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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{Short description|Concept in information theory}}

此词条暂由Henry翻译。{{Short description|Concept in information theory}}

{{Information theory}}

{{Information theory}}

 

Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Shannon to extend the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula, and rather just assumed it was the correct continuous analogue of discrete entropy, but it is not. The actual continuous version of discrete entropy is the  limiting density of discrete points (LDDP). Differential entropy (described here) is commonly encountered in the literature, but it is a limiting case of the LDDP, and one that loses its fundamental association with discrete entropy.

Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Shannon to extend the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula, and rather just assumed it was the correct continuous analogue of discrete entropy, but it is not. The actual continuous version of discrete entropy is the  limiting density of discrete points (LDDP). Differential entropy (described here) is commonly encountered in the literature, but it is a limiting case of the LDDP, and one that loses its fundamental association with discrete entropy.

微分熵(也称为连续熵)是信息论中的一个概念，最初由香农尝试将(香农)熵的概念扩展到连续的概率分布，香农熵是衡量一个随机变量的平均惊人程度的指标。不幸的是，香农没有推导出这个公式，而只是假设它是离散熵的正确连续模拟，但它不是。离散熵的实际连续形式是离散点的极限密度(LDDP)。在文献中经常会遇到微分熵，但它是 LDDP 的一个极限情况，并且它失去了与离散熵的基本联系。

微分熵(也称为连续熵)是信息论中的一个概念，最初由香农尝试将(香农)熵的概念扩展到连续的概率分布，香农熵是衡量一个随机变量的平均惊异程度的指标。不幸的是，香农没有推导出这个公式，而只是假设它是离散熵的正确连续模拟，但它并不是。离散熵的实际连续形式是离散点的极限密度(LDDP)。在文献中经常会遇到微分熵（这里提到的），但它只是LDDP的一个极限情况，并且它失去了与离散熵的基本联系。

Let <math>X</math> be a random variable with a probability density function <math>f</math> whose support is a set <math>\mathcal X</math>. The differential entropy <math>h(X)</math> or <math>h(f)</math> is defined as

Let <math>X</math> be a random variable with a probability density function <math>f</math> whose support is a set <math>\mathcal X</math>. The differential entropy <math>h(X)</math> or <math>h(f)</math> is defined as

假设数学 x / math 是一个随机变量，它的数学 f / math 支持集合 math / mathcal x / math。这个数学 f / math 是一个概率密度函数。微分熵数学 h (x) / math 或 math h (f) / math 定义为

假设x是一个随机变量，它的数学 f / math 支持集合 math / mathcal x / math。这个数学 f / math 是一个概率密度函数。微分熵数学 h (x) / math 或 math h (f) / math 定义为