Boosting 算法简介
Boosting算法,我理解的就是两个思想:
1)“三个臭皮匠顶个诸葛亮”,一堆弱分类器的组合就可以成为一个强分类器;
2)“知错能改,善莫大焉”,不断地在错误中学习,迭代来降低犯错概率
当然,要理解好Boosting的思想,首先还是从弱学习算法和强学习算法来引入:
1)强学习算法:存在一个多项式时间的学习算法以识别一组概念,且识别的正确率很高;
2)弱学习算法:识别一组概念的正确率仅比随机猜测略好;
Kearns & Valiant证明了弱学习算法与强学习算法的等价问题,如果两者等价,只需找到一个比随机猜测略好的学习算法,就可以将其提升为强学习算法。
那么是怎么实现“知错就改”的呢?
Boosting算法,通过一系列的迭代来优化分类结果,每迭代一次引入一个弱分类器,来克服现在已经存在的弱分类器组合的shortcomings
在Adaboost算法中,这个shortcomings的表征就是权值高的样本点
而在Gradient Boosting算法中,这个shortcomings的表征就是梯度
无论是Adaboost还是Gradient Boosting,都是通过这个shortcomings来告诉学习器怎么去提升模型,也就是“Boosting”这个名字的由来吧
Adaboost算法
Adaboost是由Freund 和 Schapire在1997年提出的,在整个训练集上维护一个分布权值向量W,用赋予权重的训练集通过弱分类算法产生分类假设(基学习器)y(x),然后计算错误率,用得到的错误率去更新分布权值向量w,对错误分类的样本分配更大的权值,正确分类的样本赋予更小的权值。每次更新后用相同的弱分类算法产生新的分类假设,这些分类假设的序列构成多分类器。对这些多分类器用加权的方法进行联合,最后得到决策结果。
其结构如下图所示:
前一个学习器改变权重w,然后再经过下一个学习器,最终所有的学习器共同组成最后的学习器。
如果一个样本在前一个学习器中被误分,那么它所对应的权重会被加重,相应地,被正确分类的样本的权重会降低。
这里主要涉及到两个权重的计算问题:
1)样本的权值
1> 没有先验知识的情况下,初始的分布应为等概分布,样本数目为n,权值为1/n
2> 每一次的迭代更新权值,提高分错样本的权重
2)弱学习器的权值
1> 最后的强学习器是通过多个基学习器通过权值组合得到的。
2> 通过权值体现不同基学习器的影响,正确率高的基学习器权重高。实际上是分类误差的一个函数
Gradient Boosting
和Adaboost不同,Gradient Boosting 在迭代的时候选择梯度下降的方向来保证最后的结果最好。
损失函数用来描述模型的“靠谱”程度,假设模型没有过拟合,损失函数越大,模型的错误率越高
如果我们的模型能够让损失函数持续的下降,则说明我们的模型在不停的改进,而最好的方式就是让损失函数在其梯度方向上下降。
下面这个流程图是Gradient Boosting的经典图了,数学推导并不复杂,只要理解了Boosting的思想,不难看懂
这里是直接对模型的函数进行更新,利用了参数可加性推广到函数空间。
训练F0-Fm一共m个基学习器,沿着梯度下降的方向不断更新ρm和am
GradientBoostingRegressor实现
python中的scikit-learn包提供了很方便的GradientBoostingRegressor和GBDT的函数接口,可以很方便的调用函数就可以完成模型的训练和预测
GradientBoostingRegressor函数的参数如下:
class sklearn.ensemble.GradientBoostingRegressor(loss='ls', learning_rate=0.1, n_estimators=100, subsample=1.0, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_depth=3, init=None, random_state=None, max_features=None, alpha=0.9, verbose=0, max_leaf_nodes=None, warm_start=False, presort='auto')[source]¶
loss: 选择损失函数,默认值为ls(least squres)
learning_rate: 学习率,模型是0.1
n_estimators: 弱学习器的数目,默认值100
max_depth: 每一个学习器的最大深度,限制回归树的节点数目,默认为3
min_samples_split: 可以划分为内部节点的最小样本数,默认为2
min_samples_leaf: 叶节点所需的最小样本数,默认为1
……
可以参考 http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingRegressor.html
官方文档里带了一个很好的例子,以500个弱学习器,最小平方误差的梯度提升模型,做波士顿房价预测,代码和结果如下:
import numpy as np
import matplotlib.pyplot as plt
from sklearn import ensemble
from sklearn import datasets
from sklearn.utils import shuffle
from sklearn.metrics import mean_squared_error
###############################################################################
# Load data
boston = datasets.load_boston()
X, y = shuffle(boston.data, boston.target, random_state=13)
X = X.astype(np.float32)
offset = int(X.shape[0] * 0.9)
X_train, y_train = X[:offset], y[:offset]
X_test, y_test = X[offset:], y[offset:]
###############################################################################
# Fit regression model
params = {'n_estimators': 500, 'max_depth': 4, 'min_samples_split': 1,
'learning_rate': 0.01, 'loss': 'ls'}
clf = ensemble.GradientBoostingRegressor(**params)
clf.fit(X_train, y_train)
mse = mean_squared_error(y_test, clf.predict(X_test))
