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| − | <math>
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| − | I(X;Y) = D_{\mathrm{KL}}( P_{(X,Y)} \| P_{X} \otimes P_{Y} )
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| | where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]]. | | where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]]. |
| − | Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.
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| | + | 其中<math>D_{\mathrm{KL}}</math>表示Kullback-Leibler散度。 |
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| − | {{Equation box 1
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| − | {{Equation box 1
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| − | {方程式方框1
| + | Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not. |
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| − | 不会有事的
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| − | 标题
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| − | 方程式
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| − | <math>
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| − | <math>
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| − | 数学
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| − | I(X;Y) = D_{\mathrm{KL}}( P_{(X,Y)} \| P_{X} \otimes P_{Y} )
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| − | I(X;Y) = D_{\mathrm{KL}}( P_{(X,Y)} \| P_{X} \otimes P_{Y} )
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| − | I (x; y) d { mathrm { KL }(p {(x，y)} | p { x }乘 p { y })
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| − | </math>
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| − | </math>
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| − | 数学
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| − | 0073CF
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| − | 5 / fffa }
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| − | where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].
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| − | where <math>D_{\mathrm{KL}}</math> is the Kullback–Leibler divergence.
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| − | 其中数学 d (mathrm { KL } / math)是 Kullback-Leibler 分歧。
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| − | Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells your nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not. | |
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| − | Notice, as per property of the Kullback–Leibler divergence, that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells your nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.
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| − | 注意，根据 Kullback-Leibler 散度的性质，当联合分布与边际乘积重合时，math i (x; y) / math 恰好等于零，即。当数学 x / 数学和数学 y / 数学是独立的(因此观察数学 y / 数学并不能告诉你数学 x / 数学)。在一般的数学 i (x; y) / math 是非负的，它是一种测量方法，用于将 math (x，y) / math 作为一对独立的随机变量进行编码，而实际上它们并不是。 | + | 注意，根据 Kullback-Leibler 散度的性质，当联合分布与边际乘积重合时，<math>I(X;Y)</math> 恰好等于零，即。当数学 x / 数学和数学 y / 数学是独立的(因此观察数学 y / 数学并不能告诉你数学 x / 数学)。在一般的数学 i (x; y) / math 是非负的，它是一种测量方法，用于将 math (x，y) / math 作为一对独立的随机变量进行编码，而实际上它们并不是。 |
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| | == 关于离散分布的PMF In terms of PMFs for discrete distributions == | | == 关于离散分布的PMF In terms of PMFs for discrete distributions == |