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For further discussions on the [[Approximate Dynamical Reversibility of Markov chains]], refer to the entry on [[Approximate Dynamical Reversibility]] and the relevant paper：<ref name="zhang_reversibility" />

For further discussions on the [[Approximate Dynamical Reversibility of Markov chains]], refer to the entry on [[Approximate Dynamical Reversibility]] and the relevant paper：<ref name="zhang_reversibility" />

==EI与JS散度==

==EI and JS Divergence==

根据{{EquationNote|2}}的表达式，我们知道，EI实际上是一种广义的[[JS散度]]，即[[Jensen-Shannon divergence]]。

According to the expression of {{EquationNote|2}}, we know that EI is actually a generalized [[(JS) divergence]], namely [[Jensen-Shannon divergence]].

 

The so-called [[(JS) divergence]] is an indicator that measures the difference between two probability distributions defined on the same support set. Assuming two probability distributions [math]P[/math] and [math]Q[/math] defined on the support set [math]\mathcal{X}[/math], the JS divergence between them is defined as:

所谓的[[JS散度]]是一种度量两个定义在同一个支撑集上的概率分布之间差异的指标。设两个定义在支撑集[math]\mathcal{X}[/math]上的概率分布[math]P[/math]和[math]Q[/math]，它们之间的JS散度定义为：

<math>

<math>

</math>

</math>

<nowiki>其中，[math]M=\frac{P+Q}{2}=\frac{1}{2}\sum_{x\in\mathcal{X}}\left[P(x)+Q(x)\right][/math]为P和Q的平均分布，[math]D_{KL}[/math]为</nowiki>[[KL散度]]。

<nowiki> Among them, [math]M=\frac{P+Q}{2}=\frac{1}{2}\sum_{x\in\mathcal{X}}\left[P(x)+Q(x)\right][/math] is the average distribution of P and Q, and [math]D_{KL}[/math] is</nowiki>[[KL Divergence]].

 

Compared with [[KL Divergence]], [[JS Divergence]] is a symmetric measure, i.e. [math]JSD(P||Q)=JSD(Q||P)[/math], while KL divergence is asymmetric.

 

进一步，在文献<ref name="GJS_divergence">{{cite journal|author=Jianhua Lin|title=Divergence Measures Based on the Shannon Entropy|journal=IEEE TRANSACTIONS ON INFORMATION THEORY|volume=37|issue=1|page=145-151|year=1991}}</ref>中，作者提出了[[广义的JS散度]]为：{{NumBlk|:|

进一步，在文献<ref name="GJS_divergence">{{cite journal|author=Jianhua Lin|title=Divergence Measures Based on the Shannon Entropy|journal=IEEE TRANSACTIONS ON INFORMATION THEORY|volume=37|issue=1|page=145-151|year=1991}}</ref>中，作者提出了[[广义的JS散度]]为：{{NumBlk|:|