转移熵 - 版本历史

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 |description=因果关系,非线性时间序列分析,非参数统计,熵和信息
 }}
-'''转移熵 Transfer entropy'''（也可译为<font color="#ff8000">传递熵</font>）是衡量两个随机过程之间有向（时间不对称）信息传递量的非参数统计量。<ref>{{cite journal|last=Schreiber|first=Thomas|title=Measuring information transfer|journal=Physical Review Letters|date=1 July 2000|volume=85|issue=2|pages=461–464|doi=10.1103/PhysRevLett.85.461|pmid=10991308|arxiv=nlin/0001042|bibcode=2000PhRvL..85..461S}}</ref><ref name=Scholarpedia >{{cite encyclopedia |year= 2007 |title = Granger causality |volume = 2 |issue = 7 |pages = 1667 |last= Seth |first=Anil|encyclopedia=Scholarpedia]|url=http://www.scholarpedia.org/article/Granger_causality|doi=10.4249/scholarpedia.1667 |bibcode=2007SchpJ...2.1667S|doi-access= free }}</ref><ref name=Schindler07>{{cite journal|last=Hlaváčková-Schindler|first=Katerina|author2=Palus, M |author3=Vejmelka, M |author4= Bhattacharya, J |title=Causality detection based on information-theoretic approaches in time series analysis|journal=Physics Reports|date=1 March 2007|volume=441|issue=1|pages=1–46|doi=10.1016/j.physrep.2006.12.004|bibcode=2007PhR...441....1H|citeseerx=10.1.1.183.1617}}</ref>过程X到过程Y的转移熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用<font color="#ff8000"> 香农熵 Shannon entropy</font>测量，则转移熵可以写为：
+'''转移熵 Transfer entropy'''（也可译为'''传递熵'''）是衡量两个随机过程之间有向（时间不对称）信息传递量的非参数统计量。<ref>{{cite journal|last=Schreiber|first=Thomas|title=Measuring information transfer|journal=Physical Review Letters|date=1 July 2000|volume=85|issue=2|pages=461–464|doi=10.1103/PhysRevLett.85.461|pmid=10991308|arxiv=nlin/0001042|bibcode=2000PhRvL..85..461S}}</ref><ref name=Scholarpedia >{{cite encyclopedia |year= 2007 |title = Granger causality |volume = 2 |issue = 7 |pages = 1667 |last= Seth |first=Anil|encyclopedia=Scholarpedia]|url=http://www.scholarpedia.org/article/Granger_causality|doi=10.4249/scholarpedia.1667 |bibcode=2007SchpJ...2.1667S|doi-access= free }}</ref><ref name=Schindler07>{{cite journal|last=Hlaváčková-Schindler|first=Katerina|author2=Palus, M |author3=Vejmelka, M |author4= Bhattacharya, J |title=Causality detection based on information-theoretic approaches in time series analysis|journal=Physics Reports|date=1 March 2007|volume=441|issue=1|pages=1–46|doi=10.1016/j.physrep.2006.12.004|bibcode=2007PhR...441....1H|citeseerx=10.1.1.183.1617}}</ref>过程X到过程Y的转移熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用'''香农熵 Shannon entropy'''测量，则转移熵可以写为：
-其中 H (x)是 x 的香农熵。上述转移熵的定义已被其他类型的熵测度(如<font color="#ff8000"> Rényi熵 Rényi entropy</font>)所扩展。<ref name ="  Schindler07"/><ref>{{Cite journal|last=Jizba|first=Petr|last2=Kleinert|first2=Hagen|last3=Shefaat|first3=Mohammad|date=2012-05-15|title=Rényi's information transfer between financial time series|journal=Physica A: Statistical Mechanics and Its Applications|language=en|volume=391|issue=10|pages=2971–2989|doi=10.1016/j.physa.2011.12.064|issn=0378-4371|arxiv=1106.5913|bibcode=2012PhyA..391.2971J}}</ref>
+:<math>T_{X\rightarrow Y} = H\left( Y_t \mid Y_{t-1:t-L}\right) - H\left( Y_t \mid Y_{t-1:t-L}, X_{t-1:t-L}\right)</math>,
-<math>T_{X\rightarrow Y} = I(Y_t ; X_{t-1:t-L} \mid Y_{t-1:t-L}).</math>
+其中 H (x)是 x 的香农熵。上述转移熵的定义已被其他类型的熵测度(如''' Rényi熵 Rényi entropy''')所扩展。<ref name ="  Schindler07"/><ref>{{Cite journal|last=Jizba|first=Petr|last2=Kleinert|first2=Hagen|last3=Shefaat|first3=Mohammad|date=2012-05-15|title=Rényi's information transfer between financial time series|journal=Physica A: Statistical Mechanics and Its Applications|language=en|volume=391|issue=10|pages=2971–2989|doi=10.1016/j.physa.2011.12.064|issn=0378-4371|arxiv=1106.5913|bibcode=2012PhyA..391.2971J}}</ref>
