machine-learning - 从 Andrew Moore 的教程中获取信息

Question

我现在正在自学机器学习。

一个关于信息增益的简单问题。如何从图片的数据中计算信息增益？我不明白。

谁能解释如何从第一行获得 0.992385？

非常感谢！

Answer 1

让 g(x) = -x * log(x) /log(2)

总人数48842人。

H（财富，关系）= g[52/48842] + g[111/48842] + g[309/48842] + g[1093/48842] + g[1238/48842] + g[1276/48842] + g [1454/48842] + g[4816/48842] + g[7470/48842] + g[8846/48842] + g[10870/48842] + g[11307/48842] = 2.7835

H（财富）= g（穷人/总）+ g（富人/总）= g[0.239282] + g[0.760718] = 0.793844

H（关系）= g（丈夫/总数）+ g（Not_in_familly/总数）+ ... = g[0.0308341] + g[0.0477253] + g[0.10493] + g[0.155215] + g[0.257627] + g[ 0.403669] = 2.15508

H（财富|关系）= H（财富，关系）-H（关系）= 2.7835 - 2.15508 = 0.628421

IG = H(财富) - H(财富|关系) = H(财富) + H(关系) - H(财富, 关系) = 0.165423

这是用 Mathematica 编写的源代码。如果您觉得需要查看其他语言的源代码，请使用您的首选语言在下面发表评论。如果我有时间，我会打字。- 干杯，汉斯

Mathematica 中的源代码

(* ================================================= === *)

m = {{10870, 8846}, {11307, 1276}, {1454, 52}, {7470, 111}, 
     {4816, 309}, {1238, 1093}};

iTot = Total[ Flatten[m]];

h[x_] := -x * Log[2, x];

fHAll = Sum[  h[ m[[i, j]]/ iTot ], {i, 6}, {j, 2}] // N;

fHWealth = h[ Total[ m[[All, 1]]]/iTot] + h[ Total[ m[[All, 2]]]/iTot] // N ;

fHRelation = Sum[
     h[ Total[ m[[i ]]]/iTot] , {i, Length[m]}] // N;

fWealthGivenRelation = fHAll - fHRelation;

Print[" H(relation, wealth) = ", fHAll];
Print[" H(relation) = ", fHRelation];
Print[" H(wealth) = ", fHWealth];
Print[" H(wealth | relation) = ", fWealthGivenRelation];
Print[" IG = MI = ", fHWealth - fWealthGivenRelation, " = ", 
  fHWealth + fHRelation - fHAll];

（* ===================输出====================*）

 H(relation, wealth) = 2.7835
 H(relation) = 2.15508
 H(wealth) = 0.793844
 H(wealth | relation) = 0.628421
 IG = MI = 0.165423 = 0.165423

哎呀，我没有回答你的主要问题。这是答案。

H(财富|关系=丈夫) = g(10870/(10870 + 8846)) + g(8846/(10870 + 8846)) = 0.992385