adaboost 参数选择

先看下ababoost和决策树效果对比

import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import learning_curve

def plot_learning_curve(estimator,title,X,y,ylim=None,cv=None,
                        n_jobs=None,train_sizes=np.linspace(.1,1.0,10)):
    plt.figure()
    plt.title(title)
    if ylim is not None:
        plt.ylim(*ylim)
    plt.xlabel("Training examples")
    plt.ylabel("Score")
    train_sizes, train_scores, test_scores = learning_curve(
        estimator, X, y, cv=cv, n_jobs=n_jobs, train_sizes=train_sizes)
    train_scores_mean = np.mean(train_scores, axis=1)
    train_scores_std = np.std(train_scores, axis=1)
    test_scores_mean = np.mean(test_scores, axis=1)
    test_scores_std = np.std(test_scores, axis=1)
    plt.grid()

    plt.fill_between(train_sizes, train_scores_mean - train_scores_std,
                     train_scores_mean + train_scores_std, alpha=0.1,
                     color="r")
    plt.fill_between(train_sizes, test_scores_mean - test_scores_std,
                     test_scores_mean + test_scores_std, alpha=0.1, color="g")
    plt.plot(train_sizes, train_scores_mean, 'o-', color="r",
             label="Training score")
    plt.plot(train_sizes, test_scores_mean, 'o-', color="g",
             label="Cross-validation score")

    plt.legend(loc="best")
    return plt

from sklearn.datasets import  make_gaussian_quantiles
from sklearn.model_selection import learning_curve
from sklearn.model_selection import ShuffleSplit
import numpy as np

from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import AdaBoostClassifier
# ##########################
# 生成2维正态分布，生成的数据按分位数分为两类，50个样本特征，5000个样本数据
X,y = make_gaussian_quantiles(cov=2.0,n_samples=5000,n_features=50,n_classes=2,random_state=1)
# 设置一百折交叉验证参数，数据集分层越多，交叉最优模型越接近原模型
cv = ShuffleSplit(n_splits=10,test_size=0.2,random_state=1)
# 分别画出CART分类决策树和AdaBoost分类决策树的学习曲线
estimatorCart = DecisionTreeClassifier(max_depth=1)
estimatorBoost = AdaBoostClassifier(base_estimator=estimatorCart,n_estimators=270)
# 画CART决策树和AdaBoost的学习曲线
estimatorTuple = (estimatorCart,estimatorBoost)
titleTuple =("decision learning curve","adaBoost learning curve")
title = "decision learning curve"
for i in range(2):
    estimator = estimatorTuple[i]
    title = titleTuple[i]
    plot_learning_curve(estimator,title, X, y, cv=cv)
    plt.show()

输出学习曲线

分析：随着样本数的增加，单决策树的预测精度稳定在0.5左右，是个弱分类器，而adaboost预测精度在0.85左右，明显高于单决策树，是个强分类器。

参数选择

上面的模型使用的是默认参数，其实还有优化的空间。

在集成学习中，参数调优一般是先选择框架的参数，再选择基学习器的参数

框架参数调优

以基学习器个数为例

from sklearn.model_selection import GridSearchCV
from sklearn.ensemble import AdaBoostClassifier
from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import make_gaussian_quantiles

estimatorCart = DecisionTreeClassifier(max_depth=1)
X,y = make_gaussian_quantiles(cov=2.0,n_samples=5000,n_features=50,n_classes=2,random_state=1)

### 第一轮
# 对框架参数 弱学习器个数进行择优
param_test1 = {"n_estimators":range(150,300,50)}
# 框架参数择优
gsearch1 = GridSearchCV(estimator=AdaBoostClassifier(estimatorCart),param_grid=param_test1,scoring="roc_auc",cv=5)
gsearch1.fit(X,y)
print(gsearch1.best_params_,gsearch1.best_score_)       # ({'n_estimators': 250}, 0.9360103999999999)