-熵公式中的概率可以用不同的方法估计，如<font color="#ff8000">分箱 binning</font>、<font color="#ff8000">最近邻 nearest neighbors</font>，或为了降低复杂度，使用非均匀嵌入方法。<ref>{{cite journal|last=Montalto|first=A|author2=Faes, L |author3=Marinazzo, D |title=MuTE: A MATLAB Toolbox to Compare Established and Novel Estimators of the Multivariate Transfer Entropy.|journal=PLOS ONE|date=Oct 2014|pmid=25314003|doi=10.1371/journal.pone.0109462|volume=9|issue=10|pmc=4196918|page=e109462|bibcode=2014PLoSO...9j9462M}}</ref>
+转移熵是'''<font color="#ff8000">条件<ref name = Wyner1978>{{cite journal|last=Wyner|first=A. D. |title=A definition of conditional mutual information for arbitrary ensembles|journal=Information and Control|year=1978|volume=38|issue=1|pages=51–59|doi=10.1016/s0019-9958(78)90026-8|doi-access=free}}</ref><ref name = Dobrushin1959>{{cite journal|last=Dobrushin|first=R. L. |title=General formulation of Shannon's main theorem in information theory|journal=Uspekhi Mat. Nauk|year=1959|volume=14|pages=3–104}}</ref>互信息 conditional mutual information</font>'''，其历史变量为 Yt−1:t−L:
 虽然转移熵最初定义为双变量分析，但它已经扩展到多变量形式，或者对其他潜在源变量进行调节，<ref>{{cite journal|last=Lizier|first=Joseph|author2=Prokopenko, Mikhail |author3=Zomaya, Albert |title=Local information transfer as a spatiotemporal filter for complex systems|journal=Physical Review E|year=2008|volume=77|issue=2|pages=026110|doi=10.1103/PhysRevE.77.026110|pmid=18352093|arxiv=0809.3275|bibcode=2008PhRvE..77b6110L}}</ref> 或者考虑从一组源的传递，<ref name = Lizier2011>{{cite journal|last=Lizier|first=Joseph|author2=Heinzle, Jakob |author3=Horstmann, Annette |author4=Haynes, John-Dylan |author5= Prokopenko, Mikhail |title=Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity|journal=Journal of Computational Neuroscience|year=2011|volume=30|issue=1|pages=85–107|doi=10.1007/s10827-010-0271-2|pmid=20799057}}</ref>尽管这些形式再次需要更多的样本。
 转移熵被用于估计神经元的功能连接<ref>{{cite journal|last=Vicente|first=Raul|author2=Wibral, Michael |author3=Lindner, Michael |author4= Pipa, Gordon |title=Transfer entropy—a model-free measure of effective connectivity for the neurosciences |journal=Journal of Computational Neuroscience|date=February 2011|volume=30|issue=1|pages=45–67|doi=10.1007/s10827-010-0262-3|pmid=20706781|pmc=3040354}}</ref><ref name = Shimono2014>{{cite journal|last=Shimono|first=Masanori|author2=Beggs, John |title=Functional clusters, hubs, and communities in the cortical microconnectome |url=https://cercor.oxfordjournals.org/content/early/2014/10/21/cercor.bhu252.full |journal=Cerebral Cortex|date= October 2014|volume=25|issue=10|pages=3743–57|doi=10.1093/cercor/bhu252 |pmid=25336598 |pmc=4585513}}</ref>和社交网络的社交影响。<ref name=Greg>{{cite conference |arxiv=1110.2724|title= Information transfer in social media|last1= Ver Steeg |first1= Greg|last2=Galstyan|first2=  Aram  |year= 2012|publisher= [[Association for Computing Machinery|ACM|booktitle= Proceedings of the 21st international conference on World Wide Web (WWW '12) |pages= 509–518 |bibcode=2011arXiv1110.2724V}}</ref>
 转移熵是有向信息的有限形式，1990年由詹姆斯·梅西 James Massey<ref>{{cite journal|last1=Massey|first1=James|title=Causality, Feedback And Directed Information|date=1990|issue=ISITA|citeseerx=10.1.1.36.5688}}</ref>定义为
 I(Xn→Yn)=∑ni=1I(Xi;Yi|Yi−1)，其中 Xn表示向量X1,X2,...,Xn和Yn表示 Y1,Y2,...,Yn。有向信息在描述有无反馈<ref>{{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}}</ref> <ref>{{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}}</ref>信道的基本限制(信道容量)与基于因果信息赌博<ref>{{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}}</ref>方面起着重要作用。