print("MSE: %.4f" % mse)
###############################################################################
# Plot training deviance
# compute test set deviance
test_score = np.zeros((params['n_estimators'],), dtype=np.float64)
for i, y_pred in enumerate(clf.staged_predict(X_test)):
test_score[i] = clf.loss_(y_test, y_pred)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.title('Deviance')
plt.plot(np.arange(params['n_estimators']) + 1, clf.train_score_, 'b-',
label='Training Set Deviance')
plt.plot(np.arange(params['n_estimators']) + 1, test_score, 'r-',
label='Test Set Deviance')
plt.legend(loc='upper right')
plt.xlabel('Boosting Iterations')
plt.ylabel('Deviance')
###############################################################################
# Plot feature importance
feature_importance = clf.feature_importances_
# make importances relative to max importance
feature_importance = 100.0 * (feature_importance / feature_importance.max())
sorted_idx = np.argsort(feature_importance)
pos = np.arange(sorted_idx.shape[0]) + .5
plt.subplot(1, 2, 2)
plt.barh(pos, feature_importance[sorted_idx], align='center')
plt.yticks(pos, boston.feature_names[sorted_idx])
plt.xlabel('Relative Importance')
plt.title('Variable Importance')
plt.show()
可以发现,如果要用Gradient Boosting 算法的话,在sklearn包里调用还是非常方便的,几行代码即可完成,大部分的工作应该是在特征提取上。
# -*- coding: utf-8 -*-
# @Time : 2018/8/21 10:32
# @Author : Barry
# @File : mnist_GB.py
# @Software: PyCharm Community Edition
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.metrics import accuracy_score
import tensorflow.examples.tutorials.mnist.input_data as input_data
import time
from datetime import datetime
data_dir = '../MNIST_data/'
mnist = input_data.read_data_sets(data_dir,one_hot=False)
batch_size = 50000
batch_x,batch_y = mnist.train.next_batch(batch_size)
test_x = mnist.test.images[:10000]
test_y = mnist.test.labels[:10000]
print("start Gradient Boosting")
StartTime = time.clock()
for i in range(10,200,10):
clf_rf = GradientBoostingClassifier(n_estimators=i)
clf_rf.fit(batch_x,batch_y)
y_pred_rf = clf_rf.predict(test_x)
acc_rf = accuracy_score(test_y,y_pred_rf)
print("%s n_estimators = %d, random forest accuracy:%f" % (datetime.now(), i, acc_rf))
EndTime = time.clock()
print('Total time %.2f s' % (EndTime - StartTime))
结果:
start Gradient Boosting
2018-08-22 09:39:53.114800 n_estimators = 10, random forest accuracy:0.845200
2018-08-22 09:46:25.680700 n_estimators = 20, random forest accuracy:0.883500
2018-08-22 09:56:21.176710 n_estimators = 30, random forest accuracy:0.902800
2018-08-22 10:09:17.453814 n_estimators = 40, random forest accuracy:0.917600
2018-08-22 10:25:45.233702 n_estimators = 50, random forest accuracy:0.925600
2018-08-22 10:45:38.344716 n_estimators = 60, random forest accuracy:0.929900
2018-08-22 11:09:17.834999 n_estimators = 70, random forest accuracy:0.935100
2018-08-22 11:36:38.280471 n_estimators = 80, random forest accuracy:0.939500
2018-08-22 12:06:21.974137 n_estimators = 90, random forest accuracy:0.942200
