【Python机器学习】线性模型—

【Python机器学习】线性模型——lasso

除了岭回归，还有一种正则化的线性回归是lasso，与岭回归相同，使用lasso也是约束系数使其接近于0，但方法不同，叫做L1正则化。L1正则化的结果是使用lasso时某些系数刚好为0。说明某些特征被模型完全忽略。

同样以波士顿房价数据集为例：

import mglearn.datasets
from sklearn.model_selection import train_test_split
from sklearn.linear_model import Ridge,LinearRegression,Lasso
from sklearn.neighbors import KNeighborsRegressor
import matplotlib.pyplot as plt
import numpy as np

plt.rcParams['font.sans-serif']=['SimHei']

X,y=mglearn.datasets.load_extended_boston()
X_train,X_test,y_train,y_test=train_test_split(
    X,y,random_state=0
)

lasso=Lasso().fit(X_train,y_train)
print('训练集score:{:.2f}'.format(lasso.score(X_train,y_train)))
print('测试集score:{:.2f}'.format(lasso.score(X_test,y_test)))
print('用到的特征:{}'.format(np.sum(lasso.coef_!=0)))

从结果可以看出，Lasso在训练集和测试集上表现都很差，说明存在欠拟合，因为在数据集的105个特征中只用到了4个。

与岭回归类似，Lasso也存在一个正则化参数alpha，可以控制系数趋向于0的强度，为了减低欠拟合成都，可以减小alpha，同时，增加max_iter（运行迭代的最大次数）


lasso_001=Lasso(alpha=0.01,max_iter=100000).fit(X_train,y_train)
print('训练集score:{:.2f}'.format(lasso_001.score(X_train,y_train)))
print('测试集score:{:.2f}'.format(lasso_001.score(X_test,y_test)))
print('用到的特征:{}'.format(np.sum(lasso_001.coef_!=0)))

lasso_00001=Lasso(alpha=0.0001,max_iter=100000).fit(X_train,y_train)
print('训练集score:{:.2f}'.format(lasso_00001.score(X_train,y_train)))
print('测试集score:{:.2f}'.format(lasso_00001.score(X_test,y_test)))
print('用到的特征:{}'.format(np.sum(lasso_00001.coef_!=0)

alpha变小可以拟合一个更复杂的模型，在训练集和测试集上的表现也更好，但是alpha不能设置的太小，否则就会消除正则化的效果，并出现过拟合，得到与线性回归类似的模型。

对不同alpha系数的结果进行可视化对比：

import mglearn.datasets
from sklearn.model_selection import train_test_split
from sklearn.linear_model import Ridge,LinearRegression,Lasso
from sklearn.neighbors import KNeighborsRegressor
import matplotlib.pyplot as plt
import numpy as np

plt.rcParams['font.sans-serif']=['SimHei']

X,y=mglearn.datasets.load_extended_boston()
X_train,X_test,y_train,y_test=train_test_split(
    X,y,random_state=0
)
lasso=Lasso().fit(X_train,y_train)
lasso_001=Lasso(alpha=0.01,max_iter=100000).fit(X_train,y_train)
lasso_00001=Lasso(alpha=0.0001,max_iter=100000).fit(X_train,y_train)
ridge_01=Ridge(alpha=0.1).fit(X_train,y_train)

plt.plot(lasso.coef_,'s',label='lasso alpha=1')
plt.plot(lasso_001.coef_,'^',label='lasso alpha=0.01')
plt.plot(lasso_00001.coef_,'v',label='lasso alpha=0.0001')

plt.plot(ridge_01.coef_,'o',label='岭 alpha=0.1')
plt.xlabel('index')
plt.ylabel('系数大小')
plt.ylim(-25,25)
plt.legend(ncol=2,loc=(0,1.05))
plt.show()