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 |description=因果关系,非线性时间序列分析,非参数统计,熵和信息
 }}
+'''转移熵 Transfer entropy'''（也可译为<font color="#ff8000">传递熵</font>）是衡量两个随机过程之间有向（时间不对称）信息传递量的非参数统计量。<ref>{{cite journal|last=Schreiber|first=Thomas|title=Measuring information transfer|journal=Physical Review Letters|date=1 July 2000|volume=85|issue=2|pages=461–464|doi=10.1103/PhysRevLett.85.461|pmid=10991308|arxiv=nlin/0001042|bibcode=2000PhRvL..85..461S}}</ref><ref name=Scholarpedia >{{cite encyclopedia |year= 2007 |title = Granger causality |volume = 2 |issue = 7 |pages = 1667 |last= Seth |first=Anil|encyclopedia=Scholarpedia]|url=http://www.scholarpedia.org/article/Granger_causality|doi=10.4249/scholarpedia.1667 |bibcode=2007SchpJ...2.1667S|doi-access= free }}</ref><ref name=Schindler07>{{cite journal|last=Hlaváčková-Schindler|first=Katerina|author2=Palus, M |author3=Vejmelka, M |author4= Bhattacharya, J |title=Causality detection based on information-theoretic approaches in time series analysis|journal=Physics Reports|date=1 March 2007|volume=441|issue=1|pages=1–46|doi=10.1016/j.physrep.2006.12.004|bibcode=2007PhR...441....1H|citeseerx=10.1.1.183.1617}}</ref>过程X到过程Y的转移熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用<font color="#ff8000"> 香农熵 Shannon entropy</font>测量，则转移熵可以写为：
 <math>T_{X\rightarrow Y} = H\left( Y_t \mid Y_{t-1:t-L}\right) - H\left( Y_t \mid Y_{t-1:t-L}, X_{t-1:t-L}\right)</math>,

