mutual information是什么意思，mutual information的意思翻译、用法、同义词、例句

常用词典

例句

网络扩展资料

互信息（Mutual Information） 是信息论中用于衡量两个随机变量之间相互依赖性的指标。它量化了通过观察一个变量能获得的关于另一个变量的信息量。以下是详细解释：

1.基本定义

• 核心概念：互信息描述了已知一个变量后，另一个变量的不确定性减少的程度。若两个变量完全独立，互信息为0；若存在强关联，则互信息值较高。
• 与熵的关系：基于信息熵（Entropy），即变量不确定性的度量。互信息可理解为两个变量共享的熵。

2.数学公式

互信息有两种常见表达形式：
① 基于熵的表达式：
$$ I(X; Y) = H(X) - H(X|Y) = H(Y) - H(Y|X) $$
其中，

• $H(X)$ 和 $H(Y)$ 是变量$X$和$Y$的边际熵，
• $H(X|Y)$ 是已知$Y$时$X$的条件熵。

② 基于概率分布的表达式：
$$ I(X; Y) = sum{x in X} sum{y in Y} p(x, y) log frac{p(x, y)}{p(x)p(y)} $$

• $p(x,y)$是联合分布，$p(x)$和$p(y)$是边缘分布。
• 该公式本质上是联合分布与独立分布的KL散度（相对熵）。

3.关键性质

• 非负性：$I(X; Y) geq 0$，当且仅当$X$和$Y$独立时取0。
• 对称性：$I(X; Y) = I(Y; X)$。
• 与相关性区别：互信息能捕捉非线性关系，而相关系数仅反映线性关联。

4.应用场景

• 特征选择：在机器学习中筛选与目标变量高度相关的特征。
• 图像配准：医学图像处理中，通过最大化两幅图像的互信息实现对齐。
• 自然语言处理：衡量词语共现的关联性。
• 通信理论：评估信道传输的信息量。

5.示例

假设有两个二值变量$X$和$Y$：

• 当$X$和$Y$完全独立时，$p(x,y)=p(x)p(y)$，此时$I(X; Y)=0$。
• 若$X$完全决定$Y$（例如$Y=X$），则$I(X; Y)=H(X)$，达到最大值。

互信息是一种强大的统计工具，广泛用于量化变量间任意形式的依赖性，尤其适用于复杂系统分析和机器学习模型优化。其单位通常为比特（bit，底数为2时）或纳特（nat，底数为$e$时）。

网络扩展资料二

Mutual information（互信息）is a statistical measure used to quantify the amount of information shared by two variables. It is often used in machine learning and natural language processing to evaluate the relationship between two sets of data.

Mutual information measures the degree of dependence between two variables by calculating the amount of information that one variable provides about the other. This is done by comparing the joint probability distribution of the two variables to the product of their marginal probability distributions.

For example, if we have two variables A and B, mutual information can be calculated as follows:

MI(A,B) = sum( P(A,B) * log( P(A,B) / (P(A) * P(B)) ) )

where P(A,B) is the joint probability distribution of A and B, and P(A) and P(B) are their marginal probability distributions.

In natural language processing, mutual information can be used to identify the degree of association between two words or phrases. For example, the mutual information between the words "cat" and "mouse" is likely to be higher than the mutual information between "cat" and "computer," because the former pair is more commonly associated with each other.

Some synonyms for mutual information include joint entropy and co-information. Antonyms could include independence or unrelatedness.

In summary, mutual information is a statistical measure that calculates the amount of information shared by two variables. It is commonly used in machine learning and natural language processing to evaluate the relationship between two sets of data.

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