问题描述
我正在尝试使用pyitlib python软件包并借助以下公式来查找三个离散随机变量之间的条件互信息:
I am trying to find conditional mutual information between three discrete random variable using pyitlib package for python with the help of the formula:
I(X;Y|Z)=H(X|Z)+H(Y|Z)-H(X,Y|Z)
预期的条件互助信息值为= 0.011
The expected Conditional Mutual information value is= 0.011
我的第一个代码:
import numpy as np
from pyitlib import discrete_random_variable as drv
X=[0,1,1,0,1,0,1,0,0,1,0,0]
Y=[0,1,1,0,0,0,1,0,0,1,1,0]
Z=[1,0,0,1,1,0,0,1,1,0,0,1]
a=drv.entropy_conditional(X,Z)
##print(a)
b=drv.entropy_conditional(Y,Z)
##print(b)
c=drv.entropy_conditional(X,Y,Z)
##print(c)
p=a+b-c
print(p)
我在这里得到的答案是= 0.4632245116328402
The answer i am getting here is=0.4632245116328402
我的第二个代码:
import numpy as np
from pyitlib import discrete_random_variable as drv
X=[0,1,1,0,1,0,1,0,0,1,0,0]
Y=[0,1,1,0,0,0,1,0,0,1,1,0]
Z=[1,0,0,1,1,0,0,1,1,0,0,1]
a=drv.information_mutual_conditional(X,Y,Z)
print(a)
我在这里得到的答案是= 0.1583445441575102
The answer i am getting here is=0.1583445441575102
预期结果为= 0.011
有人可以帮忙吗?我现在有大麻烦了.任何形式的帮助都将是可贵的.预先感谢.
Can anybody help? I am in big trouble right now. Any kind of help will be appreciable.Thanks in advance.
推荐答案
基于条件熵的定义，以位为单位(即以2为基础)进行计算，我得到H(X | Z)= 0.784159，H(Y | Z) = 0.325011，H(X，Y | Z)= 0.950826.根据上面提供的条件互信息的定义，我得到I(X; Y | Z)= H(X | Z)+ H(Y | Z)-H(X，Y | Z)= 0.158344.注意pyitlib默认使用基数2，drv.information_mutual_conditional(X，Y，Z)似乎在计算正确的结果.
Based on the definitions of conditional entropy, calculating in bits (i.e. base 2) I obtain H(X|Z)=0.784159, H(Y|Z)=0.325011, H(X,Y|Z) = 0.950826. Based on the definition of conditional mutual information you provide above, I obtain I(X;Y|Z)=H(X|Z)+H(Y|Z)-H(X,Y|Z)= 0.158344. Noting that pyitlib uses base 2 by default, drv.information_mutual_conditional(X,Y,Z) appears to be computing the correct result.
请注意，在第一个示例中使用drv.entropy_conditional(X，Y，Z)来计算条件熵是不正确的，但是您可以使用drv.entropy_conditional(XY，Z)，其中XY是一维数组，表示关于X和Y的联合观测，例如XY = [2 * xy [0] + xy [1]对于zip(X，Y)中的xy.
Note that your use of drv.entropy_conditional(X,Y,Z) in your first example to compute conditional entropy is incorrect, you can however use drv.entropy_conditional(XY,Z), where XY is a 1D array representing the joint observations about X and Y, for example XY = [2*xy[0] + xy[1] for xy in zip(X,Y)].
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