@@ 第52行： / 第52行： @@
 *  {{cite web|title=Multivariate Transfer Entropy (MuTE) toolbox|url=https://github.com/montaltoalessandro/MuTE|publisher=GitHub|date=2019-01-09}}, a toolbox, developed in MATLAB, for computation of transfer entropy with different estimators.
+==编者推荐==
 ====[https://campus.swarma.org/course/308 信息熵和编码]====
 本课程对常见的编码方法进行了解析，对编码的特点与性质，以及编码的相关证明方法进行了说明。

@@ 第52行： / 第52行： @@
 *  {{cite web|title=Multivariate Transfer Entropy (MuTE) toolbox|url=https://github.com/montaltoalessandro/MuTE|publisher=GitHub|date=2019-01-09}}, a toolbox, developed in MATLAB, for computation of transfer entropy with different estimators.
 本中文词条由[[用户:Henry|Henry]] 参与编译， [[用户:Vicky|Vicky]] 审校，[[用户:不是海绵宝宝|不是海绵宝宝]]编辑，欢迎在讨论页面留言。
 '''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''
 [[分类: 因果关系]] [[分类: 非线性时间序列分析]] [[分类: 非参数统计]] [[分类: 熵和信息]]

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		+	\|keywords=因果关系,非线性时间序列分析,非参数统计,熵和信息
		+	\|description=因果关系,非线性时间序列分析,非参数统计,熵和信息
		+	}}

	<font color="#ff8000"> 转移熵 Transfer entropy</font>（也可译为<font color="#ff8000">传递熵</font>）是衡量两个随机过程之间有向（时间不对称）信息传递量的非参数统计量。<ref>{{cite journal\|last=Schreiber\|first=Thomas\|title=Measuring information transfer\|journal=Physical Review Letters\|date=1 July 2000\|volume=85\|issue=2\|pages=461–464\|doi=10.1103/PhysRevLett.85.461\|pmid=10991308\|arxiv=nlin/0001042\|bibcode=2000PhRvL..85..461S}}</ref><ref name=Scholarpedia >{{cite encyclopedia \|year= 2007 \|title = Granger causality \|volume = 2 \|issue = 7 \|pages = 1667 \|last= Seth \|first=Anil\|encyclopedia=Scholarpedia]\|url=http://www.scholarpedia.org/article/Granger_causality\|doi=10.4249/scholarpedia.1667 \|bibcode=2007SchpJ...2.1667S\|doi-access= free }}</ref><ref name=Schindler07>{{cite journal\|last=Hlaváčková-Schindler\|first=Katerina\|author2=Palus, M \|author3=Vejmelka, M \|author4= Bhattacharya, J \|title=Causality detection based on information-theoretic approaches in time series analysis\|journal=Physics Reports\|date=1 March 2007\|volume=441\|issue=1\|pages=1–46\|doi=10.1016/j.physrep.2006.12.004\|bibcode=2007PhR...441....1H\|citeseerx=10.1.1.183.1617}}</ref>过程X到过程Y的转移熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用<font color="#ff8000"> 香农熵 Shannon entropy</font>测量，则转移熵可以写为：		<font color="#ff8000"> 转移熵 Transfer entropy</font>（也可译为<font color="#ff8000">传递熵</font>）是衡量两个随机过程之间有向（时间不对称）信息传递量的非参数统计量。<ref>{{cite journal\|last=Schreiber\|first=Thomas\|title=Measuring information transfer\|journal=Physical Review Letters\|date=1 July 2000\|volume=85\|issue=2\|pages=461–464\|doi=10.1103/PhysRevLett.85.461\|pmid=10991308\|arxiv=nlin/0001042\|bibcode=2000PhRvL..85..461S}}</ref><ref name=Scholarpedia >{{cite encyclopedia \|year= 2007 \|title = Granger causality \|volume = 2 \|issue = 7 \|pages = 1667 \|last= Seth \|first=Anil\|encyclopedia=Scholarpedia]\|url=http://www.scholarpedia.org/article/Granger_causality\|doi=10.4249/scholarpedia.1667 \|bibcode=2007SchpJ...2.1667S\|doi-access= free }}</ref><ref name=Schindler07>{{cite journal\|last=Hlaváčková-Schindler\|first=Katerina\|author2=Palus, M \|author3=Vejmelka, M \|author4= Bhattacharya, J \|title=Causality detection based on information-theoretic approaches in time series analysis\|journal=Physics Reports\|date=1 March 2007\|volume=441\|issue=1\|pages=1–46\|doi=10.1016/j.physrep.2006.12.004\|bibcode=2007PhR...441....1H\|citeseerx=10.1.1.183.1617}}</ref>过程X到过程Y的转移熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用<font color="#ff8000"> 香农熵 Shannon entropy</font>测量，则转移熵可以写为：

