更改

The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have

The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have

The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized outer product <math>p(x) \cdot p(y)</math>. In many problems, such as non-negative matrix factorization, one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have

The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in less extreme factorizations; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have

互信息的 Kullback-Leibler 散度公式是基于人们对数学 p (x，y) / math 与完全分解的外积 math p (x) cdot p (y) / math 的比较感兴趣。在许多问题中，比如非负矩阵分解，人们对非极端的因式分解感兴趣; 具体地说，人们希望将数学 p (x，y) / math 与某个未知变量 math w / math 中的低秩矩阵近似值进行比较; 也就是说，人们可能具有的程度

相互信息的Kullback-Leibler散度公式是基于这样一个结论的：人们有兴趣将𝑝（𝑥，𝑦）与完全分解的外积𝑝（𝑥）进行比较。在许多问题中，例如非负矩阵因式分解，人们对较不极端的因式分解感兴趣；具体地说，人们希望将𝑝（𝑥，𝑦）与某个未知变量𝑤中的低秩矩阵近似进行比较；也就是说，在多大程度上可能会有这样的结果

:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math>

:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math>

<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math>

<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math>

 

Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence

Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence

在进程数学 w / math 只有一个数学 w / math 值的极端情况下，恢复了互信息的传统定义。

在进程数学 w / math 只有一个数学 w / math 值的极端情况下，恢复了互信息的传统定义。

== 变形 Variations ==

== 变形 Variations ==