到线性回归预测（k折交叉验证法）图与lasso预测（k折交叉验证法）以及各项指标数据（k=22），但因为图太多（k=22，意味着共有22*2张图片），就不放出来了。我们直接通过指标分析：
指标数据图3
通过指标可看出，线性回归+k折交叉验证法更加好。并且比较k=2与k=22的指标数据，可看出当k=22时，回归得更加好，指标数据明显优化。
因此可总结，线性回归在留出法中、k折交叉验证法（k=22）时，都表现得比较好，且在本实验中，线性回归在留出法中，比在k折交叉验证法中，要更好。
