961
个编辑
更改
跳到导航
跳到搜索
第205行：
第205行： − + + +
→Note on notation
其中被积函数是'''<font color="#ff8000"> 拉东-尼科迪姆导数Radon–Nikodym derivative</font>'''的对数，涉及我们刚刚定义的一些条件概率测度。
其中被积函数是'''<font color="#ff8000"> 拉东-尼科迪姆导数Radon–Nikodym derivative</font>'''的对数，涉及我们刚刚定义的一些条件概率测度。
==Note on notation==
== Note on notation 注释符号 ==
In an expression such as <math>I(A;B|C),</math> <math>A,</math> <math>B,</math> and <math>C</math> need not necessarily be restricted to representing individual random variables, but could also represent the joint distribution of any collection of random variables defined on the same [[probability space]]. As is common in [[probability theory]], we may use the comma to denote such a joint distribution, e.g. <math>I(A_0,A_1;B_1,B_2,B_3|C_0,C_1).</math> Hence the use of the semicolon (or occasionally a colon or even a wedge <math>\wedge</math>) to separate the principal arguments of the mutual information symbol. (No such distinction is necessary in the symbol for [[joint entropy]], since the joint entropy of any number of random variables is the same as the entropy of their joint distribution.)
In an expression such as <math>I(A;B|C),</math> <math>A,</math> <math>B,</math> and <math>C</math> need not necessarily be restricted to representing individual random variables, but could also represent the joint distribution of any collection of random variables defined on the same [[probability space]]. As is common in [[probability theory]], we may use the comma to denote such a joint distribution, e.g. <math>I(A_0,A_1;B_1,B_2,B_3|C_0,C_1).</math> Hence the use of the semicolon (or occasionally a colon or even a wedge <math>\wedge</math>) to separate the principal arguments of the mutual information symbol. (No such distinction is necessary in the symbol for [[joint entropy]], since the joint entropy of any number of random variables is the same as the entropy of their joint distribution.)
在诸如<math>I(A;B|C)</math>的表达式中，<math>A</math> <math>B</math> 和 <math>C</math>不限于表示单个随机变量，它们同时可以表示在同一概率空间上定义的任意随机变量集合的联合分布。类似概率论中的表达方式，我们可以使用逗号来表示这种联合分布，例如<math>I(A_0,A_1;B_1,B_2,B_3|C_0,C_1).</math>。因此，使用分号（或有时用冒号或楔形<math>\wedge</math>）来分隔交互信息符号的主要参数。（在联合熵的符号中，不需要作这样的区分，因为任意数量随机变量的联合熵与它们联合分布的熵相同。）
== Properties ==
== Properties ==