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Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as：

Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as：

定向信息I（𝑋𝑛→𝑌𝑛）测量从过程𝑋𝑛流向𝑋𝑛的信息量，其中𝑋𝑛表示矢量𝑋1，𝑋2，…，𝑌𝑛表示𝑌1，𝑌𝑛。定向信息这个术语是由 James Massey 创造的，它被定义为：

'''<font color="#ff8000">定向信息 Directed information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量，其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>，<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的，它被定义为：

Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.

Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.

注意，如果𝑛=1，则定向信息成为互信息。有向信息在因果关系问题中有着广泛的应用，如反馈信道的容量问题。

注意，当<math>n=1</math>时，则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用，如反馈'''<font color="#ff8000">信道容量问题 Channel capacity</font>'''。

=== 标准化变形 Normalized variants ===

=== 标准化变形 Normalized variants ===