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In [[information theory]], '''joint [[entropy (information theory)|entropy]]''' is a measure of the uncertainty associated with a set of [[random variables|variables]].<ref name=korn>{{cite book |author1=Theresa M. Korn |author2=Korn, Granino Arthur |title=Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review |publisher=Dover Publications |location=New York |year= |isbn=0-486-41147-8 |oclc= |doi=}}</ref>

In [[information theory]], '''joint [[entropy (information theory)|entropy]]''' is a measure of the uncertainty associated with a set of [[random variables|variables]].<ref name=korn>{{cite book |author1=Theresa M. Korn |author2=Korn, Granino Arthur |title=Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review |publisher=Dover Publications |location=New York |year= |isbn=0-486-41147-8 |oclc= |doi=}}</ref>

==Definition 定义 ==

==Definition 定义 ==

其中<math>x_1,...,x_n</math>分别是<math>X_1,...,X_n</math>的特定值，<math>P(x_1, ..., x_n)</math>是这些值产生交集时的概率，如果<math>P(x_1, ..., x_n)=0</math>则<math>P(x_1, ..., x_n) \log_2[P(x_1, ..., x_n)]</math>定义为0。

其中<math>x_1,...,x_n</math>分别是<math>X_1,...,X_n</math>的特定值，<math>P(x_1, ..., x_n)</math>是这些值产生交集时的概率，如果<math>P(x_1, ..., x_n)=0</math>则<math>P(x_1, ..., x_n) \log_2[P(x_1, ..., x_n)]</math>定义为0。

== Properties 属性 ==

== Properties 属性 ==

:<math>H \bigl(X_1,\ldots, X_n \bigr) \geq \max_{1 \le i \le n}  

:<math>H \bigl(X_1,\ldots, X_n \bigr) \geq \max_{1 \le i \le n}  

     \Bigl\{H\bigl(X_i\bigr) \Bigr\}</math>

     \Bigl\{H\bigl(X_i\bigr) \Bigr\}</math>

=== Less than or equal to the sum of individual entropies 小于或等于单个熵的总和===

=== Less than or equal to the sum of individual entropies 小于或等于单个熵的总和===

:<math>H(X_1,\ldots, X_n) \leq H(X_1) + \ldots + H(X_n)</math>

:<math>H(X_1,\ldots, X_n) \leq H(X_1) + \ldots + H(X_n)</math>

== Relations to other entropy measures 与其他熵测度的关系 ==

== Relations to other entropy measures 与其他熵测度的关系 ==

提供了一个python软件包，用于计算n个变量的数据集中的所有多元联合熵，交互信息，条件交互信息，总相关性，信息距离。

提供了一个python软件包，用于计算n个变量的数据集中的所有多元联合熵，交互信息，条件交互信息，总相关性，信息距离。

== Joint differential entropy 联合微分熵 ==

== Joint differential entropy 联合微分熵 ==