←上一版本		2020年12月13日 (日) 13:47的版本
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−	<font color="#ff8000"> 转移熵 Transfer entropy</font>（也可译为<font color="#ff8000">传递熵</font>）是衡量两个随机过程之间有向（时间不对称）信息传递量的非参数统计量。<ref>{{cite journal\|last=Schreiber\|first=Thomas\|title=Measuring information transfer\|journal=Physical Review Letters\|date=1 July 2000\|volume=85\|issue=2\|pages=461–464\|doi=10.1103/PhysRevLett.85.461\|pmid=10991308\|arxiv=nlin/0001042\|bibcode=2000PhRvL..85..461S}}</ref><ref name=Scholarpedia >{{cite encyclopedia \|year= 2007 \|title = Granger causality \|volume = 2 \|issue = 7 \|pages = 1667 \|last= Seth \|first=Anil\|encyclopedia=[[Scholarpedia]] \|url=http://www.scholarpedia.org/article/Granger_causality\|doi=10.4249/scholarpedia.1667 \|bibcode=2007SchpJ...2.1667S\|doi-access= free }}</ref><ref name=Schindler07>{{cite journal\|last=Hlaváčková-Schindler\|first=Katerina\|author2=Palus, M \|author3=Vejmelka, M \|author4= Bhattacharya, J \|title=Causality detection based on information-theoretic approaches in time series analysis\|journal=Physics Reports\|date=1 March 2007\|volume=441\|issue=1\|pages=1–46\|doi=10.1016/j.physrep.2006.12.004\|bibcode=2007PhR...441....1H\|citeseerx=10.1.1.183.1617}}</ref>过程X到过程Y的转移熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用<font color="#ff8000"> 香农熵 Shannon entropy</font>测量，则转移熵可以写为：	+	<font color="#ff8000"> 转移熵 Transfer entropy</font>（也可译为<font color="#ff8000">传递熵</font>）是衡量两个随机过程之间有向（时间不对称）信息传递量的非参数统计量。<ref>{{cite journal\|last=Schreiber\|first=Thomas\|title=Measuring information transfer\|journal=Physical Review Letters\|date=1 July 2000\|volume=85\|issue=2\|pages=461–464\|doi=10.1103/PhysRevLett.85.461\|pmid=10991308\|arxiv=nlin/0001042\|bibcode=2000PhRvL..85..461S}}</ref><ref name=Scholarpedia >{{cite encyclopedia \|year= 2007 \|title = Granger causality \|volume = 2 \|issue = 7 \|pages = 1667 \|last= Seth \|first=Anil\|encyclopedia=Scholarpedia]\|url=http://www.scholarpedia.org/article/Granger_causality\|doi=10.4249/scholarpedia.1667 \|bibcode=2007SchpJ...2.1667S\|doi-access= free }}</ref><ref name=Schindler07>{{cite journal\|last=Hlaváčková-Schindler\|first=Katerina\|author2=Palus, M \|author3=Vejmelka, M \|author4= Bhattacharya, J \|title=Causality detection based on information-theoretic approaches in time series analysis\|journal=Physics Reports\|date=1 March 2007\|volume=441\|issue=1\|pages=1–46\|doi=10.1016/j.physrep.2006.12.004\|bibcode=2007PhR...441....1H\|citeseerx=10.1.1.183.1617}}</ref>过程X到过程Y的转移熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用<font color="#ff8000"> 香农熵 Shannon entropy</font>测量，则转移熵可以写为：

