线性模型——线性回归模型的正则化
import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets,linear_model,discriminant_analysis,cross_validation加载数据
def load_data():
diabetes=datasets.load_diabetes()
return cross_validation.train_test_split(diabetes.data,diabetes.target,
test_size=0.25,random_state=0)岭回归
模型原型
class sklearn.linear_model.Ridge(alpha=1.0,fit_intercept=True,
normalize=False,copy_X=True,max_iter=None,tol=0.001,
solver=’auto’,random_state=None)
参数
- alpha:a值，值越大则正则化的占比越大
- fit_intercept
- normalize
- copy_X
- max_iter:最大迭代数
- tol:判断迭代是否收敛的阙值
- solver:求解最优化问题的算法
- auto:自动选择算法
- svd:使用奇异值分解来计算回归系数
- cholesky:使用scipy.linalg.solve函数来求解
- sparse_cg:使用scipy.sparse.linalg.cg函数来求解
- lsqr:使用scipy.sparse.linalg.lsqr函数来求解（运算速度快）
- sag:使用Stochastic Average Gradient descent算法（求解最优化问题）
- random_state
- 整数:指定随机数生成器的种子
- RandomState实例:指定随机数生成器
- None:使用默认的随机数生成器
属性
- coef_
- intercept_
- niter:实际迭代次数
方法
- it(X,y[,sample_weight])
- predict(X)
- score(X,y(,sample_weight))
使用Ridge
def test_Ridge(*data):
x_train,x_test,y_train,y_test=data
regr=linear_model.Ridge()
regr.fit(X_train,y_train)
print('Coefficients:%s,\nintercept %.2f'%(regr.coef_,regr.intercept_))
print('Residual sum of squares:%.2f'%np.mean((regr.predict(X_test)-y_test)**2))
print('Score:%.2f'%regr.score(X_test,y_test))
X_train,X_test,y_train,y_test=load_data()
test_Ridge(X_train,X_test,y_train,y_test)a系数对预测性能的影响
def test_Ridge_alpha(*data):
X_train,X_test,y_train,y_test=data
alphas=[0.01,0.02,0.05,0.1,0.2,0.5,1,2,5,10,20,50,100,200,500,1000]
scores=[]
for i,alpha in enumerate(alphas):
regr=linear_model.Ridge(alpha=alpha)
regr.fit(X_train,y_train)
scores.append(regr.score(X_test,y_test))
#绘图
fig=plt.figure()
ax=fig.add_subplot(1,1,1)
ax.plot(alphas,scores)
ax.set_xlabel(r"$\alpha$")
ax.set_ylabel(r"score")
ax.set_xscale('log')
ax.set_title("Ridge")
plt.show()
X_train,X_test,y_train,y_test=load_data()
test_Ridge_alpha(X_train,X_test,y_train,y_test)Lasso回归
模型原型
class sklearn.linear_model.Lasso(alpha=1.0,fit_intercept=True,
normalize=False,precompute=False,copy_X=True,
max_iter=1000,tol=0.0001,warm_start=False,positive=False,
random_state=None,selection=’cyclic’)
参数
- alpha
- fit_intercept
- normalize
- precompute:是否计算Gram矩阵来加速计算
- copy_X
- max_iter
- tol
- warm_start:是否使用前一次训练结果继续训练
- positive:如果为True,那么强制要求权重向量的分量都为正数
- random_state
- selection
- random:更新的时候，随机选择权重向量的一个分量来更新
- cyclic:更新的时候，从前向后依次选择权重向量的分量来更新
属性
- coef_
- intercept_
- niter
方法
- fit(X,y[,sample_weight])
- predict(X)
- score(X,y[,sample_weight])
使用Lasso
def test_Lasso(*data):
X_train,X_test,y_train,y_test=data
regr=linear_model.Lasso()
regr.fit(X_train,y_train)
print('Coefficients:%s,\nintercept %.2f'%(regr.coef_,regr.intercept_))
print('Residual aum of squares:%.2f'%np.mean((regr.predict(X_test)-y_test)**2))
print('Score:%.2f'%regr.score(X_test,y_test))
X_train,X_test,y_train,y_test=load_data()
test_Lasso(X_train,X_test,y_train,y_test)a系数对预测性能的影响
def test_Lasso_alpha(*data):
X_train,X_test,y_train,y_test=data
alphas=[0.01,0.02,0.05,0.1,0.2,0.5,1,2,5,10,20,50,100,200,500,1000]
scores=[]
for i,alpha in enumerate(alphas):
regr=linear_model.Lasso(alpha=alpha)
regr.fit(X_train,y_train)
scores.append(regr.score(X_test,y_test))
#绘图
fig=plt.figure()
ax=fig.add_subplot(1,1,1)
ax.plot(alphas,scores)
ax.set_xlabel(r'$\alpha$')
ax.set_ylabel(r'score')
ax.set_xscale('log')
ax.set_title("Lasso")
plt.show()
X_train,X_test,y_train,y_test=load_data()
test_Lasso_alpha(X_train,X_test,y_train,y_test)ElasticNet回归
模型原型
class sklearn.linear_model.ElasticNet(alpha=1.0,l1_ratio=0.5,
fit_intercept=True,normalize=False,precompute=False, copy_X=True,max_iter=1000,tol=0.0001,warm_start=False,
positive=False,random_state=None,selection=’cyclic’)
参数
- alpha
- l1_ratio:p值
- fit_intercept
- normalize
- precompute
- copy_X
- max_iter
- tol
- warm_start
- positive
- random_state
- selection
属性
- coef_
- intercept_
- niter
方法
- fit(X,y[,sample_weight])
- predict(X)
- score(X,y[,sample_weight])
使用ElasticNet
def test_ElasticNet(*data):
X_train,X_test,y_train,y_test=data
regr=linear_model.ElasticNet()
regr.fit(X_train,y_train)
print('Coefficients:%s,\nintercept %.2f'%(regr.coef_,regr.intercept_))
print('Residual sum of squares:%.2f'%np.mean((regr.predict(X_test)-y_test)**2))
print('Score:%.2f'%regr.score(X_test,y_test))
X_train,X_test,y_train,y_test=load_data()
test_ElasticNet(X_train,X_test,y_train,y_test)a系数对预测能力的影响
def test_ElasticNet_alpha_rho(*data):
alphas=np.logspace(-2,2)
rhos=np.linspace(0.01,1)
scores=[]
for alpha in alphas:
for rho in rhos:
regr=linear_model.ElasticNet(alpha=alpha,l1_ratio=rho)
regr.fit(X_train,y_train)
scores.append(regr.score(X_test,y_test))
#绘图
alphas,rhos=np.meshgrid(alphas,rhos)
scores=np.array(scores).reshape(alphas.shape)
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
fig=plt.figure()
ax=Axes3D(fig)
surf=ax.plot_surface(alphas,rhos,scores,rstride=1,cstride=1,cmap=cm.jet,linewidth=0,antialiased=False)
fig.colorbar(surf,shrink=0.5,aspect=5)
ax.set_xlabel(r"$\alpha$")
ax.set_ylabel(r"$\rho$")
ax.set_zlabel("score")
ax.set_title("ElasticNet")
plt.show()
X_train,X_test,y_train,y_test=load_data()
test_ElasticNet_alpha_rho(X_train,X_test,y_train,y_test)