机器学习之Adaboost算法原理
转自:http://www.cnblogs.com/pinard/p/6133937.html
在集成学习原理小结中,我们讲到了集成学习按照个体学习器之间是否存在依赖关系可以分为两类,第一个是个体学习器之间存在强依赖关系,另一类是个体学习器之间不存在强依赖关系。前者的代表算法就是是boosting系列算法。在boosting系列算法中, Adaboost是最著名的算法之一。Adaboost既可以用作分类,也可以用作回归。本文就对Adaboost算法做一个总结。
1. 回顾boosting算法的基本原理
在集成学习原理小结中,我们已经讲到了boosting算法系列的基本思想,如下图:
从图中可以看出,Boosting算法的工作机制是首先从训练集用初始权重训练出一个弱学习器1,根据弱学习的学习误差率表现来更新训练样本的权重,使得之前弱学习器1学习误差率高的训练样本点的权重变高,使得这些误差率高的点在后面的弱学习器2中得到更多的重视。然后基于调整权重后的训练集来训练弱学习器2.,如此重复进行,直到弱学习器数达到事先指定的数目T,最终将这T个弱学习器通过集合策略进行整合,得到最终的强学习器。
不过有几个具体的问题Boosting算法没有详细说明。
1)如何计算学习误差率e?
2) 如何得到弱学习器权重系数α?
3)如何更新样本权重D?
4) 使用何种结合策略?
只要是boosting大家族的算法,都要解决这4个问题。那么Adaboost是怎么解决的呢?
2. Adaboost算法的基本思路
我们这里讲解Adaboost是如何解决上一节这4个问题的。
假设我们的训练集样本是
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训练集的在第k个弱学习器的输出权重为
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首先我们看看Adaboost的分类问题。
分类问题的误差率很好理解和计算。由于多元分类是二元分类的推广,这里假设我们是二元分类问题,输出为{-1,1},则第k个弱分类器Gk(x)在训练集上的加权误差率为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
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接着我们看弱学习器权重系数,对于二元分类问题,第k个弱分类器Gk(x)的权重系数为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
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为什么这样计算弱学习器权重系数?从上式可以看出,如果分类误差率ek越大,则对应的弱分类器权重系数
αk越小。也就是说,误差率小的弱分类器权重系数越大。具体为什么采用这个权重系数公式,我们在讲Adaboost的损失函数优化时再讲。
第三个问题,更新更新样本权重D。假设第k个弱分类器的样本集权重系数为D(k)=(wk1,wk2,...wkm),则对应的第k+1个弱分类器的样本集权重系数为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
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![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
这里Zk是规范化因子
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/005A.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0070.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
从wk+1,i计算公式可以看出,如果第i个样本分类错误,则
yiGk(xi)<0,导致样本的权重在第k+1个弱分类器中增大,如果分类正确,则权重在第k+1个弱分类器中减少.具体为什么采用样本权重更新公式,我们在讲Adaboost的损失函数优化时再讲。
最后一个问题是集合策略。Adaboost分类采用的是加权平均法,最终的强分类器为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0073.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/004B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
接着我们看看Adaboost的回归问题。由于Adaboost的回归问题有很多变种,这里我们以Adaboost R2算法为准。
我们先看看回归问题的误差率的问题,对于第k个弱学习器,计算他在训练集上的最大误差
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0045.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0061.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/007C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/007C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
然后计算每个样本的相对误差
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/007C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/007C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0045.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
这里是误差损失为线性时的情况,如果我们用平方误差,则eki=(yi−Gk(xi))2Ek2,如果我们用的是指数误差,则
(
)eki=1−exp(−yi+Gk(xi))Ek)
最终得到第k个弱学习器的 误差率
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
我们再来看看如何得到弱学习器权重系数α。这里有:
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
对于更新更新样本权重D,第k+1个弱学习器的样本集权重系数为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/005A.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
这里Zk是规范化因子
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/005A.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
最后是结合策略,和分类问题一样,采用的也是加权平均法,最终的强回归器为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/004B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
3. AdaBoost分类问题的损失函数优化
刚才上一节我们讲到了分类Adaboost的弱学习器权重系数公式和样本权重更新公式。但是没有解释选择这个公式的原因,让人觉得是魔法公式一样。其实它可以从Adaboost的损失函数推导出来。
从另一个角度讲, Adaboost是模型为加法模型,学习算法为前向分步学习算法,损失函数为指数函数的分类问题。
模型为加法模型好理解,我们的最终的强分类器是若干个弱分类器加权平均而得到的。
前向分步学习算法也好理解,我们的算法是通过一轮轮的弱学习器学习,利用前一个弱学习器的结果来更新后一个弱学习器的训练集权重。也就是说,第k-1轮的强学习器为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
而第k轮的强学习器为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
上两式一比较可以得到
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
可见强学习器的确是通过前向分步学习算法一步步而得到的。
Adaboost损失函数为指数函数,即定义损失函数为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0061.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0072.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E152.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E153.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E151.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E150.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0070.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
利用前向分步学习算法的关系可以得到损失函数为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0061.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0072.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E152.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E153.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E151.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E150.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0070.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/005B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/005D.png?rev=2.6.1)
令wki′=exp(−yifk−1(x)), 它的值不依赖于
α,G,因此与最小化无关,仅仅依赖于
fk−1(x),随着每一轮迭代而改变。
将这个式子带入损失函数,损失函数转化为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0061.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0072.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E152.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E153.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E151.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E150.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/168/2032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0070.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/005B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/005D.png?rev=2.6.1)
首先,我们求Gk(x).,可以得到
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0061.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0072.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E152.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E153.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E151.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E150.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/336/E154.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/168/2032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0049.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2260.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
