【结合实例】信息增益的计算
参考文章：
https://www.cnblogs.com/qcloud1001/p/6735352.html
http://blog.csdn.net/lixuemei504/article/details/7278748http://blog.csdn.net/u013164528/article/details/44359677
信息增益原理介绍
X={x1,x2…xn}，它对应在集合的概率分别是P={p1,p2…pn}。那么这个集合的熵表示为：
!
使用Hive SQL实现信息熵的计算
SELECT
t1.feature_name,
SUM((ea_all/es)*EA) as gain,
SUM(NVL(-(ea_all/ES)*log2(ea_all/es),0)) as info,--计算信息增益率的分母 SUM((ea_all/es)*EA)/SUM(NVL(-(ea_all/es)*log2(ea_all/es),0)) as gain_rate--信息增益率计算 FROM ( SELECT feature_name, feature_value, ea_all, --Key Step2 对于整体熵，要记得更换符号,NVL的出现是防止计算log2(0)得NULL case when feature_value='-100' then -(NVL((ea_positive/ea_all)*log2(ea_positive/ea_all),0)+NVL((ea_negative/ea_all)*log2(ea_negative/ea_all),0)) else (NVL((ea_positive/ea_all)*log2(ea_positive/ea_all),0)+NVL((ea_negative/ea_all)*log2(ea_negative/ea_all),0)) end as EA FROM ( SELECT feature_name, feature_value, SUM(case when is_lost=-100 then user_cnt else 0 end) as ea_all, SUM(case when is_lost=1 then user_cnt else 0 end) as ea_positive, SUM(case when is_lost=0 then user_cnt else 0 end) as ea_negative FROM ( SELECT feature_name, --Key Step1 对feature值和label值做汇总统计，1、用于熵计算的分母，2、计算整体熵情况 case when grouping(feature_value)=1 then '-100' else feature_value end as feature_value, case when grouping(is_lost)=1 then -100 else is_lost end as is_lost, COUNT(1) as user_cnt FROM ( SELECT feature_name,feature_value,is_lost FROM gain_caculate )GROUP BY feature_name,cube(feature_value,is_lost) )GROUP BY feature_name,feature_value ) )t1 join ( --Key Step3信息增益计算时，需要给出样本总量作为分母 SELECT feature_name,COUNT(1) as es FROM gain_caculate GROUP BY feature_name )t2 on t1.feature_name=t2.feature_name GROUP BY t1.feature_name 
结束语：
参考文档
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