“Directed information”的意思、由来-开放百科全书

Directed information,

, is a measure of information theory and it measures the amount of information that flows from the process

, where

denotes the vector

and

denotes

. The term directed information was coined by James Massey and is defined as

Note that if

, directed information becomes mutual information

. Directed information has many applications in problems where causality plays an important role such as capacity of channel with feedback,^[1]^[2] capacity of discrete memoryless networks with feedback,^[3] gambling with causal side information,^[4] compression with causal side information,^[5]

References

1. ^{{cite journal|last1=Massey|first1=James|title=Causality, Feedback And Directed Information|date=1990|issue=ISITA|url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.5688&rep=rep1&type=pdf}}
2. ^{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}
3. ^{{cite journal|last1=Kramer|first1=G.|title=Capacity results for the discrete memoryless network|journal=IEEE Transactions on Information Theory|date=January 2003|volume=49|issue=1|pages=4–21|doi=10.1109/TIT.2002.806135}}
4. ^{{cite journal|last1=Permuter|first1=Haim H.|last2=Kim|first2=Young-Han|last3=Weissman|first3=Tsachy|title=Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing|journal=IEEE Transactions on Information Theory|date=June 2011|volume=57|issue=6|pages=3248–3259|doi=10.1109/TIT.2011.2136270|arxiv=0912.4872}}
5. ^{{cite journal|last1=Simeone|first1=Osvaldo|last2=Permuter|first2=Haim Henri|title=Source Coding When the Side Information May Be Delayed|journal=IEEE Transactions on Information Theory|date=June 2013|volume=59|issue=6|pages=3607–3618|doi=10.1109/TIT.2013.2248192|arxiv=1109.1293}}
6. ^{{cite journal|last1=Charalambous|first1=Charalambos D.|last2=Stavrou|first2=Photios A.|title=Directed Information on Abstract Spaces: Properties and Variational Equalities|journal=IEEE Transactions on Information Theory|date=August 2016|volume=62|issue=11|pages=6019–6052|doi=10.1109/TIT.2016.2604846|arxiv=1302.3971}}