离散与真实AdaBoost¶
此示例基于Hastie等人2009 [1]的图10.2，并说明了离散的SAMME [2]提升算法与实SAMME.R提升算法在表现上的差异。这两种算法都是在一个二分类任务上评估的，其中目标Y是一个由10个输入特征组成的非线性函数。
离散的 SAMME AdaBoost基于预测类标签中的错误进行调整，而真正的SAMME.R使用预测的类概率。
1 T. Hastie, R. Tibshirani and J. Friedman, “Elements of Statistical Learning Ed. 2”, Springer, 2009.
2 Zhu, H. Zou, S. Rosset, T. Hastie, “Multi-class AdaBoost”, 2009.
print(__doc__)
# Author: Peter Prettenhofer <peter.prettenhofer@gmail.com>,
# Noel Dawe <noel.dawe@gmail.com>
#
# License: BSD 3 clause
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
n_estimators = 400
# A learning rate of 1. may not be optimal for both SAMME and SAMME.R
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)
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_real_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)
plt.show()
脚本的总运行时间：(0分6.194秒)