将Gk(x)带入损失函数,并对
α求导,使其等于0,则就得到了
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006F.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
其中,ek即为我们前面的分类误差率。
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size1/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/168/2032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0049.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2260.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size1/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/168/2032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0049.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2260.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
最后看样本权重的更新。利用fk(x)=fk−1(x)+αkGk(x)和
wki′=exp(−yifk−1(x)),即可得:
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/168/2032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/168/2032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0070.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/005B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/005D.png?rev=2.6.1)
这样就得到了我们第二节的样本权重更新公式。
4. AdaBoost二元分类问题算法流程
这里我们对AdaBoost二元分类问题算法流程做一个总结。
输入为样本集T={(x,y1),(x2,y2),...(xm,ym)},输出为{-1, +1},弱分类器算法, 弱分类器迭代次数K。
输出为最终的强分类器f(x)
1) 初始化样本集权重为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0044.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
2) 对于k=1,2,...K:
a) 使用具有权重Dk的样本集来训练数据,得到弱分类器
Gk(x)
b)计算Gk(x)的分类误差率
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0050.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2260.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0049.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2260.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
c) 计算弱分类器的系数
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006F.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
d) 更新样本集的权重分布
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/005A.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/004B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0070.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
这里Zk是规范化因子
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/005A.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0070.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
3) 构建最终分类器为:
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0073.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/004B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
对于Adaboost多元分类算法,其实原理和二元分类类似,最主要区别在弱分类器的系数上。比如Adaboost SAMME算法,它的弱分类器的系数
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006F.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006F.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0067.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0052.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
其中R为类别数。从上式可以看出,如果是二元分类,R=2,则上式和我们的二元分类算法中的弱分类器的系数一致。
5. Adaboost回归问题的算法流程
这里我们对AdaBoost回归问题算法流程做一个总结。AdaBoost回归算法变种很多,下面的算法为Adaboost R2回归算法过程。
输入为样本集T={(x,y1),(x2,y2),...(xm,ym)},,弱学习器算法, 弱学习器迭代次数K。
输出为最终的强学习器f(x)
1) 初始化样本集权重为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0044.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
2) 对于k=1,2,...K:
a) 使用具有权重Dk的样本集来训练数据,得到弱学习器
Gk(x)
b) 计算训练集上的最大误差
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0045.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0061.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/007C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0079.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/007C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0032.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006D.png?rev=2.6.1)
c) 计算每个样本的相对误差:
如果是线性误差,则eki=|yi−Gk(xi)|Ek;
如果是平方误差,则eki=(yi−Gk(xi))2Ek2
如果是指数误差,则(
)eki=1−exp(−yi+Gk(xi))Ek)
d) 计算回归误差率
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
c) 计算弱学习器的系数
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
d) 更新样本集的权重分布为
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/002C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/005A.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
这里Zk是规范化因子
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/005A.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0077.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/0065.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/168/0069.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
3) 构建最终强学习器为:
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/336/2211.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/004B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006C.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/006E.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
6. Adaboost算法的正则化
为了防止Adaboost过拟合,我们通常也会加入正则化项,这个正则化项我们通常称为步长(learning rate)。定义为ν,对于前面的弱学习器的迭代
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
如果我们加上了正则化项,则有
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/003D.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0066.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/2212.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/238/0031.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/002B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03BD.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/03B1.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0047.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/238/006B.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0028.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/336/0078.png?rev=2.6.1)
![](https://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/336/0029.png?rev=2.6.1)
ν的取值范围为
0<ν≤1。对于同样的训练集学习效果,较小的
ν意味着我们需要更多的弱学习器的迭代次数。通常我们用步长和迭代最大次数一起来决定算法的拟合效果。
7. Adaboost小结
到这里Adaboost就写完了,前面有一个没有提到,就是弱学习器的类型。理论上任何学习器都可以用于Adaboost.但一般来说,使用最广泛的Adaboost弱学习器是决策树和神经网络。对于决策树,Adaboost分类用了CART分类树,而Adaboost回归用了CART回归树。
这里对Adaboost算法的优缺点做一个总结。
Adaboost的主要优点有:
1)Adaboost作为分类器时,分类精度很高
2)在Adaboost的框架下,可以使用各种回归分类模型来构建弱学习器,非常灵活。
3)作为简单的二元分类器时,构造简单,结果可理解。
4)不容易发生过拟合
Adaboost的主要缺点有:
1)对异常样本敏感,异常样本在迭代中可能会获得较高的权重,影响最终的强学习器的预测准确性。