October 2021
Intermediate to advanced
289 pages
8h 31m
Chinese
Content preview from 数据科学中的实用统计学(第2版)
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统计机器学习
｜
209
信息熵的计算公式是：
22
(A) log ( ) (1 ) log (1 )I pp p p=− −− −
从图
6-5
可知，
Gini
不纯度（缩放后的）和信息熵非常相似，对于中等和较高的准确率，
信息熵可以给出较高的不纯度分数。
图 6-5：Gini 不纯度与信息熵
Gini
系数
不要将
Gini
不纯度与
Gini
系数
相混淆。它们表示的概念类似，但
Gini
系数
只适用于二元分类问题，而且与
AUC
这种度量方式相关（参见
5.4.5
节
）。
前面讨论过的分割算法中使用了不纯度。对于每次分割数据得到的每个分区都要计算不纯
度。计算时会使用加权平均，最终选择能得到最小的加权平均结果的分割方式（每个阶段
都是这样）。
6.2.4
让树停止生长
树原本是用来识别“大”规则的，即识别出数据之间真实而可靠的关系，但随着树的不断
增长，分割规则也变得越来越细致，这时树的功能就逐渐发生了转变，只能识别“微”规
则了，而这种规则只能反映出数据中的噪声。一棵充分生长的树会分出所有的叶子节点，
因此它对训练数据的分类准确度可以达到
100%
。当然
，这种准确度只是一种表象，其实
210
｜
第
6
章
数据被过拟合了（参见
6.1.5
节中的“偏差与方差的权衡”部分），我们拟合的只是训练数
据中的噪声，并不是我们需要的能识别新数据的信号。 ...
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