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In [[probability theory]], particularly [[information theory]], the '''conditional mutual information'''<ref name = Wyner1978>{{cite journal|last=Wyner|first=A. D. |title=A definition of conditional mutual information for arbitrary ensembles|url=|journal=Information and Control|year=1978|volume=38|issue=1|pages=51–59|doi=10.1016/s0019-9958(78)90026-8|doi-access=free}}</ref><ref name = Dobrushin1959>{{cite journal|last=Dobrushin|first=R. L. |title=General formulation of Shannon's main theorem in information theory|journal=Uspekhi Mat. Nauk|year=1959|volume=14|pages=3–104}}</ref> is, in its most basic form, the [[expected value]] of the [[mutual information]] of two random variables given the value of a third.
In [[probability theory]], particularly [[information theory]], the '''conditional mutual information'''<ref name = Wyner1978>{{cite journal|last=Wyner|first=A. D. |title=A definition of conditional mutual information for arbitrary ensembles|url=|journal=Information and Control|year=1978|volume=38|issue=1|pages=51–59|doi=10.1016/s0019-9958(78)90026-8|doi-access=free}}</ref><ref name = Dobrushin1959>{{cite journal|last=Dobrushin|first=R. L. |title=General formulation of Shannon's main theorem in information theory|journal=Uspekhi Mat. Nauk|year=1959|volume=14|pages=3–104}}</ref> is, in its most basic form, the [[expected value]] of the [[mutual information]] of two random variables given the value of a third.
==Definition==
在'''<font color="#ff8000"> 概率论Probability theory</font>'''中，特别是与'''<font color="#ff8000"> 信息论Information theory</font>'''相关的情况下，最基本形式的'''<font color="#ff8000"> 条件交互信息Conditional mutual information </font>'''，是在给定第三个值的两个随机变量间交互信息的期望值。
== Definition 定义 ==
For random variables <math>X</math>, <math>Y</math>, and <math>Z</math> with [[Support (mathematics)|support sets]] <math>\mathcal{X}</math>, <math>\mathcal{Y}</math> and <math>\mathcal{Z}</math>, we define the conditional mutual information as
For random variables <math>X</math>, <math>Y</math>, and <math>Z</math> with [[Support (mathematics)|support sets]] <math>\mathcal{X}</math>, <math>\mathcal{Y}</math> and <math>\mathcal{Z}</math>, we define the conditional mutual information as