### 第二轮
# 继续优化弱学习器个数，在最优学习器个数的范围内再次搜寻
n_estimator1 = 250
param_test2 = {"n_estimators":range(n_estimator1-30,n_estimator1+30,10)}
gsearch2 = GridSearchCV(estimator=AdaBoostClassifier(estimatorCart),param_grid=param_test2,scoring="roc_auc",cv=5)
gsearch2.fit(X,y)
print(gsearch2.best_params_,gsearch2.best_score_)           # ({'n_estimators': 270}, 0.9387719999999999)

基学习器参数调优

以max_depth和min_samples_split为例

import numpy as np
from sklearn.model_selection import cross_validate
n_estimators2 = 270
score = 0
for i in range(1,3):  # 决策树最大深度循环
    print(i)
    for j in range(18,22):
        print(j)
        bdt=AdaBoostClassifier(DecisionTreeClassifier(max_depth=i,min_samples_split=j),n_estimators=n_estimators2)
        cv_result = cross_validate(bdt,X,y,return_train_score=False,cv=5)
        cv_value_vec = cv_result["test_score"]
        cv_mean = np.mean(cv_value_vec)
        print(cv_mean)
        if cv_mean>=score:
            score = cv_mean
            tree_depth = i
            samples_split = j

用最优参数构建模型

from sklearn.model_selection import train_test_split
tree_depth = 1
X_train, y_train, X_test, y_test = train_test_split(X, y)
bdt = AdaBoostClassifier(DecisionTreeClassifier(max_depth=tree_depth),
                         n_estimators=n_estimators2)
bdt.fit(X_train,y_train)
print(bdt.score(X_test,y_test))

85.6%，略有提高

学习率与基学习器个数的探索

import matplotlib.pyplot as plt

from sklearn.ensemble import  AdaBoostClassifier
from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import  make_gaussian_quantiles
from sklearn.model_selection import learning_curve
from sklearn.model_selection import ShuffleSplit
import numpy as np

from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import AdaBoostClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import  accuracy_score
from sklearn.metrics import zero_one_loss

n_estimators = 200
# 生成2维正态分布，生成的数据按分位数分为两类，50个样本特征，5000个样本数据
X,y = make_gaussian_quantiles(cov=2.0,n_samples=5000,n_features=50,n_classes=2,random_state=1)
# 数据划分为训练集和测试集
X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.2,random_state=1)
# 根据上一节的参数择优，选择最优参数来构建模型
estimatorCart = DecisionTreeClassifier(max_depth=1)
dt_stump1 = AdaBoostClassifier(base_estimator=estimatorCart,n_estimators=n_estimators,learning_rate=0.8)
dt_stump2 = AdaBoostClassifier(base_estimator=estimatorCart,n_estimators=n_estimators,learning_rate=0.1)
dt_stump1.fit(X_train,y_train)
dt_stump_err1 = 1.0 - dt_stump1.score(X_test,y_test)
#
dt_stump2.fit(X_train,y_train)
dt_stump_err2 = 1.0 - dt_stump2.score(X_test,y_test)

############
test_errors1 = []
# 每迭代一次，得到一个测试结果
ada_discrete_err1 = np.zeros((n_estimators,))
ada_discrete_err2 = np.zeros((n_estimators,))
for i,ypred in enumerate(dt_stump1.staged_predict(X_test)):
    ada_discrete_err1[i] = zero_one_loss(ypred,y_test)

for i,ypred in enumerate(dt_stump2.staged_predict(X_test)):
    ada_discrete_err2[i] = zero_one_loss(ypred,y_test)

# 画出迭代次数与准确率的关系
fig = plt.figure()
ax = fig.add_subplot(111)

ax.plot(np.arange(n_estimators) + 1, ada_discrete_err1,label='learning rate = 0.8',color='red')
ax.plot(np.arange(n_estimators) + 1, ada_discrete_err2,label='learning rate = 0.1',color='green')
ax.set_ylim((0.0, 1))
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()

输出

针对当前数据，学习率大，错误率低

总结

基学习器的复杂度尽量低，可以通过增加学习器个数提高泛化能力，

但是当数据噪声较大或者基学习器复杂度较高时，增加基学习器个数很难提高泛化能力

这只是大致方向，不绝对。

参考资料：

https://zhuanlan.zhihu.com/p/57319411