	<math>T_{X\rightarrow Y} = H\left( Y_t \mid Y_{t-1:t-L}\right) - H\left( Y_t \mid Y_{t-1:t-L}, X_{t-1:t-L}\right)</math>,		<math>T_{X\rightarrow Y} = H\left( Y_t \mid Y_{t-1:t-L}\right) - H\left( Y_t \mid Y_{t-1:t-L}, X_{t-1:t-L}\right)</math>,

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 *  {{cite web|title=Java Information Dynamics Toolkit (JIDT)|url=https://github.com/jlizier/jidt|publisher=GitHub|date=2019-01-16}}, a toolbox, developed in Java (programming language)|Java and usable in MATLAB, GNU Octave and Python (programming language)|Python, for computation of transfer entropy and related information-theoretic measures in both discrete and continuous-valued data.
-*  {{cite web|title=Multivariate Transfer Entropy (MuTE) toolbox|url=https://github.com/montaltoalessandro/MuTE|publisher=[[GitHub]]|date=2019-01-09}}, a toolbox, developed in [[MATLAB]], for computation of transfer entropy with different estimators.
+*  {{cite web|title=Multivariate Transfer Entropy (MuTE) toolbox|url=https://github.com/montaltoalessandro/MuTE|publisher=GitHub|date=2019-01-09}}, a toolbox, developed in MATLAB, for computation of transfer entropy with different estimators.
 本中文词条由[[用户:Henry|Henry]] 参与编译， [[用户:Vicky|Vicky]] 审校，[[用户:不是海绵宝宝|不是海绵宝宝]]编辑，欢迎在讨论页面留言。

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 == 外部链接 ==
-*  {{cite web|title=Transfer Entropy Toolbox|url=http://code.google.com/p/transfer-entropy-toolbox/|publisher=[[Google Code]]}}, a toolbox, developed in [[C++]] and [[MATLAB]], for computation of transfer entropy between spike trains.
+*  {{cite web|title=Transfer Entropy Toolbox|url=http://code.google.com/p/transfer-entropy-toolbox/|publisher=Google Code}}, a toolbox, developed in C++ and MATLAB, for computation of transfer entropy between spike trains.
-*  {{cite web|title=Java Information Dynamics Toolkit (JIDT)|url=https://github.com/jlizier/jidt|publisher=[[GitHub]]|date=2019-01-16}}, a toolbox, developed in [[Java (programming language)|Java]] and usable in [[MATLAB]], [[GNU Octave]] and [[Python (programming language)|Python]], for computation of transfer entropy and related information-theoretic measures in both discrete and continuous-valued data.
+*  {{cite web|title=Java Information Dynamics Toolkit (JIDT)|url=https://github.com/jlizier/jidt|publisher=GitHub|date=2019-01-16}}, a toolbox, developed in Java (programming language)|Java and usable in MATLAB, GNU Octave and Python (programming language)|Python, for computation of transfer entropy and related information-theoretic measures in both discrete and continuous-valued data.
 *  {{cite web|title=Multivariate Transfer Entropy (MuTE) toolbox|url=https://github.com/montaltoalessandro/MuTE|publisher=[[GitHub]]|date=2019-01-09}}, a toolbox, developed in [[MATLAB]], for computation of transfer entropy with different estimators.

@@ 第26行： / 第26行： @@
 * [[条件互信息]]
-* [[因果关系]]
+* 因果关系
-* [[因果关系（物理）]]
+* 因果关系（物理）
-* [[结构方程模型]]
+* 结构方程模型
-* [[虚拟事实模型 ]]
+* 虚拟事实模型
 * [[互信息]]