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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).

Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).

不仅限于实值随机变量和相关系数之类的线性依赖，互信息更为普遍，它决定了一对变量<math>(X,Y)</math>的联合分布以及 <math>X</math> 和 <math>Y</math> 的边际分布之积有多大的不同。互信息 是'''点态互信息指数 PMI'''的期望值。

除了实值随机变量和线性依赖之类的的相关系数之外，互信息更为普遍，它决定了一对变量<math>(X,Y)</math>的联合分布以及 <math>X</math> 和 <math>Y</math> 的边际分布之积有多大的不同。互信息 是'''点态互信息指数 PMI'''的期望值。

Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as

Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as

设 math (x，y) / math 是一对值超过空间 math  mathcal { x } times  mathcal { y } / math 的随机变量。如果它们的联合分布是数学 p {(x，y)} / math，边际分布是数学 p x / math 和数学 p y / math，则互信息定义为

设 <math>(X,Y)</math> 是一对值超过空间 math  mathcal { x } times  mathcal { y } / math 的随机变量。如果它们的联合分布是数学 p {(x，y)} / math，边际分布是数学 p x / math 和数学 p y / math，则互信息定义为