2018-08-22 12:40:35.648684 n_estimators = 100, random forest accuracy:0.944300
2018-08-22 13:17:52.943346 n_estimators = 110, random forest accuracy:0.947300
2018-08-22 14:00:00.915921 n_estimators = 120, random forest accuracy:0.948600
2018-08-22 14:47:46.923277 n_estimators = 130, random forest accuracy:0.950300
2018-08-22 15:41:09.575049 n_estimators = 140, random forest accuracy:0.952400
2018-08-22 16:38:04.491657 n_estimators = 150, random forest accuracy:0.954200
2018-08-22 17:38:36.862459 n_estimators = 160, random forest accuracy:0.955000
2018-08-22 18:42:45.162086 n_estimators = 170, random forest accuracy:0.956600
2018-08-22 19:51:19.596696 n_estimators = 180, random forest accuracy:0.957500
mnist_AB.py
# -*- coding: utf-8 -*-
# @Time : 2018/8/21 10:39
# @Author : Barry
# @File : mnist_AB.py
# @Software: PyCharm Community Edition
from sklearn.ensemble import AdaBoostClassifier
from sklearn.metrics import accuracy_score
import tensorflow.examples.tutorials.mnist.input_data as input_data
import time
from datetime import datetime
data_dir = '../MNIST_data/'
mnist = input_data.read_data_sets(data_dir,one_hot=False)
batch_size = 50000
batch_x,batch_y = mnist.train.next_batch(batch_size)
test_x = mnist.test.images[:10000]
test_y = mnist.test.labels[:10000]
print("start Gradient Boosting")
StartTime = time.clock()
for i in range(10,200,10):
clf_rf = AdaBoostClassifier(n_estimators=i)
clf_rf.fit(batch_x,batch_y)
y_pred_rf = clf_rf.predict(test_x)
acc_rf = accuracy_score(test_y,y_pred_rf)
print("%s n_estimators = %d, random forest accuracy:%f" % (datetime.now(), i, acc_rf))
EndTime = time.clock()
print('Total time %.2f s' % (EndTime - StartTime))
运行结果:
start Gradient Boosting
2018-08-22 19:47:39.340555 n_estimators = 10, random forest accuracy:0.590400
2018-08-22 19:48:06.411962 n_estimators = 20, random forest accuracy:0.692200
2018-08-22 19:48:45.641367 n_estimators = 30, random forest accuracy:0.692800
2018-08-22 19:49:34.456253 n_estimators = 40, random forest accuracy:0.710300
2018-08-22 19:50:38.019661 n_estimators = 50, random forest accuracy:0.717800
2018-08-22 19:51:56.216605 n_estimators = 60, random forest accuracy:0.730200
2018-08-22 19:53:21.201670 n_estimators = 70, random forest accuracy:0.734600
2018-08-22 19:54:58.991348 n_estimators = 80, random forest accuracy:0.735000
2018-08-22 19:56:51.498537 n_estimators = 90, random forest accuracy:0.728900
2018-08-22 19:59:01.355309 n_estimators = 100, random forest accuracy:0.733200
2018-08-22 20:01:11.853150 n_estimators = 110, random forest accuracy:0.720400
2018-08-22 20:03:34.914754 n_estimators = 120, random forest accuracy:0.707800
2018-08-22 20:06:12.198900 n_estimators = 130, random forest accuracy:0.711600
2018-08-22 20:09:07.673904 n_estimators = 140, random forest accuracy:0.711800
2018-08-22 20:12:14.946045 n_estimators = 150, random forest accuracy:0.719700
2018-08-22 20:15:34.760213 n_estimators = 160, random forest accuracy:0.722100
Adaboost算法运行比Gradientboost算法运行更快! 但是从准确度上来看,梯度提升算法效果更好。