逻辑回归中使用正则化
scikit-learn中的逻辑回归 import numpy as np
import matplotlib.pyplot as plt
np.random.seed(666)
X = np.random.normal(0,1,size=(200,2))
y = np.array(X[:,0]**2 + X[:,1] < 1.5,dtype='int')
for _ in range(20):
y[np.random.randint(200)] = 1
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test = train_test_split(X,y,random_state=666)
# 使用逻辑回归
from sklearn.linear_model import LogisticRegression
log_reg = LogisticRegression()
log_reg.fit(X_train,y_train)
LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False)
log_reg.score(X_train,y_train)
0.7933333333333333
log_reg.score(X_test,y_test)
0.86
def plot_decision_boundary(model, axis):
x0, x1 = np.meshgrid(
np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),
np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1), )
X_new = np.c_[x0.ravel(), x1.ravel()]
y_predict = model.predict(X_new)
zz = y_predict.reshape(x0.shape)
from matplotlib.colors import ListedColormap
custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])
plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)
plot_decision_boundary(log_reg,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()
/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
s)
# 使用多项式逻辑回归
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.preprocessing import StandardScaler
def PolynomialLogisticRegression(degree):
return Pipeline([
('poly',PolynomialFeatures(degree)),
('std_scaler',StandardScaler()),
('log_reg',LogisticRegression())
])
ploy_log_reg = PolynomialLogisticRegression(degree=2)
ploy_log_reg.fit(X_train,y_train)
Pipeline(memory=None,
steps=[('poly', PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('log_reg', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))])
ploy_log_reg.score(X_train,y_train)
0.9133333333333333
plot_decision_boundary(ploy_log_reg,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()
/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
s)
ploy_log_reg2 = PolynomialLogisticRegression(degree=20)
ploy_log_reg2.fit(X_train,y_train)
Pipeline(memory=None,
steps=[('poly', PolynomialFeatures(degree=20, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('log_reg', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))])
plot_decision_boundary(ploy_log_reg2,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()
/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
s)
def PolynomialLogisticRegression(degree,C):
return Pipeline([
('poly',PolynomialFeatures(degree)),
('std_scaler',StandardScaler()),
('log_reg',LogisticRegression(C=C))
])
ploy_log_reg3 = PolynomialLogisticRegression(degree=20,C=0.1)
ploy_log_reg3.fit(X_train,y_train)
Pipeline(memory=None,
steps=[('poly', PolynomialFeatures(degree=20, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('log_reg', LogisticRegression(C=0.1, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))])
ploy_log_reg3.score(X_train,y_train)
0.8533333333333334
ploy_log_reg3.score(X_test,y_test)
0.92
plot_decision_boundary(ploy_log_reg3,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()
/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
s)
def PolynomialLogisticRegression(degree,C,penalty='l2'):
return Pipeline([
('poly',PolynomialFeatures(degree)),
('std_scaler',StandardScaler()),
('log_reg',LogisticRegression(C=C,penalty=penalty))
])
ploy_log_reg4 = PolynomialLogisticRegression(degree=20,C=0.1,penalty="l1")
ploy_log_reg4.fit(X_train,y_train)
Pipeline(memory=None,
steps=[('poly', PolynomialFeatures(degree=20, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('log_reg', LogisticRegression(C=0.1, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l1', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))])
ploy_log_reg4.score(X_train,y_train)
0.8266666666666667
ploy_log_reg4.score(X_test,y_test)
0.9
plot_decision_boundary(ploy_log_reg4,axis=[-4,4,-4,4])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()
/Users/shirukai/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'
s)
