Bootstrapping算法主要思路:
i)重复地从一个样本集合D中采样n个样本
ii)针对每次采样的子样本集,进行统计学习,获得假设Hi
iii)将若干个假设进行组合,形成最终的假设Hfinal
iv)将最终的假设用于具体的分类任务
(2)Bagging算法主要思路:
i)训练分类器
从整体样本集合中,抽样n* < N个样本 针对抽样的集合训练分类器Ci
ii)分类器进行投票,最终的结果是分类器投票的优胜结果
这两个算法提供的主要是思路,真正的实用性是基于这两个算法思想的AdaBoost算法:
AdaBoost算法过程:
这就是Adaboost的结构,最后的分类器YM是由数个弱分类器(weak classifier)组合而成的,相当于最后m个弱分类器来投票决定分类,而且每个弱分类器的“话语权”α不一样。
skit-learnd一个例子如下:
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.tree import DecisionTreeClassifier
from sklearn.metrics import zero_one_loss
from sklearn.ensemble import AdaBoostClassifier
import time
a=time.time()
n_estimators=400
learning_rate=1
X,y=datasets.make_hastie_10_2(n_samples=12000,random_state=1)
X_test,y_test=X[2000:],y[2000:]
X_train,y_train=X[:2000],y[:2000]
dt_stump=DecisionTreeClassifier(max_depth=1,min_samples_leaf=1)
dt_stump.fit(X_train,y_train)
dt_stump_err=1.0-dt_stump.score(X_test,y_test)
dt=DecisionTreeClassifier(max_depth=9,min_samples_leaf=1)
dt.fit(X_train,y_train)
dt_err=1.0-dt.score(X_test,y_test)
ada_discrete=AdaBoostClassifier(base_estimator=dt_stump,learning_rate=learning_rate,n_estimators=n_estimators,algorithm='SAMME')
ada_discrete.fit(X_train,y_train)
ada_real=AdaBoostClassifier(base_estimator=dt_stump,learning_rate=learning_rate,n_estimators=n_estimators,algorithm='SAMME.R')
ada_real.fit(X_train,y_train)
fig=plt.figure()
ax=fig.add_subplot(111)
ax.plot([1,n_estimators],[dt_stump_err]*2,'k-',label='Decision Stump Error')
ax.plot([1,n_estimators],[dt_err]*2,'k--',label='Decision Tree Error')
ada_discrete_err=np.zeros((n_estimators,))
for i,y_pred in enumerate(ada_discrete.staged_predict(X_test)):
ada_discrete_err[i]=zero_one_loss(y_pred,y_test) ######zero_one_loss
ada_discrete_err_train=np.zeros((n_estimators,))
for i,y_pred in enumerate(ada_discrete.staged_predict(X_train)):
ada_discrete_err_train[i]=zero_one_loss(y_pred,y_train)
ada_real_err=np.zeros((n_estimators,))
for i,y_pred in enumerate(ada_real.staged_predict(X_test)):
ada_real_err[i]=zero_one_loss(y_pred,y_test)
ada_real_err_train=np.zeros((n_estimators,))
for i,y_pred in enumerate(ada_real.staged_predict(X_train)):
ada_discrete_err_train[i]=zero_one_loss(y_pred,y_train)
ax.plot(np.arange(n_estimators)+1,ada_discrete_err,label='Discrete AdaBoost Test Error',color='red')
ax.plot(np.arange(n_estimators)+1,ada_discrete_err_train,label='Discrete AdaBoost Train Error',color='blue')
ax.plot(np.arange(n_estimators)+1,ada_real_err,label='Real AdaBoost Test Error',color='orange')
ax.plot(np.arange(n_estimators)+1,ada_real_err_train,label='Real AdaBoost Train Error',color='green')
ax.set_ylim((0.0,0.5))
ax.set_xlabel('n_estimators')
ax.set_ylabel('error rate')
leg=ax.legend(loc='upper right',fancybox=True)
leg.get_frame().set_alpha(0.7)
b=time.time()
print('total running time of this example is :',b-a)
plt.show()